Channel estimator circuit for wireless communications and method for channel estimation

Abstract

A channel estimator circuit receives in one slot a multiplexed representation of one or more time- domain code division multiplexed, TD-CDM, spread received signals. An initial estimator circuit processes a pre-estimation signal that is formed therefrom, uses a base pilot signal as a reference signal, and outputs an initial estimate signal. A frequency-domain processing circuit receives and processes a first set of one or more TD-CDM spread channel estimate signals that is representative of the initial estimate signal, and outputs a second set of signals. An interpolation buffer buffers the second set of signals. A TD-CDM de-spreading circuit de-spreads the buffered second set of signals and outputs TD- CDM de-spread channel estimate signals. In this manner, the frequency-domain-related signal processing and the time-domain-related signal processing are separated, and a significant reduction in the amount of hardware, energy and time resources required may be achieved, improving latency and reducing cost.

Description

[0001]ACL-2022-002WO 13-Jun-2025 Specification_Final Channel Estimator Circuit for Wireless Communications and Method for Channel EstimationDescription Field of the inventionThe field of the invention relates to a channel estimator circuit for wireless communications, and amethod for channel estimation. The field is applicable to, but not limited to, channel estimation forcurrent and future generations of communication standards. BackgroundWireless communications may be characterized by various communication channel effects beingimposed upon the transmitted signal, including multipath (frequency selective) fading, time selectivefading, etc. In order for the receiver to equalize the received signal, it is first necessary to estimate thechannel impairments. This may be achieved by transmitting pilot symbols for the receiver to receive andprocess in order to establish channel estimation. The receiver is given prior knowledge of what pilotsymbols are transmitted, as well as what time and frequency resources are used for the transmittedpilot symbols, so that the receiver may compare the known transmitted signal with the received signal and infer that the transmission between these represents the fading imposed by the channel. Forexample, in 3rd generation partnership project (3GPP)’s fifth generation new radio (5GNR) standard [1],the Physical Uplink Shared Channel (PUSCH) and Physical Downlink Shared Channel (PDSCH) employdemodulation reference signals (DM-RS) as pilots.FIG.1 depicts the time frequency and spatial resources used in multiple-in multiple out orthogonalfrequency division multiplexing (MIMO-OFDM) communications. In state-of-the-art wirelesscommunication systems, an orthogonal frequency division multiplexing (OFDM) technique is used,which allows bits to be transmitted in both the time- and the frequency-domains. In order to achievehigh spectral efficiency, more specifically, the time resources are split into OFDM symbols 101, while thefrequency resources are split into subcarriers 102. Each combination of an OFDM symbol in the timedomain (TD) and a subcarrier in the frequency domain (FD), i.e., each subcarrier in a particular OFDMsymbol, is referred to as a resource element (RE) 103. REs from all allocated FD and TD resources form atwo-dimensional resource grid (RG) 104. For example, FIG. 2 shows the resource segmentation 200 in3GPP’s 5GNR standard [1], every 12 subcarriers form a resource block (RB) 107, every 12 or 14 OFDMssymbols form a slot 106, and an RG contains 1 ≤ ^^^ ≤ 273 RBs and one slot, depending on thescheduling strategy.Some REs may carry payload information and are referred to as a payload RE 108. In some applications,there may be some REs that do not carry any information and so these REs are referred to as an empty RE 109. Some REs may carry pilot information and are referred to as a pilot RE 110. An OFDM symbol that includes one or more pilot REs 110 is referred to as a pilot OFDM symbol 111. Note that a pilot OFDM symbol 111 may also carry payload REs 108 and / or empty REs 109, in addition to one or more pilot REs 110. Similarly, a sub-carrier that includes one or more pilot REs 110 is referred to as a pilot Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final subcarrier 112. Note that a pilot subcarrier 112 may also carry payload REs 108 and / or empty REs 109, in addition to one or more pilot REs 110.FIG. 3 depicts a known MIMO system 300. A third dimension of multiplexing can be provided in the caseof using multiple input multiple output (MIMO) communications, whereby multiple transmittingantennas 301 are used by the transmitting device 302 and multiple receiving antenna paths 303 areused by the receiving device 304, an improved spatial efficiency may be achieved using spatialmultiplexing. More specifically, for each RE, each transmitting antenna 301 transmits a different set of bits as a quadrature amplitude modulation (QAM) signal or a phase-shift keying (PSK) signal, which may transport Qm = 2 bits in the case of quadrature phase shift keying (QPSK), Qm = 4 bits for 16 quadrature amplitude modulation (16QAM), and Qm= 8 bits for 64QAM, for example. Here, the number of transmitted QAM or PSK signals simultaneously on different antennas for each RE is referred to thenumber of layers NP, which may be equal to or less than the number of transmitting antennas NT.Following coding / modulation 306 and before radio frequency processing in the low-PHY 307, themapping of an RE 103 from a layer 105 to a transmitting antenna 301 is through the precoding process305. The signals are conveyed from each transmitting antenna 301 to each receiving antenna path 303via a channel having a particular channel gain 308 and is received in the presence of noise 309. In thereceiving device 304, radio frequency processing is performed in the low-PHY 310, before a channel estimator circuit 311 is used to estimate the channel gains 308. Finally, equalization / demodulation / decoding 312 is performed to complete the receiving process. Examplesherein described focus on new aspects of the channel estimator circuit 311.FIG. 4 shows the multi-user MIMO (MU-MIMO) uplink and downlink transmissions 400. Note that thelayers 105 may not all belong to the same user equipment (UE) (401, 402), sometimes referred to as auser terminal, and there may be different UEs with different number of transmit antennas 301 sharingthe layer resource, each having a different fraction of the total layers. Different UEs (401, 402) mayinterfere with each other, as shown in FIG. 4. In the uplink the base station (BS) 403 can use signalprocessing to separate the signals from all of the different UEs, while in the downlink each UE can usesignal processing to separate its signal from those of all the other UEs. As the example given in FIG. 4 thebase station (BS) 403 is associated with three UEs (UE0401, UE1402, and UE2402). The BS 403 has acapacity of processing ^^ = 9 layers, which are shared with the three UEs. Specifically, UE0 is assigned^^^ = 3 layers, namely layers 0, 1, and 2; UE2 is assigned ^^^ = 2 layers, namely layers 3, and 4; UE3 isassigned the rest ^^^ = 4 layers, namely layers 5, 6, 7, and 8. In the uplink, each UE prepares its owndata and transmits them to the BS 403, while the BS 403 separates the arriving stream into three usingUE separation 404, each with the data solely from one UE, which are separately forwarded for further processes. In the downlink, the BS 403 prepares the nine layers of data of all three UEs and multiplexes them into one stream for transmission. Each UE receives the nine layers of data for all UEs and canseparate the respective ^^^, ^^^ , or ^^^ layers for itself from the others.In the channel, transmitted signals sent for different users / UEs (401, 402) interfere with each other andare received at multiple received antenna (such as received antenna paths 303) of FIG. 3. The channelestimator 311 has the role of estimating the channel 308 between each combination of transmittingantenna and receive antenna, in order that the equalizer 312 can separate out the signals transmittedby different transmitting antennas 301.Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalThe four dimensions (layer 105, receiving antenna 303, frequency i.e., subcarrier 102, and time i.e.,OFDM symbol 101) are depicted in FIG. 1 and FIG. 3, where the frequency resources in an RG 104 aresplit into 12 subcarriers 102 (^^ = 0, … ,11), the time resources into 14 OFDM symbols (^^ = 0, … ,13),three layers 105 (^ = 0,1,2,3) each having a RG are mapped to four transmitting antennas 301 throughthe precoding process 305, and four receiving antenna paths 303 (^ = 0, … ,3) each receives anindependently faded copy of the transmitted signal. It is worth noting that the resource allocated for thetransmission, such as the number of subcarriers (102), number of layers (105), transmitting antennas(301), receiving antennas (303), etc., are subjected to the resource allocation strategies employed and may change from slot to slot. However, in order to estimate each channel between each transmitting antenna and each receiving antenna, a corresponding set of pilot symbols is needed. Further, the pilot symbols need to be local to the transmitted data, which means that the pilot symbols of different transmitting antennas arecontending to have access to the same time and frequency resources. In order to grant them all accessto the same time and frequency resources, code-division multiplexing (CDM) spreadings can be applied.The CDM spreading enables the share of same time and frequency resources by pilots from multiplelayers, at the expense of creating mutual dependencies between each of the those participating layers [2].As discussed above, the use of CDM spreading a transmitted signal introduces dependencies betweenpilot REs in different subcarriers across the frequency domain and across different OFDM symbols in the time domain. The inventors have recognized and appreciated that this is problematic in practical channel estimators, which have the job of estimating the channel effects in the receiving device, in order to support the mitigation of the channel effects during equalization. More specifically, in a practical channel estimator, the pilot symbols are processed in sub-carrier order, one OFDM symbol at a time. However, the inventors have also recognized and appreciated that the interdependencies between pilot REs in different OFDM symbols imposes a requirement for large buffers to store intermediate signal processing results between the processing of one OFDM symbol into the next. In cases where the signal processing alternates back and forth between frequency domain processing (e.g., Frequency Domain (FD) CDM de-spreading, FD interpolation) and time domain processing (e.g., Time Domain (TD) CDM de- spreading, TD interpolation), large buffers are required to store intermediate results relating to different OFDM symbols each time the processing switches from the frequency domain to the time domain. These large buffers consume large amounts of hardware, energy and time resources, which would result in high-latency channel estimator devices that are expensive to build and run. Summary Examples described herein reformulate the signal processing to separate all frequency domainprocessing into a first stage and all time domain processing into a second stage, such that only a singlelarge buffer is required between them. In this manner, a significant reduction in the amount ofhardware, energy and time resources required can be achieved, thereby improving latency and the costto build and run the design. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalIn a first aspect, a channel estimator circuit comprises an input configured to receive in one slot amultiplexed representation of one or more time-domain code division multiplexed, TD-CDM, spreadreceived signals an initial estimator circuit that is configured to process a pre-estimation signal that isformed from the multiplexed representation of the one or more TD-CDM spread received signals, to usea base pilot signal from a base pilot signal generator circuit as a reference signal, and to output an initialestimate signal; a frequency-domain processing circuit that is configured to receive and process a firstset of one or more TD-CDM spread channel estimate signals that is representative of the initial estimatesignal, and to output a second set of one or more TD-CDM spread channel estimate signals; aninterpolation buffer that is operably coupled to an output of the frequency-domain processing circuitand configured to buffer the second set of one or more TD-CDM spread channel estimate signals; and aTD-CDM de-spreading circuit operably coupled to an output of the interpolation buffer and configured to de-spread the buffered second set of one or more TD-CDM spread channel estimate signals from theinterpolation buffer and output TD-CDM de-spread channel estimate signals. In this manner, thefrequency-domain-related signal processing and the time-domain-related signal processing are separated, and a significant reduction in the amount of hardware, energy and time resources requiredmay be achieved, thereby improving latency and the cost to build and run the design.In an optional example of the channel estimator circuit, the frequency-domain processing circuit mayfurther comprise a frequency-domain de-noising circuit that is configured to receive an input signal thatis representative of the first set of one or more TD-CDM spread channel estimate signals, to removenoise from the input signal and to provide a de-noised output signal as the second set of one or moreTD-CDM spread channel estimate signals. In this manner, the performance of the channel estimator maybe improved when the noise interference is suppressed.In an optional example of the channel estimator circuit, the frequency-domain de-noising circuit may be further configured to use one of: a linear de-noising algorithm or a pseudo-linear de-noising algorithm.In this manner, the estimation process can execute a linear de-noising algorithm or a pseudo-linear de-noising algorithm. In an optional example of the channel estimator circuit, the frequency-domain processing circuit may further comprise a frequency-domain interpolation circuit that is configured to receive an input signal that is representative of the first set of one or more TD-CDM spread channel estimate signals, and to provide a frequency interpolated output signal as the second set of one or more TD-CDM spreadchannel estimate signals. In this manner, the channel estimator can produce channel estimates on REswithout a pilot. In an optional example of the channel estimator circuit, the channel estimator circuit may furthercomprise a frequency domain code division multiplexing (FD-CDM) de-spreading circuit that isconfigured to receive and perform a FD-CDM de-spread operation on an input signal that is formed fromthe multiplexed representation of the one or more TD-CDM spread received signals, wherein the outputsignal of the FD-CDM de-spreading circuit forms a basis of the pre-estimation signal to the initialestimator circuit; or to receive from the initial estimator circuit and perform a FD-CDM de-spreadoperation on an input signal that is formed from the initial estimate signal, wherein an output signal ofthe FD-CDM de-spreading circuit forms a basis of the first set of one or more TD-CDM spread channel Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Finalestimate signals. In this manner, the channel estimator circuit can process input signals whose pilots areFD-CDM spread.In an optional example of the channel estimator circuit, the FD-CDM de-spreading circuit may beconfigured to perform a FD-CDM de-spread operation on an input signal to the FD-CDM de-spreadingcircuit that uses a Walsh-Hadamard code with a length of two. In this manner, the channel estimationcircuit can process input signals whose pilots are FD-CDM spread using a Walsh-Hadamard code with a length of two. In an optional example of the channel estimator circuit, the TD-CDM de-spreading circuit may be configured to perform a TD-CDM de-spread operation on the buffered second set of one or more TD-CDM spread channel estimate signals that uses a Walsh-Hadamard code with a length of two. In thismanner, the channel estimation circuit can process input signals whose pilots are TD-CDM spread usinga Walsh-Hadamard code with a length of two.In an optional example of the channel estimator circuit, the channel estimator circuit may furthercomprise an FDM de-multiplexing circuit configured to receive and perform a FDM de-multiplexoperation on an input signal that is formed from the multiplexed representation of the one or more TD-CDM spread received signals, wherein an output signal of the FDM de-multiplexing circuit forms a basisof the pre-estimation signal, or to receive and perform a FDM de-multiplex operation on therepresentation of the initial estimate signal, wherein an output signal of the FDM de-multiplexing circuitforms a basis of the first set of one or more TD-CDM spread channel estimate signals. In this manner,the channel estimator circuit can process input signals whose pilots are frequency-domain multiplexed.In an optional example of the channel estimator circuit, the channel estimator circuit may furthercomprise a time-division multiplexed (TDM) de-multiplexing circuit configured to receive and perform aTD-de-multiplex operation on an input signal that is formed from the multiplexed representation of theone or more TD-CDM spread received signals, wherein an output signal of the TDM de-multiplexingcircuit (808) forms a basis of the pre-estimation signal, or to receive and perform a TD-de-multiplexoperation on the representation of the initial estimate signal from the initial estimation circuit, wherein an output signal of the TDM de-multiplexing circuit forms a basis of the first set of one or more TD-CDMspread channel estimate signals. In this manner, the channel estimator circuit can process input signalswhose pilots are time-domain multiplexed.In an optional example of the channel estimator circuit, the channel estimator circuit may furthercomprise a channel matrix TD processing circuit operably coupled to an output of the TD-CDM de-spreading circuit and comprising at least one of a time-domain interpolation circuit that is configured toperform time-domain interpolation on the TD-CDM de-spread channel estimate signals, or a time-domain filtering circuit that is configured to perform a time-domain smoothing operation on the TD-CDM de-spread channel estimate signals, or a timing compensation circuit that is configured to performphase error compensation on TD-CDM de-spread channel estimate signals. In this manner, the channelestimator circuit can benefit from improved performance with the help of additional refinement in the time domain. In an optional example of the channel estimator circuit, each of a plurality of the multiplexed representation of the one or more TD-CDM spread received signals may be a vector having a length Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Finalequal to a number of receive antenna ports ^^, wherein each of the first set of one or more TD-CDMspread channel estimate signals and each of the second set of one or more TD-CDM spread channel estimate signals is a matrix having a first dimension equal to a number of layers ^^^divided by a TD-CDM spreading factor ^^^ , and having a second dimension equal to the number of receive antenna ports ^^.In this manner, the sizes of the signals processed by the channel estimator circuits are defined.In an optional example of the channel estimator circuit, the number of receive antenna ports ^^, thenumber of layers ^^^, and the TD-CDM spreading factor ^^^may be configured to vary from slot to slot.In this manner, the sizes of the data processed by the channel estimator circuit may be varied at run-time.In a second aspect of the invention, a method for channel estimation performed by a channel estimatorcircuit comprises: receiving in one slot a multiplexed representation of one or more time-domain codedivision multiplexed, TD-CDM, spread received signals; processing a pre-estimation signal, by an initial estimator circuit, formed from the multiplexed representation of the one or more TD-CDM spread received signals and using a base pilot signal provided by a base pilot signal generator circuit as areference signal; outputting an initial estimate signal by the initial estimator circuit; receiving andprocessing by a frequency-domain processing circuit a first set of one or more TD-CDM spread channelestimate signals that is representative of the initial estimate signal, and outputting a second set of oneor more TD-CDM spread channel estimate signals; buffering, by an interpolation buffer, the second setof one or more TD-CDM spread channel estimate signals; and de-spreading, by a TD-CDM de-spreadingcircuit, the buffered second set of one or more TD-CDM spread channel estimate signals and outputtingTD-CDM de-spread channel estimate signals. In this manner, the frequency-domain-related signalprocessing and the time-domain-related signal processing are separated, and a significant reduction in the amount of hardware, energy and time resources required can be achieved, thereby improving latency and the cost to build and run the design. Brief description of the drawings Further details, aspects and example embodiments will be described, by way of example only, with reference to the drawings. In the drawings, like reference numbers are used to identify like or functionally similar elements. Elements in the FIG’s are illustrated for simplicity and clarity and have not necessarily been drawn to scale.FIG. 1 illustrates the known time, frequency, and spatial resources of a MIMO communications system,for an example 3GPP 5GNR resource allocation using ^^ = 4 layers, ^^^ = 3 resource blocks, ^^ = 36subcarriers, ^^^ = 18 pilot subcarriers per RG, ^^ = 14 OFDM symbols, and ^^^ = 4 pilot OFDMsymbols. FIG.2 illustrates a known example of one frame of frequency and time resources segmentation, for anexample 3GPP 5GNR resource allocation using ^^^ = 273 resource blocks, ^^ = 14 OFDM symbols perslot, and ^^^^^ = 10 slots per frame, which corresponds to numerology ^ = 0.Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final FIG.3 illustrates a known single-user MIMO communications system featuring multiple layers mappedto multiple transmitting antennas by a precoder, and received by multiple receiving antennas, for anexample using ^^ = 3 layers, ^^ = 4 transmit antenna ports and ^^ = 4 receive antenna ports.FIG. 4 illustrates the known multi-user MIMO communications uplink and downlink, where three UEseach having 3, 2, and 4 layers of data are communicating with a BS.FIG. 5 illustrates one example of a CDM spreading process at the transmitter, and its de-spreadingprocess at the receiver, for an example of ^^ = 2 layers, each spread by a CDM spread code at thetransmitter, and de-spread by the same CDM spread code at the receiver, according to some example embodiments.FIG. 6 illustrates one example of a pilot signal processing at a transmitter, according to some exampleembodiments.FIG. 7 illustrates one example of CDM grouping, as well as FDM mapping and TDM mapping of the pilotREs, for an example scheme using ^^^ = 4 pilot subcarriers (^ = 0, … ,3), split into ^^^^^^^^^^^ = 2FD-CDM groups, each having ^^ = 2 pilot subcarriers, ^^^ = 4 pilot OFDM symbols (^ = 0, … ,3), splitinto ^^^^^^ = 2 TD-CDM groups, each having ^^ = 2 pilot OFDM symbols, ^^ = 3 layers (^ = 0,1,2),each are FDM and TDM mapped to different locations of the physical resource having ^^ = 8subcarriers (^^ = 0, … ,7) and ^^ = 9 OFDM symbols (^^ = 0, … ,8) , according to some exampleembodiments.FIG. 8 illustrates one example block diagram of a proposed Channel Estimator 1, according to someexample embodiments.FIG. 9 illustrates one example of CDM de-spreading dependencies between pilot REs, according to someexample embodiments.FIG. 10 illustrates one example block diagram of a proposed Channel Estimator 2, according to someexample embodiments.FIG. 11 illustrates one exemplary flow chart for an operation of Channel Estimator 2 of FIG. 10, excludingan error estimation circuit, in accordance with some examples.FIG. 12 illustrates an alternative exemplary flow chart for an operation of Channel Estimator 2 of FIG. 10,including an error estimation circuit, in accordance with some examples.FIG.13 illustrates three example arrangements of the circuits between the input and the frequency-domain processing circuit in Channel Estimator 2 of FIG.10. Detailed descriptionTo facilitate understanding, several tables summarizing the meanings of various symbols usedthroughout this section are provided at the end of the detailed description.Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final Pilot-Symbol-Aided Channel Estimation For enabling channel estimation for multiple layers on the same frequency and resources, CDM is achieved by spreading the pilot symbols using a spreading code / sequence drawn from a spreadingcode / sequence set / family, such as the family of Walsh-Hadamard codes [3], the family of Gold codes[4], and the maximum length sequences. For example, in 3GPP’s 5GNR standard [1], two sets of length-2Walsh-Hadamard codes, each containing two codes, may be employed, which are referred to asorthogonal covering codes (OCCs). A list of comparisons between general terms and 3GPP 5GNR’sspecific names are summarized in Table 1. Explicitly, CDM can be applied to the pilots in either or bothof the time domain (TD) and the frequency domain (FD), which enables the simultaneous transmission and the detection of pilot symbols transmitted on multiple layers. In addition, frequency-division multiplexing (FDM) and time-division multiplexing (TDM) can also be applied to the pilots to further enhance the capacity. At the receiver, FDM and / or TDM de-multiplexing process is required to separate different layers, accordingly.FIG. 5 shows an example of the known CDM process 500, where a base pilot symbol sequence 501containing two elements ^ = [^^, ^^] is generated by base pilot sequence generation 502 and spreadCDM spreading 503. A bold lower case letter represents a vector, while a regular lower case letterrepresents a scalar, as summarized in Table 7. Here, the spread codes are drawn from a spread code sethaving a length ^^ = 2 to form the pilot symbols of ^^ = 2 layers. In the example of FIG. 5, layer ^ = 0uses CDM spread code [+1, +1] 504, while layer ^ = 1 uses CDM spread code [+1, −1] 505. For layer^ = 0, the CDM spread multiples each element of ^ by the corresponding element in the CDM spreadcode to obtain ^^ = [+^^, +^^] 506, while for layer ^ = 1 this leads to ^^ = [+^^, −^^] 507. Eachlayer will transmit its own CDM spread coded pilot symbols, which are corrupted by the channel with channel gains ℎ^and ℎ^308, respectively. The superimposed corrupted pilot symbols received is givenas ^ = [(ℎ^ + ℎ^)^^, (ℎ^ − ℎ^)^^] 508, assuming a noise-free transmission. The known transmittedpilots ^ can be removed during initial channel estimation (in initial channel circuit 509) throughelementwise division to obtain ^^^^ = [ℎ^ + ℎ^, ℎ^ − ℎ^] 510. Then, the channel gains between thereceiver and each layer can then be estimated through CDM de-spreading 511, which is carried outthrough elementwise multiplication of ^^^^and the corresponding spread code of each layer, followedby the averaging of the product’s two elements. Therefore, the channel gain of layer ^ = 0 is ℎ^^ =^[(ℎ + ℎ ) × (+1) + (ℎ − ℎ ) × (+1)] = 512, while tha ^^^ ^ ^ ^ t of layer ^ = 1 is ℎ^ =^ ^[(ℎ^ + ℎ^) × (+1) + (ℎ^ − ℎ^) × (−1)] = 513. Following this, further channel estimationprocessing 514 may be performed, together with equalization / demodulation / decoding 312 and higher layer processing 515. A CDM code with a given codeword length ^^may be used for CDM spread coding a pilot sequence ofmuch longer length ^^^ > ^^, in which case the ^^^ elements are partitioned into ^^^^^^^^^ groups,each having ^^ elements, such that ^^^ = ^^ ⋅ ^^^^^^^^^ and that CDM spread coding can be carriedout within each CDM group individually. For example, assume a pilot sequence with length ^^^ = 12 isto be CDM spread using a spread code with a codeword of ^^ = 4. The ^^^ = 12 pilot sequenceelements are firstly partitioned into ^^^^^^^^^ = 3 CDM groups, each having the same number of pilotsequence elements as the CDM spread code codeword length ^^ = 4. Each of the ^^^^^^^^^ = 3 CDMAccelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Finalgroup can then be individually spread by the same CDM spread code. The frequency-domain, time-domain, and general constants used here are summarized in Table 4, in Table 5, and in Table 6, respectively. Meanwhile, a CDM code set may have multiple CDM codes, each may be used to serve an individual layer. The maximum number of supported layers using joint FD-CDM and TD-CDM is the product of the number of individual CDM codes within the two CDM sets. These potential layers are numbered from 0 onwards and are referred to as port number, while a fraction of them may be selected for transmission, which is equal to the number of layers. The port number of the ^th layer is denoted by^^^, where ^ is the layer index. In other examples, it is envisaged that more layers can be employed usingFDM and TDM. For example, in 3GPP’s 5GNR standard [1], ignoring the FDM and assuming only the firstFDM group is used, the physical shared uplink channel (PUSCH)with DM-RS configuration type 1 has the following port numbers available: 0, 1, 4, 5. The transmitter may be configured to transmit only threelayers. According to Table 7.3.1.1.2-14 of [5], when ‘Antenna Port’ is set to 1, the selected port numbersare ^^^ = 0, ^^^ = 1, and ^^^ = 4.In the example of 3GPP’s 5GNR standard [1], the pilot symbols for its physical shared uplink channel(PUSCH) are provided by a demodulation reference signal (DMRS), and successive pilot symbols in successive resource elements in TD and FD are generated according to a pseudo-random sequence. The same base pilot symbol sequence is used for the transmission of all layers. For the remainder of thisdocument, this assumption is adopted, but a skilled practitioner would recognize that this may beexpanded to other cases where each layer has different base pilot sequences. For each individual layer,the base pilot sequence r is firstly gone through CDM spread, before mapping to the individual resourceelements (REs) in the allocated physical resource. These pilot REs are deployed across the resource grid (RG), occupying multiple subcarriers in the FD, and possibly also multiple OFDM symbols in the timedomain (TD). In the example of 3GPP’s 5GNR standard [1]’s PUSCH and PDSCH, the pilot (DM-RS) REs aremore densely populated in the FD (four or six per RB per layer) and sparsely in the TD (one to four per slot per layer). However, additional phase tracking reference signal may be deployed densely in the TD if required. Transmitter Signal Processing for PilotsThe transmitter signal processing 600 for pilots is shown in FIG. 6. Let ^ be an array of base pilot symbols601 prepared by the transmitting device 302. Its element ^^,^,^means the IQ for the ^th layer’s ^th pilotsubcarrier 112 in the pilot sequence that is prepared for the ^th pilot OFDM symbol 111, where 0 ≤ ^ ≤^^ − 1, 0 ≤ ^ ≤ ^^^ − 1, and 0 ≤ ^ ≤ ^^^ − 1, with ^^, ^^^, and ^^^ being the number of layers, thenumber of pilot OFDM symbols per slot, and the number of pilot subcarrier per pilot OFDM symbol,respectively. In the examples described herein, it is assumed that the same set of base pilot symbolsapply to all layers. Therefore, the first dimension in ^ is omitted and its elements are simply referred toas ^^,^. However, it can be envisaged that different layers 105 can have different base pilot symbol sets,provided that the receiving device 304 is specially designed to accommodate this, as discussed later. Asshown in FIG.6, the array of base pilot symbols 601 may be configured for the ^th layer 105 using some or all of FD-CDM spreading 602, TD-CDM spreading 603, FDM mapping 604 and TDM mapping 605, depending on the port number ^^^606 assigned to the layer 105, as will be detailed below. In this way, Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final the array of base pilot symbols 601 may be configured and mapped into the RG 104, before being pre-coded 305, radio frequency processed in the low-PHY layer 307 and transmitted.FIG. 7 shows the CDM grouping 700, as well as the FDM and TDM mappings of the pilots. The ^^^ pilotsubcarriers within the same pilot OFDM symbol can be grouped, where each of the ^^^^^^^^^^^groupscomprises ^^ consecutive pilot subcarriers, thus ^^ ⋅ ^^^^^^^^^^^ = ^^^. Similarly, the ^^^ pilotOFDM symbols within the pilot grid can be grouped, where each of the ^^^^^^^^^^^groups comprises^^ consecutive pilot OFDM symbols, thus ^^ ⋅ ^^^^^^^^^^^ = ^^^. For 3GPP 5GNR PUSCH and PDSCH[1], the groupings may be selected flexibly from ^^ ∈ {1,2} and ^^ ∈ {1,2}. Therefore, the indices ofeach element in ^ can also be expressed by its FD- and TD-CDM group indices (^^, ^^), and its indiceswithin the group (^^, ^^): ^^,^ where the relationships are detailed below in Eq.(1).^ = ^^^^ + ^^ ^^ = ⌊^ / ^^⌋ ^^ = mod(^, ^^)^ = ^^^^ + ^^ ^^ = ⌊^ / ^^⌋ ^^ = mod(^, ^^) In the example given in FIG. 7, the pilot RG consists of ^^^ = 4 pilot OFDM symbols 111, each having^^^ = 4 pilot subcarriers 112, while the overall RG has ^^^ = 9 OFDM symbols 101, each having ^^ =8 subcarriers 102. Observe from FIG. 7 that the FDM & TDM mapped physical resource grids, the pilotOFDM symbols (such as OFDM symbol ^^ = 1 in layer ^ = 0’s RG) contain both pilot subcarriers (^^ =0,1,4,5 in the aforementioned OFDM symbol) and non-pilot subcarriers (^^ = 2,3,6,7 in the sameaforementioned OFDM symbol). Explicitly, a pilot OFDM symbol 111 is any OFDM symbol that containsat least one pilot subcarrier, which may be mixed in with non-pilot subcarriers. In the FD, the FD-CDMdivides the pilot subcarriers into ^^^^^^^^^^^ = 2 groups 701, where each group has ^^ = 2 elements.Similarly, in the TD, the TD-CDM divides the pilot OFDM symbols into ^^^^^^^^^^^ = 2 groups 702,where each group has ^^ = 2 samples. Subcarriers belonging to the same FD- and TD-CDM group aremarked by triangles at the same corner in the RE box of FIG. 7.The base pilot sequence ^ 601 is firstly gone through both FD-CDM spreading 602 and TD-CDMspreading 603 processes. Denote by ^^ and ^^ respectively the CDM spreading code set matrices usedin the FD-CDM and TD-CDM multiplexing process. Each spreading code set matrix contains multiple spreading code vectors, where is FD-CDM and TD-CDM spreading code vector designated for the ^th layer is given by^ ^ , respectively. Moreover, the ^ th elements within the vectors and ^^^^ ^^^are given by ^^^(^^) and ^^^^^ (^^), respectively. Mind that two different layers may have the same FD-CDM spreading code but different TD-CDM spreading code, like in the example below, and vice versa. Let ^^^^^^and ^^^^^^be the total number of codes within the respective code sets ^^and ^^, then the total number of layers used fortransmission ^^ should be 1 ≤ ^^ ≤ ^^^^^^ ⋅ ^^^^^^, where ^^^^^^ ⋅ ^^^^^^ is the maximumnumber of layers supported by the FD-CDM and TD-CDM spread code sets. Mind that the number of FD- CDM and TD-CDM spread codes used for transmission, denoted by ^^^and ^^^, respectively, may be lower than their corresponding total numbers, i.e., ^^ ≤ ^^ and ^ ^ ≤ ^ . Their product ^^ ^^^^^ ^ ^^^^^ ^is no smaller than the total number of layers used ^^, and no bigger than the maximum number oflayers supported by the spread code sets, i.e. ^ ^ ^ ^^ ≤ ^^ ⋅ ^^ = ^^ ≤ ^^^^^^ ⋅ ^^^^^^ . Moreover, forthe ^th layer used for transmission, where 0 ≤ ^ ≤ ^^ − 1, if it uses the ^^^th code from code set ^^and Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final -11 -the ^^^th code from code set ^^, its port number ^^^can be uniquely determined by ^^^and ^^^ . Theindexing and data variables used are summarized in Table 2 and in Table 3, respectively.For example, consider in 3GPP’s 5GNR standard [1], for a PUSCH transmission using DM-RS configurationtype 1, where a length-2 (^^ = 2) FD-CDM OCC set ^^ = {(+1, +1), (+1, −1)} and a length-2 (^^ = 2)TD-CDM OCC set ^^ = {(+1, +1), (+1, −1)} are used, each with ^^^^^^ = 2 and ^^^^^^ = 2 OCCs,respectively. This arrangement allows a maximum of ^^^^^^ ⋅ ^^^^^^ = 4 layers to be used, with portnumbers [0,1,4,5] according to Table 6.3.1.1.3-1 in [1]. Assuming ^^ = 2 layers are used, and assumingfurthermore that their port numbers are ^^^ = 1 and ^^^ = 5, respectively, their corresponding CDMinformation is shown in Table below, based on TS 38.211 Table 6.3.1.1.3-1. The inventors have recognized and appreciated that under this particular assumption and port number selection, only ^^^=1 of the ^^^^^^ = 2 spread codes from the FD-CDM spread code set is used, code (+1, −1), while the ^ ^^ = 2 of the ^^^^^^ = 2 spread codes from the TD-CDM spread code setare used, namely both the ^^^ = 0th code (+1, +1) and the ^ ^^ = 1st code (+1, −1).Table 1 Code Division Multiplexing for A Two-Layer 5GNR PUSCH SignalLayer Port FD-CDM FD-CDM TD-CDM TD-CDM OCC Index Number OCC index OCC OCC index^^^^^^^^ ^ ^ ^^^^^ ^ ^^^^0 1 1 (+1, −1) 0 (+1, +1)1 5 1 (+1, −1) 1 (+1, −1)As another example, in 3GPP’s 5GNR standard [1], a PUSCH transmission has the capacity of transmitting 12 layers simultaneously. This can be achieved by using DM-RS configuration type 2, where both(^^^^^^ = 2) FD-CDM OCCs from a length-2 (^^ = 2) FD-CDM OCC set and both (^^^^^^ = 2) TD-CDM OCCs from a length-2 (^^ = 2) TD-CDM OCC set are used, resulting a capacity of ^^^^^^ ⋅^^^^^^ = 4 layers. Moreover, in DM-RS configuration type 2, ^^^^ = 3 different FDM mappings canbe used to further enhance capacity, thus resulting into a total of ^^^^ ⋅ ^^^^^^ ⋅ ^^^^^^ = 12 layers.The resultant CDM spreading coded sequences ^ can be expressed in Eq.(2): The indices ^^and ^^are used because the CDM spreading is separately carried out for each CDM group, while ^^and ^^are the corresponding pilot subcarrier and pilot OFDM symbol indices within the respective FD-CDM and TD-CDM groups.As another example, a FD-CDM spreading code set based on length-4 (^^ = 4) Walsh-Hadamard codecan support a maximum of ^^^^^^ = 4 layers, each with the FD-CDM spreading code given in Eq. (3). Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalCombined with another length-2 (^^ = 2) Walsh-Hadamard code-based TD-CDM spreading codescapable of supporting ^^^^^^ = 2 layers, a total of ^^^^^^ ⋅ ^^^^^^ = 8 layers may be supported.The layer capacity can be further increased with FDM and TDM, as will be described later.After FD-CDM spreading 602 and TD-CDM spreading 603, FDM mapping 604 and TDM mapping 605 canbe adopted to further increase the layer capacity by mapping the same CDM spread coded pilot RE to different physical frequency and / or time resources for different layers. Denoting by ^^^^and ^^^^the FDM and TDM mapping / multiplexing operations, the frequency and time domain locations, or the subcarrier and OFDM symbol coordinates, of the mapped resource after FDM and TDM can beexpressed as in Eq. (4). In the above equations ^ and ^ are OFDM ^,while ^^ and ^^ are the subcarrier and OFDM symbol indices in the mapped physical RG.For the example shown in FIG. 7, FDM and TDM are employed to support three layers, namely ^^^, ^^^,and ^^^, all share the same FD-CDM and TD-CDM spread coded pilots ^^,^with the same OCC. Todifferentiate them, the FDM maps the ^^^ = 4 pilot subcarriers into the ^^ = 8 subcarriers in the RGaccording to the port number, and similarly the TDM maps the ^^^ = 4 pilot OFDM symbols into the^^ = 9 OFDM symbols in the RG according to the port number. Explicitly, for layer ^^^, the FDM maps^ = 0,1 to ^^ = 0,1, and maps ^ = 2,3 to ^^ = 4,5, while for layers ^^^ and ^^^, the FDM maps ^ = 0,1 to^^ = 2,3, and maps ^ = 2,3 to ^^ = 6,7. Likewise, for layers ^^^ and ^^^, the TDM maps ^ = 0,1 to ^^ = 0,1,and maps ^ = 2,3 to ^^ = 7,8. Therefore, the pilot REs of each layer are orthogonal in the frequency andtime domain, so that they can be separated out even with the same FD-CDM and TD-CDM. The FDM and TDM mapping strategies in this particular example can be expressed as in Eq.(5). 4(^ − 1) + ^^ if ^^ { }^^^^^^, ^ ^ ^ ∈ 0^^^ = ^4(^^ − 1) + 2 + ^^ if ^^^ ∈ {1,2}5(^^ − 1) + ^^ if ^^ ∈ {0,1} ^^^, ^^ ^ = ^ ^^^^ ^ 5(^^ − 1) + 2 + ^^ if ^^^ ∈ {2}After the FDM mapping 604 and TDM mapping 605 of FIG.6, the output pilot signal for each layer wouldthen be given as ^^ ^ ^ where the mappings of ^ → ^ and ^ → ^ are the results of FDM and TDM,respectively. It is worth noting that the parameters mentioned above, such as the number of receive antenna ports^^, the number of layers ^^, the number of FD-CDM and TD-CDM spread codes used for transmission^^^and ^^^ , the indices of all of them, etc., are subjected to the resource allocation strategies adoptedand may be configured to vary from slot to slot.For the sake of simplicity and without loss of generality, the rest of the document does not considerFDM and TDM further, and it is assumed that all layers are separated solely by FD-CDM and TD-CDM.Therefore, no two layers have the identical FD-CDM and TD-CDM OCCs. However, a skilled practitionerwould recognize that the examples described herein can be readily applied in the presence of FDM andTDM, since these represent remapping operations in the time and frequency domains. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final Channel Estimator 1: All CDM De-Spreading Performed before Interpolation Buffering In the receiver, channel estimation is used to estimate the channel state information, so that thechannel equalizer can use the information to undo the impairments. Channel estimation at the receivermay involve, initial estimation, FD-CDM de-spreading, TD-CDM de-spreading, (main) frequency-domain processing, error estimation, time-domain processing, among other components. In this section, a firstchannel estimator design is introduced, referred to as Channel Estimator 1, which is shown in FIG. 8 andperforms all CDM de-spreading before the main frequency-domain processing. However, it issubsequently shown that this creates a problem that requires multiple large buffers to solve. Inexamples herein described, this motivates a second channel estimator design, that rearranges CDM de-spreading so that fewer large buffers may be required.According to the block diagram of a first Channel Estimator 1801 in FIG.8, following optional FDM de-multiplexing (in FDM de-multiplexing circuit 807) and TDM de-multiplexing (in TDM de-multiplexingcircuit 808) and initial channel estimation (in initial channel estimation circuit 509), the CDM de-spreading for each layer 105 may be carried out by element-wisely multiplying each received CDM group(701, 702) with the corresponding CDM spread code of that layer, and then averaging the resultant products. The averaging output is applied to all REs within the CDM group for that layer. Due to thechronological arrival of the received signal, which may be serialized following fast Fourier transform(FFT) in the low-PHY 310, the last subcarrier 102 of one OFDM symbol 101 may arrive before the firstsubcarrier of the next OFDM symbol. Therefore, in some examples, FD-CDM de-spreading 802 isprocessed prior to the TD-CDM de-spreading 803. While the FD-CDM de-spreading can be carried out asthe received subcarriers arrive, or ‘over the air’, this is not possible for the TD-CDM de-spreading. The TD-CDM de-spreading requires pilot REs from the same subcarrier of multiple pilot OFDM symbols at thesame time. As discussed below and in accordance with some examples as recognized and appreciated bythe inventors, this motivates the use of a CDM buffer 809 to store the FD-CDM de-spread pilot REs untilmultiple pilot OFDM symbols are available, so that the pilot REs from the same subcarrier can beprovided to the TD-CDM de-spreading 803 at the same time. For example, if a TD-CDM with codewordlength ^^^^^^ = 4 is employed, and each pilot OFDM symbols contain ^^^ = 1000 pilot Res, in orderto carry out TD-CDM de-spreading 803 for the first pilot RE in the first pilot OFDM symbol, the TD-CDMde-spreader 803 requires the REs on the first subcarrier of all four pilot OFDM symbols, namely the 1st,the 1001st, the 2001st, as well as the 3001st RE. This implies that the CDM buffer 809 should store each ofthese REs in order to support the time domain processing of the first sub-carrier. Similarly, it should store a number and preferably all of the other REs in order to support the time domain processing of the other sub-carriers. Afterwards, the TD-CDM de-spread pilot OFDM symbols are sent to the frequency domain processingcircuit 804, which may carry out tasks such as de-noising process 805 and FD interpolation process 806,to obtain a near noise-free estimate of all REs 103, including non-pilot REs, of the pilot OFDM symbols.The estimates of the pilot REs may be extracted 812 and used as the basis of error estimation 818, whichmay include noise variance estimation 810 or covariance matrix (CVM) estimation 811. In someexamples, these techniques may be used to support enhanced channel equalization algorithms, such asminimum mean square error interference rejection combining (MMSE-IRC). Each layer has its ownAccelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final channel gain estimate de-noising process, while the covariance matrix estimation 811 requires the de- noised channel gain estimates of all layers at the same time. Note that the de-noising process 805 maybe omitted if the channel may be considered as noise- and interference-free (or close thereto), in whichcase the TD-CDM de-spread signal can be readily used as a de-noised signal. Meanwhile, the FDinterpolation process 806 may not be necessary if all subcarriers in the input pilot OFDM symbol arepilot subcarriers, in which case the input de-noised signal can be readily used as an FD-interpolatedsignal. Furthermore, the CVM estimation 811 is also optional and only required when the relevantchannel equalization algorithm (such as MMSE-IRC) is employed.The channel gains of REs on the non-pilot OFDM symbols can be obtained through time domainprocessing (e.g., by Channel Matrix TD processing circuit 815), including the time domain interpolation(e.g., by time domain interpolation circuit 814) of the channel gains on the pilot OFDM symbols.Likewise, the CVMs of REs on the non-pilot OFDM symbols can be obtained through time domainprocessing 816, including the time domain interpolation 817 of the CVMs on the pilot OFDM symbols. While some interpolation algorithms, such as nearest neighbour [6], relies on only one pilot RE(^^^^^^^^^ = 1), more sophisticated ones require pilot REs on multiple OFDM symbols, such as for splineinterpolation [6], which needs at least ^^^^^^^^^ = 3. Similar to the problem of TD-CDM de-spreading803 mentioned above, the TD interpolation circuit (814, 817) also requires REs on a specific subcarrier inone or multiple de-noised and FD interpolated pilot OFDM symbols at the same time. As discussedbelow, this motivates the use of interpolation buffers (813, 823) to store the channel gains and CVMsuntil multiple pilot OFDM symbols are available, so that the channel gains and CVMs from the same subcarrier can be provided to the time domain interpolation circuit (814, 817) at the same time. Forexample, if each FD-interpolated pilot OFDM symbol has ^^ = 2000 subcarriers (Res), and a splineinterpolation algorithm is adopted for the TD interpolation, requiring, in order to carry out TD interpolation for the first RE in the first OFDM symbol, the TD interpolator requires one RE from each ofthe three pilot OFDM symbols, namely the 1st, 2001st, as well as the 4001st REs on the FD interpolatedpilot RE. This implies that the interpolation buffers (813, 823) should store each of these REs in order tosupport the time domain processing of the first sub-carrier. Similarly, it should store all of the other REsin order to support the time domain processing of the other sub-carriers. Moreover, even in the case of algorithms relying on one pilot RE, it is not uncommon that the first pilot OFDM symbol occurs after thefirst OFDM symbol in the RG, thus the TD interpolation of the first OFDM symbol relies on the de-noisingand FD interpolation processing of OFDM symbols arriving later. Note that besides time domaininterpolation circuit (814, 817), the time domain processing (815, 816) may also or alternatively include time domain filtering (819, 820) and / or a timing compensation circuit 821, 822 for either or both of thechannel matrices and error estimates and for compensating, say, phase error imposed by inaccuratelocal oscillators.The first Channel Estimator 801 shown in FIG. 8 is proposed for solving the problem discussed above. Inexamples described herein, observe from FIG. 8 that the scheme uses three buffers, namely:(1) A CDM buffer 809 between the FD-CDM de-spreader 802 and the TD-CDM de-spreader 803, toensure that the TD-CDM de-spreader 803 has access to the spread samples on all relevantOFDM symbols before commencing its de-spreading process. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final (2) An Interpolation Buffer 813 between the FD processing circuit 804 and the Channel Matrix TDprocessing circuit 815, to ensure that the TD interpolation circuit 814 have access to the datasamples on all relevant OFDM symbols before commencing their interpolation processes. (3) An Interpolation Buffer 823 between the error estimator circuit 818 and the error estimate TDprocessing circuit 816, to ensure that the TD interpolation circuits 817 have access to the datasamples on all relevant OFDM symbols before commencing their interpolation processes.The TD-CDM de-spreading 803 requires the CDM Buffer 809 to store at least the same number of OFDMsymbols as the length of TD-CDM spread code minus one, because REs from the last FD-CDM de-spread pilot OFDM symbol can be directly sent to the TD-CDM de-spreader 803 without waiting to be providedwith anymore. In the aforementioned example with ^^^^^^ = 4 and ^^^ = 1000, a CDM buffer 809 isrequired to store the channel estimates of the first three (^^^^^^ − 1) FD-CDM de-spread pilot OFDMsymbols, while the FD-CDM de-spreader 802 is processing the fourth pilot OFDM symbol. Explicitly, theFD-CDM de-spreading output of the 1st, the 1001st and the 2001st REs should preferably be buffered untilthat of the 3001st RE is obtained, whereupon the TD-CDM de-spreading processing 803 can beperformed. Likewise, FD-CDM de-spreading output for all of the other REs before the 3001st shouldpreferably be buffered, in order to support the TD-CDM de-spreading of the REs that arrive after the 3001stone. In this way, the first subcarriers of all de-spread pilot OFDM symbols are available to the TD- CDM de-spreader 803 at the same time when the TD-CDM de-spreading job commences. If the FD-CDM de-spreader 802 outputs a total of ^^^ = 2 TD-CDM spread coded layers, and all of which requires TD-CDM de-spreading, then the CDM buffer 809 size requirement may be doubled to accommodate FD- CDM de-spreader outputs of both TD-CDM spread coded layers. In many cases, each pilot OFDM symbol contains a high number of pilot REs, such as for 3GPP’s 5GNR PUSCH, which may contain a maximum of6 pilot REs 112 per RB 107 and 273 RBs per pilot OFDM symbol 111, leading to a total of 1638 REs perFD-CDM de-spread layer, all of which have to be buffered for TD-CDM de-spreading.The TD interpolation circuit(s) 814, 817 requires the interpolation buffers (813,823) to store at least thesame number of channel estimates and CVMs for CDM de-spread, de-noised and FD interpolated pilot OFDM symbols as the number inputs of the specific TD interpolation algorithm. In the aforementionedexample with ^^^^^^^^^ = 3 and ^^ = 2000, an interpolation buffer is required to store the channelestimates of the first three CDM de-spread, de-noised and FD interpolated pilot OFDM symbols, while the TD interpolator is processing the interpolation of the first non-pilot OFDM symbol. Explicitly, the FD-interpolation output of the 1st and the 2001st REs should preferably be buffered until that of the 4001stRE is obtained, whereupon the TD-interpolation processing can be performed. Likewise, FD-interpolation output for all of the other REs before the 2001stshould preferably be buffered, in order tosupport the TD-interpolation of the REs that arrive after the 2001st one. If the MIMO system transmits^^ = 4 layers and has ^^ = 4 receiving antennas, to accommodate the estimate data for all layers, thechannel gain matrix storage requirement in the interpolation buffer is then quadrupled (^^-tupled). In many cases, each pilot OFDM symbol contains a high number of REs, such as for 3GPP’s 5GNR PUSCH, which may contain 12 REs per RB and a maximum of 273 RBs per pilot OFDM symbol, leading to a total of 3276 REs per FD-CDM de-spread layer, all of which have to be buffered for TD interpolation. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final The rest of this section explains how the signal processing works in the proposed first Channel Estimator1801. Mind that some processes are optional, some of which are marked by dashed line border framesin FIG.8, which will also be explained in the following text. Furthermore, certain boxes with solid outlines are only needed if certain outputs are required. Forexample, the TD-CDM spreading circuit 603, the error estimator circuit 818, and the error estimatesinterpolation buffer 823 are not needed if the circuit designer only cares about the output the 2nd set ofTD-CDM de-spread estimate signals 825. Similarly, the channel matrix estimates’ interpolation buffer813 is not needed if the circuit designer only cares about the output error estimate signals 826.Signal Processing Before CDM De-Spreading Once a pilot RE located at the ^^th subcarrier and the ^^th OFDM symbol in the mapped physical RG, ^^^ ,^^of size (^^ × 1) has been transmitted by the transmitting device 302, it will suffer from multi-pathchannel fading and additive noise, before being received at the receiving device 304. For this RE, thereceived signal can be expressed as ^^^ ,^^ = ^^^ ,^^, where ^^^ ,^^ is of size (^^ × 1) and its ^thelement ^ ^ ^^ ,^^ is received from the ^th receiving antenna, ^^ ^^ ,^^ is the precoded channel gain matrix of size(^^ × ^^) for each RE describing the channel gains for the spatial streams between each layertransmitted and each receiving antenna path, and ^^^ ,^^ is the additive white Gaussian noise (AWGN)having size (^^ × 1) for each RE. For the sake of simplification, unless useful or necessary, the AWGN isomitted for the examples described herein, under the assumption that the de-noising process is capable of sufficiently mitigating all AWGN and interference.FDM de-multiplexing (in FDM de-multiplexing circuit 807) and TDM de-multiplexing (in TDM de-multiplexing circuit 808) may be firstly carried out, extracting the pilot REs and mapping them from thereceived physical to a received pilot grid ^ as ^^,^according to the strategy ^^^^and ^^^^.An initial channel estimation process (in initial channel estimation circuit 509) may then be carried outby the receiver on the input pre-estimation signal ^^^^^,^1018 to obtain the initial estimate signal of thepilot RE on the ^th pilot subcarrier and the ^th pilot OFDM symbol for the ^th receiving antenna ℎ^^ ^^^,^1016, with the help of one or more base pilot signal(s) (1009) that is locally generated at the receiverusing a base pilot signal generation circuit (502). For example, initial channel estimation may beperformed using the least square (LS) error algorithm, which is expressed as in Eq. (6). The hat notation in ℎ^^^^,^means the variable represents data estimated by the receiver, as summarized in Table 7.Alternatively, a least absolute (LA) error algorithm [7] could be used to perform initial channelestimation, in which case the initial channel estimate may be obtained by finding the corresponding that minimises the absolute estimation error Unlike LS, the LA algorithm Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final not have an analytical solution expression, requires iterative processing, may not necessarily end up with a stable solution, but has the potential to avoid disturbance from large errors. This process involves locally generating the base pilot symbols ^^,^502 at the receiver, and assumes that the receiver has all the information required to generate it, such as cell ID, scrambling ID, etc.Note that the initial channel estimation circuit 509 can alternatively be carried out at a later stage, suchas after FD-CDM de-spreading 802 and TD-CDM de-spreading 803, so long as it is performed before theFD de-noising process 805. However, moving initial channel estimation circuit 509 to a later stage mayincrease the number of complex multiplications, thus increasing the overall complexity. The remainder of the channel estimator’s task includes, in the order they appear in first channelestimator 1801, FD-CDM de-spreading 802, TD-CDM de-spreading 803, channel estimate de-noisingprocess 805, FD interpolation process 806, TD interpolation (e.g., by TD interpolation circuit 814), as wellas noise variance estimation 810 or covariance matrix estimation 811, as shown in FIG. 8.FD-CDM and TD-CDM De-Multiplexing In some examples, CDM de-multiplexing process assumes that the channel gain does not change within adjacent ^^^^^^subcarriers after FDM and ^^^^^^OFDM symbol time samples after TDM, while any distortion imposed by this approximation can be minimized at the subsequent de-noising stage, as shown in Eq.(7). FD-CDM de-spreading 802 may be operated by multiplying each pilot subcarrier in ^^^^by its corresponding FD-CDM spreading code ^^and averaging across every set of ^^^^^^pilot subcarriers inthe FD, expressed as in Eq. (8). Detailed explanation can be found in [8].This may be carried out for all pilot subcarriers ^ and for all pilot OFDM symbols ^. The results may betemporarily buffered in the CDM Buffer 809 of FIG.8, in preparation for the following TD-CDM de-spreading 803, which may be operated by multiplying each pilot subcarrier in ^^^^^^^^^^^^ by itscorresponding TD-CDM spreading code ^^and averaging across every set of ^^^^^^elements in theTD, expressed as in Eq.(9). Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalEquation (9) above shows that the TD-CDM de-spread operation 803 requires all ^^^^^^ pilotsubcarriers within the same TD-CDM group, which are spread across ^^pilot OFDM symbols in the TD, while each operation of FD-CDM de-spreading only gives pilot subcarriers from a single OFDM symbol,thus explaining why a CDM buffer 809 is required.As an example, FIG. 9 shows the CDM de-spreading dependencies between REs. In the FD, the pilotresource grid in FIG. 9 has ^^^ = 8 pilot subcarriers 112, which are split into ^^^^^^^^^^^ = 2 groups701, each having ^^ = 4 pilot subcarriers. In the TD, the pilot resource grid has ^^^ = 4 pilot OFDMsymbols 111, which are split into ^^^^^^^^^^^ = 2 groups 702, each having ^^ = 2 pilot OFDMsymbols.As another example, in 3GPP’s 5GNR standard [1], a PUSCH transmission uses DMRS configuration type1 and utilises DMRS ports ^ = [0,1,4,5], thus having both FD-CDM and TD-CDM applied. Both the FD-and TD-CDM use the length-2 spread code (+1, +1), (+1, −1). The FD-CDM de-spreading can be givenas in Eq.(10). TD-CDM DMRS port 0 can as Eq. 11 . The TD-CDM de-spreading for other ports can be similarly carried out.The CDM de-spreading process is roughly formed of two parts: to multiply with the correspondingspread code, and then to average across the CDM group. For both FD-CDM and TD-CDM de-spreading, the averaging across CDM group part is only necessary when the corresponding number of employed spread code is greater than one, i.e., when ^^^ > 1 and ^ ^^ > 1, respectively. Otherwise, when ^ ^^ = 1or ^^^ = 1, the result after the elementwise spread code multiplication can be readily output, and theaveraging process is not necessary, because there is no interference in that FD-CDM or TD-CDM codedomain. Furthermore, for FD-CDM, if ^^^ = 1 and all the elements in the sole FD-CDM spread code usedare +1, the spread code multiplication part may also be omitted, because multiplying by +1 has noinfluence on the signal value, in which case the complete FD-CDM de-spreading circuit 802 is optional.Therefore, the FD-CDM de-spreading circuit 802 is only necessary when the input signal is FD-CDM spread. Recall from the example given when explaining that two different layers may have the same FD-CDMspread code but different TD-CDM spread code, where ^^ = 2 layers are transmitted using the same^^^ = 1 FD-CDM spread code ^ ^ ^ ^^ = ^^ = (+1, −1) but ^^ = 2 different TD-CDM spread codes. In thiscase, the averaging across CDM group part in the FD-CDM de-spreading process is unnecessary, becausethe FD-CDM de-spreading results for the two layers are identical, since they share the same FD-CDM de- spread code. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final De-Noising The received pilots may be corrupted by noise, and thus in some examples a de-noising process 805 maybe employed to provide more accurate channel estimates. The multi-path fading channel gains changerelatively slowly in both the frequency and time domain, compared to the duration of each subcarrierand each OFDM symbol, respectively. Hence, the channel gains on neighboring pilot REs are expected tobe correlated in both dimensions. In some examples, these observations by the inventors may beexploited to remove noise, which is uncorrelated.De-noising process can be carried out in the FD and / or TD direction to every pair’s de-spreadchannel matrices. Most de-noising process is linear or can be expressed in a linear format, using a de- noising weight matrix ^.If the de-noising is carried out in the frequency domain, ^^^ would be an ^^^^ matrix and theoperation is carried out as in Eq.(12). If the de-noising is carried out in the time domain, ^^^ would be an ^^^^ × ^^^^ matrix and theoperation is carried out as in Eq.(13). When both FD and TD de-noising operations are carried out, the process can be merged and a four-dimensional de-noising weight matrix of size × ^^^ × ^^^ × ^^^^ may be required, whoseelement,^,^ ̅ represents the contribution from the pilot at ^^^, ^^̅ to the one at (^, ^). The de-noisingprocess can be expressed as in Eq.(14). As an example, a 1-dimensional moving mean method of de-noising with a sliding window length of ^^^^^^would correspond to a weight matrix ^^^^^^^^^^^, whose only non-zero elements are located on the diagonal line, the parallel lines above it, and the parallel ^^^^^^^^^^^ lines below it. Non-zero elements on the same row of ^^^^^^^^^^^have the same value and each row adds up to 1.Therefore, for de-noising a pilot OFDM symbol with ^^^ = 6 pilot subcarriers that are mapped to thephysical RG with equal frequency distance to each other, a moving mean method de-nosing weightmatrix of size (6 × 6) and ^^^^^^ = 3 would be given as in Eq.(15).Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final On each row of ^^^^^^^^^^^, the weights of the non-zero elements may not necessarily be identical, as long as they add up to ‘one’. For example, the non-zero elements on the 2nd, 3rd, 4th, and 5throws can bechanged into centre RE has a higher weight during the averaging process.In a second example, if the minimum mean-square error (MMSE) method [9] is adopted, the weightmatrices ^^^^^are the auto-correlation matrices between each pilot symbols.As a third example, if a discrete Fourier transform (DFT) based windowing method [8] is used, the weightmatrix ^^^^would be the product of the inverse DFT transform matrix ^^^, the windowing diagonalmatrix ^ and the DFT transform matrix ^, i.e., ^^^^ = ^^^^^.Interpolation After the de-noised channel gain estimates at subcarriers and OFDM symbols with a pilot are obtained,interpolation (806, 814, 817) is carried out in order to provide estimates of the channel gains on thosesubcarriers and OFDM symbols without a pilot. A skilled artisan will recognize that various algorithmscan be used in this process, which include but are not limited to nearest neighbor interpolation, linearinterpolation, polynomial interpolation, spline interpolation, etc. Let ℎ^ ^,^^^^^ ,^^be the estimated channel gain between the ^^^th layer and the ^th receiving antenna for the ^^th subcarrier on the ^^th OFDM symbol in the mapped resource. If a pilot element is transmitted at thelayer-subcarrier-symbol coordinate ^^^^ , ^^, ^^^, i.e., if there exists a pilot layer-subcarrier-symbolcoordinate ^^^^ , ^, ^^ such that ^^ = ^^^^^^, ^^^^ and ^^ = ^^^^^^, ^^^^, then the de-noised channel gainresult will directly be applied, as shown in Eq.(16). Otherwise, if ℎ^ ^,^^^^^ ,^^is not located at an element with a pilot, but within an OFDM symbol with a pilot, a FD interpolation process 806 algorithm ^^can be used to interpolate its value based on the de-noised channel gains of some, or all, of the pilot subcarriers within this OFDM symbol, as shown in Eq.(17). Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalSimilarly, a TD interpolation algorithm ^^ (e.g., performed by TD interpolation circuit 814),can be usedin the case of being a non-pilot element on a subcarrier with pilot elements in other OFDMsymbols, as shown in Eq.(18). Finally, if ℎ^ ^,^^^^^ ,^^corresponds to an element with no pilots in neither the same subcarrier nor the same OFDM symbol, the interpolation could only be based on the interpolated channel gains of its nearby elements, who belong to the previous two categories. In this case, two-dimensional interpolation may be preferred. For example, consider the FDM & TDM mappings depicted in FIG.7. If a linear interpolation algorithm isemployed for obtaining all channel estimates on OFDM symbol ^^ = 0 of port number ^^^, where the de-noised channel estimates on pilot subcarriers ^ = 0,1,2,3, or equivalently mapped subcarriers ^^ =0,1,4,5 are available, the interpolation process ^^ can be given as in Eq.(19). Notice that no interpolation is carried out for mapped subcarriers ^ = 0,1,4,5, linear interpolation iscarried out for subcarriers ^^ = 2,3 based on subcarriers ^^ = 1,4 (equivalently pilot subcarriers ^ = 1,2),while linear extrapolation is carried out for subcarriers ^^ = 6,7 based on subcarriers ^^ = 4,5(equivalently pilot subcarriers ^ = 2,3).If the interpolation is firstly carried out along the FD, the channel gain estimates of all subcarriers in the OFDM symbols containing pilot will be produced, denoted by ^^^^^^^^^^^, which are temporarily bufferedin the Interpolation buffer 813 of FIG. 8. After all OFDM symbols containing a pilot are processed, the TDpart of the first channel estimator 801 is operated, calculating the channel gain estimates of all otherOFDM symbols without pilot. This can be mathematically expressed as in Eq.(20). Likewise, if the interpolation is firstly carried out along the TD, the channel gain estimates of all OFDMsymbols’ pilot subcarriers, denoted by ^^^^^^^^^^ , are buffered in the interpolation buffer. As shown inEq.(21). Moreover, in some examples envisaged herein, a joint time-domain and frequency-domain interpolationmethod can be used, where the value of the interpolant RE may be dependent on pilot REs from bothnearby subcarriers and nearby OFDM symbols. In this case, a two-dimensional interpolation algorithm^^^ can be used, whose input comprises of all of the interpolant’s nearby pilots. As shown in Eq.(22). Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final The pilot symbol-aided channel estimation samples the channel profile using pilot Res. The density of pilots is closely related to the channel gain fluctuation in both FD and TD. For the FD, if a hostile communications environment causes strong multipath effect, such as through reflections from buildings, the receiving signals’ delay spread will be long, which leads to narrower coherence bandwidth, meaning the channel changes fast in the FD, thus requiring high pilot density in the FD. Similarly, for the TD, if the UE moves fast with respect to the BS, the doppler frequency will be high, which leads to short coherence time, meaning the channel changes fast in the TD, thus requiring high pilot density in the TD. Provided that the pilots are sufficiently densely populated in both FD and TD, the sampled channel gain would change relatively slowly, and smoothly, between every two consecutive pilots. The differencebetween the interpolated channel gains ^^ and the actual channel gains ^ should be minimum (denotedby ^). As shown in Eq.(23). Hence, the assumption made is canon those subcarriers and OFDM symbols without a pilot. In some examples, including the moving mean method, the interpolation can be merged with the de-noising processing to form a single joint process. In such case, the weight matrix ^ will be increased up for the FD-only, TD-only, and two-processing cases, respectively. The enlargement of the first dimension (as well as the third in the two- dimensional case) is to accommodate the weight contribution of pilots to non-pilot elements.Mind that the FD-, TD-, and 2D-interpolation operations are only necessary when pilot REs and non-pilotREs co-exist in the respective dimension. For example, if all pilot subcarriers on pilot OFDM symbol isone-to-one mapped to an OFDM symbol using ^ ^^, ^^^^ = thus ^^^ = ^^, all channelon this mapped OFDM symbol are known since they are all pilots, therefore FD-interpolation is no longer required.Error EstimationIn addition to providing the equalize with channel estimates, the channel estimator may also providenoise and / or covariance matrix estimates, in order to enhance the equalization. Noise variance estimation 810 and covariance matrix estimation 811 is based on the de-noise channel matrices^^ ^^^^^^^. The instantaneous interference plus noise (IpN) component for each pilot location at thereceived antenna ^ can be estimated first as in Eq.(24). This process involves locally generating the base pilot symbols of one or more base pilot signals 1009 and carrying out FD-CDM spreading 602 and TD-CDM spreading 603 on them at the receiver. It is assumed that the receiver has all the information required for doing so, such as the CDM spread code set, list of used port numbers, etc. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final This is followed by averaging the power across multiple other IpNs nearby to obtain the covariancematrix. Denote by ℒ^^^ ^^^ ^ and ^^ the lists of nearby pilot OFDM symbol and element indices for (^, ^),the averaging process can be expressed as in Eq.(25). In the above equation, ^^and ^^are the indices of receiving antenna ports, which may or may not bethe same antenna. When ^^ ≠ ^^, ^^^,^^,^^quantifies the interference correlation between the twoantennas at pilot RE (^, ^) and ^ ^^,^^∗ ^,^ = ^^ , while when ^^ = ^^ = ^, ^^^,^is the real-valued noisevariance at the pilot RE (^, ^). The estimated covariance matrices may be used at MMSE-IRC channelequalization process [9].The overall noise power for receiving antenna ^ is the averaging of ^ ^^,^ or all pilot subcarriers ^ and allpilot OFDM symbols ^. Further, assuming the noise power is of the same level for all ^^receiving antennas, the average value for all can be estimated as the averaging diagonal IpN elements of all estimates, as shown in Eq.(26). The estimated noise power may be used the minimum mean square error (MMSE) channel de-noising process, as well as MMSE channel equalization process. Following error estimation 818, a sequence of one or more error estimate signals are obtained according to the equations above. In some examples these may be written to the interpolation buffer 813, until error estimate signals have been accumulated across one or more pilot OFDM symbols. Following this, time domain processing 816 may be performed. This may include time domain interpolation 817, which may be employed to generate error estimate signals for non-pilot OFDMsymbols. Note that, in some examples, this process is not required in situations where all OFDM symbolsare pilot OFDM symbols. Note that besides time domain interpolation 817, the time domain processing 816 may also or alternatively include time domain filtering 820 and / or noise power matrix generation 822. Channel Estimator 2: TD-CDM De-Spreading Performed after Interpolation BufferingFIG. 10 shows another channel estimator example, referred to as Channel Estimator 2 circuit 1001. Thisis motivated by the observation that the TD-CDM de-spreading and FD de-noising and interpolation structure of first Channel Estimator 1801 would potentially create the following problems: (1) The CDM buffer 809 requires a significant amount of memory to store the FD-CDM de-spreadoutputs of the (^^^^^^ − 1)^^^^^^pilot Res. This large amount of memory may impose a large chip area and / or a high power consumption in a practical implementation, leading to high deployment and running costs. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final (2) The channel matrix estimates’ interpolation buffer 813 requires a significant amount of memoryto store the ^^^^^^^^^^^^^entries of pilot OFDM symbol REs’ de-spread, de-noised and FD interpolated channel gain outputs, as well as their covariance matrix estimates. Again, this large amount of memory may impose a large chip area and / or a high power consumption in a practical implementation, leading to high deployment and running costs. (3) The FD de-noising process 805 and FD interpolation process 806 should preferably separatelyprocess each of the ^^layers of the TD-CDM de-spread channel estimates, requiring high computational complexity and / or time delay. This high computational complexity and / or time delay may impose a low hardware efficiency, leading to a large chip area and / or a high power consumption in a practical implementation, as well as high deployment and running costs.These problems may be observed in most modern wireless communications protocols, where CDM isapplied to the pilots in the time domain. This includes, but not limited to, the following physical layer channels in 3GPP’s 5G standard: (1) Physical Uplink Shared Channel (PUSCH) with TD-CDM(2) Physical Downlink Shared Channel (PDSCH) with TD-CDMFurthermore, it can be envisaged that other forms of OFDM-MIMO communication systems may employthis technique that has TD-CDM de-spreading performed after interpolation buffering.In order to reduce the total buffer size requirement and power consumption of a channel estimator, and to reduce the calculation complexity and time delay of the de-noising and FD-interpolation process, thefollowing implementation technique shown in Fig. 10 is proposed.Fig. 10 shows the proposed Channel Estimator 2 circuit 1001, where the differences to the first ChannelEstimator 1801 of FIG. 8 are marked by double-line framed rectangles in both figures. Observe that theTD-CDM de-spreading circuit 1008 is moved after the Interpolation Buffer 1013, and the CDM Buffer 809is missing, which will be discussed in this section, and that a different pilot sequence input to the error estimation circuit 1014 is used, which will be discussed in the next section.In the proposed Channel Estimator 2 circuit 1001, the TD-CDM de-spreading circuit 1003 is moved to alater stage, after the Interpolation Buffer 1013 and before the TD interpolation. Therefore, the numberof layers at the input to the FD de-noiser 1005 and FD-interpolator 1006 is reduced from ^^ down to^^^, because layers multiplexed by TD-CDM have yet to be separated and are forwarded to the de-noiseras a single layer. This size reduction also applies to the error estimator circuit 1014 and the interpolationbuffer 1013, which are also placed before the TD-CDM de-spreading circuit 1003 in Channel Estimator 2circuit 1001. As a result, the following improvement has been made to solve the problem of first Channel Estimator 1801 mentioned above: (1) Having the TD-CDM de-spreading circuit 803 removed, then no CDM buffer 809 is required, thusreducing the total memory requirement for CDM buffer from (^^^^^^ − 1)^^^^^^pilot REs down to zero, which also reduces chip area, power consumption, deployment costs and running costs. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final (2) The interpolation buffer 1013 memory size requirement for storing the channel gain matrices isreduced by^^^^^times, in terms of the number entries of pilot OFDM symbol REs, which also reduces chip area, power consumption, deployment costs and running costs. (3) The computational complexity and / or time delay of the FD de-noiser 1005 and FD interpolator1006 is reduced, because the number of input layers per job is reduced by^^^^^times, which also reduces chip area, power consumption, deployment costs and running costs. However, this arrangement causes two new challenges detailed below, both of which require a re- formulation of the calculations given for Channel Estimator 1. (1) The FD de-noiser 1005 and FD interpolator 1006 should preferably process channel gainestimates of multiple layers multiplexed together by TD-CDM, instead of individual TD-CDM de- spread layers, and (2) The error estimation circuit 1014 should preferably process de-noised channel gain estimates ofmultiple layers multiplexed together by TD-CDM, instead of individual TD-CDM de-spread layers. The rest of this section discusses the channel estimation operation carried out by Channel Estimator 2circuit 1001, its difference to the operations carried out by first Channel Estimator 1801, as well as howthese operations solve the above two additional challenges. In some examples, it is envisaged that someof the processes marked by dashed line border frames in FIG. 10 may be excluded in some applications,.Furthermore, in some examples, it is envisaged that certain boxes with solid outlines may only bepotentially relevant or needed if certain outputs are required, as would be understood by a skilledperson. For example, the error estimation circuit 1014 and the error estimates interpolation buffer 1017are not needed if the circuit designer only cares about the output TD-CDM de-spread estimate signals1015. Similarly, the channel matrix estimates interpolation buffer 1013 and the TD-CDM de-spreadingcircuit 1003 are not needed if the circuit designer only cares about the output error estimate signals1012. Signal Processing Before CDM De-Spreading The input to Channel Estimator 2 circuit 1001 is a sequence of one or more TD-CDM spread received signals 1002, which may optionally also be FD-CDM spread, FDM multiplexed and / or TDM multiplexed,as discussed below. As a result, the one or more TD-CDM spread received signals 1002 is a multiplexedrepresentation if any one or more of the multiplexing schemes is applied. Here, the number of TD-CDMspread received signals depends on the number of pilot REs included in the transmitted signal, which may be only one in an extreme example but is more typically higher. The pilot signal processing in Channel Estimator 2 circuit 1001 before CDM de-spreading may involve optional FDM de-multiplexing(in FDM de-multiplexing circuit 807), optional TDM de-multiplexing (in TDM de-multiplexing circuit 808),as well as initial channel estimation (in circuit 509). These operations may be carried out in the sameway as in first Channel Estimator 1801, and the resultant least squared (LS) channel estimate is also ^^^^.Therefore, these operations will not be repeated here for simplicity reasons only. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final A skilled artisan will readily appreciate that the FD-CDM de-spreading 802 may equally be placed in various locations in order to achieve the same aim, albeit in handling / processing different signals. The following lists some, but not all, of the possible locations of the FD-CDM de-spreading circuit 802 as well as the orders of task that the channel estimator can perform, between the input and the CDM buffering 809. (1) Input, then FDM de-multiplexing an output from first Channel Estimator 1801, then TDM de-multiplexing (in circuit 808), then an initial channel estimation (in circuit 509), then FD-CDM de-spreading (in circuit 802), then frequency-domain processing (in circuit 1004). (2) Input, then FDM de-multiplexing an output from first Channel Estimator 1801, then TDM de-multiplexing (in circuit 808, then FD-CDM de-spreading 802, then an initial estimation (in circuit509), frequency-domain processing (in circuit 1004). (3) Input, then FD-CDM de-spreading (in circuit 802), then FDM de-multiplexing an output from firstChannel Estimator 1801, then TDM de-multiplexing (in circuit 808), then an initial channel estimation (in circuit 509), then frequency-domain processing (in circuit 1004).Hence, the specific illustrated location of the FD-CDM de-spreading circuit 802 in the figures is for explanatory purposes only and should not be viewed as a strict physical location. FD-CDM De-SpreadingThe next step in Channel Estimator 2 circuit 1001 is FD-CDM De-spreading 802, which is also identical tothe same operation carried out by first Channel Estimator 1801, obtaining the FD-CDM de-spreadchannel estimates ^^ ^,^^^^^^^^^^^^^ ^,^.In contrast to first Channel Estimator 1801, in Channel Estimator 2 circuit 1001 after FD-CDM de-spreading 802, no TD-CDM de-spreading process is immediately followed. The FD-CDM de-spreadchannel estimates ^^^,^^^^^^^^^^^^^ ^,^ may be directly forwarded to the FD de-noising circuit 1005.Note that, in some examples, the FD-CDM de-spreading 802 component can be omitted if the inputsignal is not FD-CDM spread, in which case the input initially estimated signal can be readily used as the FD-CDM de-spread signal. De-Noising As in first Channel Estimator 1801, Channel Estimator 2 performs frequency-domain processing 1004,which may include FD de-noising circuit 1005 and FD interpolation 1006. However, in Channel Estimator2 circuit 1001, no TD-CDM de-spreading is carried out to the input of the FD de-noising circuit 1005,therefore the input is a sequence of one or more TD-CDM spread estimate signals 1007, where the number of signals depends on the number of pilot REs in the transmitted signal. It is envisaged that in some examples, any of the FD de-noising algorithms ^^^mentioned before for first Channel Estimator Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final1801 can be applied to the TD-CDM spread estimate signals 1007 to obtain the de-noised channelestimate shown in Eq.(27). Since the input to the de- 1005 a TD-CDM output a TD-CDM spread de-noised signal. Note that in TD-CDM spread signals, layers having the same FD-CDMspread code but different TD-CDM spread codes cannot be differentiated. Therefore, these unseparated layers have the same de-noised channel gain values which is the superposition of all their de-noised channel gains with TD-CDM. This results in a reduced layer dimension size in turn reduces the de-noising processing complexity, which is from processing ^^ layers down to ^^ ^ layers only, because the operation for all layers with same FD-CDM spread code can be performed only once, and there are only ^^^unique FD-CDM spread codes being used. The obtained TD-CDM spread de-noised signal ^^^^^^^^^^ ^^^^^^^is equivalent to the output of ChannelEstimator 1’s de-noising process 805 ^^^^^^^^^ if TD-CDM spreading had been applied, because both theFD de-noising and the TD-CDM de-spreading are linear processes and their order can be exchanged, which is shown by Eq.(28). In some examples, it is envisaged that the FD de-noising component can be omitted if the input signalcan be considered noise- and interference-free, or very close thereto, in which case the FD-CDM de-spread signal can be readily used as a de-noised signal. FD-Interpolation The TD-CDM spread de-noised estimates sent to the FD interpolation circuit 1006, resulting in a sequence of one or more TD-CDM spread FD-interpolated channel estimates 1008 of all subcarriers on all pilot OFDM symbols^^ ^^^^^^^^ ^^^^^^^^^ . Here, the number of channel estimates may dependon at least the total number of REs in the transmitted signal. If necessary, an FD-interpolation algorithm^ may be employed for calculating the estimates of non- ^^^^^^^^^^,^^^^ pilot REs ℎ^^^^^^^^^ ^^ ,^^based on the pilot REs ^,^^^^^^^^^^^^^^^^^^^^:,^in the current pilot OFDM symbol ^^. This can be mathematically expressed as in Eq.(29).ℎ^^^^^^^^^ ^,^^^^,^^ ^^^^^^^^^ ^^ ,^^ = ℎ^^^^^^^^^^^^^^^^^^,^, if ∃^^^^, ^^ , ^^^ s. t. ^^ = ^^^^^^, ^^^^ and ^^ = ^^^^^^, ^^^^^,^^ ^ ℎ^^^^^^^^^^^^^^^^^^^ ^^ ,^^ = ^^ ^^^^^^^^^^^^,^^^^^^^^^:,^, ^^^^ , ^^^ , if ∃^^^^ , ^^^ s. t. ^^ = ^^^^^^, ^^^^Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalThe second operation in the above equations may be employed when pilot REs 110 and non-pilot REsco-exist in the mapped OFDM symbol corresponding to the input pilot OFDM symbol 111. Otherwise, ifall subcarriers in the mapped OFDM symbol are pilots, the FD interpolation circuit 1006 may carry outonly the first operation in the above equations in some examples, and only if FDM is employed, in whichcase it maps the input de-noised channel estimates ^^^^^^^^^^ ^^^^^^^to the physical OFDM symbol ^^^^^^^^^^ ^^^^^^^^^based on the FDM function used.If the actual channel gains ^ had passed through TD-CDM spreading to obtain a TD-CDM spread channelgain ^^^^^^, the process would be shown in Eq.(30). When the pilot density in the FD is sufficient, the difference between the FD-interpolated channel gains^^^^^^^^^^ ^^^^^^^^^ and the actual TD-CDM spread channel gain ^^^^^^ should be minimum (denoted by ^). Thiscan be mathematically expressed as in Eq.(31). The resultant FD- 1008 may to1013. Since the input to the FD interpolation circuit 1006 is a TD-CDM spread de-noised signal, theoutput 1008 is a TD-CDM spread FD-interpolated signal. This means the FD interpolation circuit 1006 inChannel Estimator 2 circuit 1001, like its de-noising circuit 1005, has reduced complexity, from ChannelEstimator 1’s ^^layers down to ^^^layers only, because the layers have same FD-CDM spread code but different TD-CDM spread codes are still processed together. Likewise, the memory requirement for the interpolation buffer 1013 to store the channel gain estimates is also reduced by^^^^^, because the layershaving the same FD-CDM spread code but different TD-CDM spread codes can share the same FD-interpolated data and only one of these TD-CDM spread layers needs to be stored.It is envisaged that in some examples the FD interpolation circuit 1006 can be omitted if all subcarriersin the input pilot OFDM symbol are pilot subcarriers 102, in which case the input de-noised signal can bereadily used as an FD-interpolated signal. TD-CDM De-SpreadingThe TD-CDM de-spreading circuit 1003 in Channel Estimator 2 circuit 1001 is placed after theinterpolation buffer 1013 and starts to operate once the FD-interpolation of all pilot OFDM symbols inan TD-CDM group are finished and the results written to the interpolation buffer 1013. This is differentto the TD-CDM de-spreader 803 in first Channel Estimator 1801, which is placed after the FD-CDM de-spreader 802 and reads its input from the CDM buffer 809.Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final The TD-CDM de-spreading circuit 1003 is carried out upon the FD-interpolated channel gains 1008 by multiplying all subcarriers in ^^^^^^^^^^ ^^^^^^^^^, including both pilot REs and non-pilot REs, by theircorresponding TD-CDM spreading code ^^ and averaging across every set of ^^^^^^ elements in theTD, expressed as in Eq.(32). Recall from the previous discussion about CDM for pilot signals, that the layer can be jointly identified byits FD-CDM and TD-CDM spread codes. Therefore, if two layer indices ^ and ^^ have both an identical FD-CDM spread code (^^^^ = ^^^) and an identical TD-CDM spread code (^^^^ = ^^^), it is guaranteed that theycorrespond to the same layer, thus ^ = ^′. As a result, for the first term in the bracket of the aboveequation’s last line, only layer ^^^is included in the summation, which can be expressed as in Eq.(33). The last step is based on the assumption that the channel gains do not change within the ^^^^^^pilotOFDM symbol’s time period, which has been discussed when describing Channel Estimator 1’s TD-CDMde-spreading 803.For the second term in the bracket of the above equation’s last line, due to the orthogonality of CDM spread codes, the dot product of two different TD-CDM spread codes within the same TD-CDM spread code set is zero, which means the whole term is zero, as shown in Eq.(34). Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalTherefore, the TD-CDM de-spreading circuit 1003 in Channel Estimator 2’s output ℎ^^^^^^^^^^,^^^^^^^^^^^^^is just ^,^ ℎ^,^^^^^ ,^^. TD-Interpolation Channel matrix TD processing can be performed by channel matrix TD processing circuit 815 in Channel Estimator 2 circuit 1001 can be carried out on the TD-CDM de-spread channel which may include TD interpolation circuit 814. A TD-interpolation algorithm may be employed forcalculating the estimates of REs on non-pilot OFDM symbols ℎ^^^^^^^^^ ^,^^^^^ ,^^based on the pilot OFDM symbols ^^^^^^^^^^ ^^^^^^^^^^, as shown in Eq.(35). The second operation in the above equations may only be necessary when pilot REs and non-pilot REsco-exist in the mapped subcarrier corresponding to the input pilot subcarrier. Otherwise, if all OFDM symbols in the mapped subcarrier are pilots, the TD-interpolation circuit only carries out the first operation in the above equations and only if TDM is employed, in which case it maps the input TD-CDM de-spread channel estimates ^^^^^^^^^^ ^^^^^^^^^^to the physical subcarrier ^^^^^^^^^^based on the TDM function used. It is envisaged that in some examples the TD-interpolation component can be omitted if all OFDMsymbols in the input TD-CDM spread received signal are pilot OFDM symbols 111, in which case theinput TD-CDM de-spread channel estimate signal can be readily used as an TD-interpolated channelestimate signal.Note that besides time domain interpolation, the time domain processing in channel matrix TDprocessing circuit 815 may also or alternatively include time domain filtering 819 for further smoothingthe estimated signal in the time domain, and / or a timing compensation circuit 821 for compensating thephase error imposed by inaccurate local oscillators.Error EstimationIn Channel Estimator 2 circuit 1001, error estimation performed by error estimation circuit 1014 mayinvolve noise variance estimation 1010 and / or covariance matrix estimation 1011. For the covariancematrix estimation 1011 in Channel Estimator 21001, a different sequence of one or more pilot signals1019 may be used, unlike the un-multiplexed pilot sequence multiplied with both the FD-CDM and theTD-CDM spreading codes of first Channel Estimator 1801. Instead, only FD-CDM spreading codes602 are multiplied to the base sequence ^ of the one or more base pilot signal(s) 1009 to obtain thepilot sequence ^^^^ ^^^^^^^^^,^ 1019 for Channel Estimator 2 circuit 1001, as shown in Eq. (36).Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final Like the pilot sequence ^^^^^,^used in first Channel Estimator 1801, the pilot sequence ^^^^^^^^^^,^1019used in Channel Estimator 2 circuit 1001 has three dimensions: frequency, time, and layer. Unlike thepilot sequence ^^^^^,^used in first Channel Estimator 1801, which is of size (^^^ × ^^^ × ^^), the size of^ the pilot sequence ^^^^^^^^^ ^^^,^ 1019 used in Channel Estimator 2 is (^^^ × ^^^ × ^^^), wherein its layer dimension size is reduced from the total number of layers ^^down to the number of layers withdifferent FD-CDM spreading codes of spread codes ^^^.Then, the IpN may be calculated using ^^^^^^^^^ 1019 and the FD-CDM de-spread and de-noisedchannel gains ^^^^^^^^^^ ^^^^^^^ for the pilot REs 1020, which may be extracted 812 from the set of TD-CDMspread estimate signals 1008 obtained for all REs by the FD processing circuit 1004, as shown in Eq.(37). It is envisaged that in some examples the decreased number of summation elements from ^^down to ^^^ compared to the covariance matrix estimation in Channel Estimator 1801 may be used to match thereduced number of separated layers in ^^^^^^^^^. The second half of the above equationcan be expanded as shown in Eq.(38). In some two Eq. to sum FD-CDMcode ^^ TD-CDM spread code and ^^ combinations, i.e., all layers. Therefore, Eq. (37) can be furthersimplified as in Eq.(39). Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_FinalThis leads to the same result as in the IpN calculation of Channel Estimator 1, while Channel Estimator 2has reduced complexity, due to the reduced input size from ^^layers of ^^^^^^^^^in Channel Estimator 1 down to ^^^layers of ^^^^^^^^^^ ^^^^^^^in Channel Estimator 2. Following the instantaneous IpN ^ ^^^^^^^^ ^ ^^^^,^estimation, averaging process may be carried out toproduce the covariance matrix, as shown in Eq.(40). Alternatively, the noise variance 1010 can also be estimated by averaging across the whole pilot RG, as shown in Eq.(41). It is envisaged that in some examples the noise variance estimation 1010 component and CVMestimation component can be omitted if, the relevant channel equalization algorithms requiring them(such as MMSE and MMSE-IRC, respectively) are not employed.Following error estimation circuit 1014, a sequence of one or more error estimate signals 1012 are obtained according to the equations above. These may be written to the error estimate interpolation buffer 1017, until error estimate signals 1012 have been accumulated across one or more pilot OFDM symbols. Following this, time processing 816 may be performed. This may include time domain interpolation 817, which may be employed to generate error estimate signals for non-pilot OFDM symbols. Note that this process is not required in situations where all OFDM symbols are pilot OFDM symbols. Note that besides time domain interpolation 817, the time domain processing 816 may also or alternatively include time domain filtering 820 further smoothing the estimated error signal in the timedomain, and / or noise power matrix generation 822 for generating noise power matrices.Flowcharts In summary, the operation of Channel Estimator 2 circuit 1001 may be described by the flowcharts of FIG.11 and FIG.12. FIG.11 presents a flowchart 1100 for the case where the focus is only channel estimate calculation,without error estimation. The process begins at 1011, which collects the inputs that are provided by asequence of one or more TD-CDM spread received signals 1002. At the same time, a sequence of one ormore base pilot signals 1009 is generated at 1102. The TD-CDM spread received signals 1002 and theone or more base pilot signals 1009 are used to perform initial estimation at 1103, in order to generateAccelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final a first set of one or more TD-CDM spread channel estimate signals 1007. Frequency domain processing 1104 is then applied to these, in order to generate a second set of one or more TD-CDM spread channel estimate signals 1008. These are then written to an interpolation buffer 1105 and then later read back from the interpolation buffer 1106, when channel estimate signals have been collected in the interpolation buffer for a set of one or more pilot OFDM symbols. Finally, TD-CDM de-spreading isapplied at 1107.FIG.12 presents a flowchart 1200 for the case where channel estimate calculation is performed togetherwith error estimation. As in FIG. 11, the process begins at 1011, which collects the inputs that areprovided by a sequence of one or more TD-CDM spread received signals 1002. At the same time, asequence of one or more pilot signals 1009 is generated at 1102. The TD-CDM spread received signals1002 and the one or more base pilot signals 1009 are used to perform initial estimation at 1103, in orderto generate a first set of one or more TD-CDM spread channel estimate signals 1007. Frequency domain processing 1104 is then applied to these, in order to generate a second set of one or more TD-CDMspread channel estimate signals 1008, which are then written to an interpolation buffer 1105.Simultaneously with this, the TD-CDM spread received signals 1002, the one or more base pilot signals 1009 and a subset of the second set of one or more TD-CDM spread channel estimate signals 1008 areused to perform error estimation at 1201. The resultant error estimate signals are then written to theinterpolation buffer at 1202. Later on, when channel estimate signals and error estimate signals havebeen collected in the interpolation buffer for a set of one or more pilot OFDM symbols, these are readback from the interpolation buffer at 1106 and 1203. Finally, TD-CDM de-spreading is applied to thechannel estimate signals at 1107.Circuit Orders A skilled artisan will readily appreciate that the FD-CDM de-spreading 802, the FDM de-multiplexing 807,and the TDM de-multiplexing circuit 808 may equally be placed in various locations in order to achievethe same aim, albeit in handling / processing different signals. The following lists some envisaged, but not all of the, possible locations of the FD-CDM de-spreading circuit 802, the FDM de-multiplexing circuit807, and the TDM de-multiplexing circuit 808 as well as the orders of task that the channel estimatorcan perform, between the input 1101 and the FD processing circuit 1004, which are demonstrated inFIG.13, as a supplementary to the cases already shown in FIG.10. (0) Input, then FDM de-multiplexing 807, then TDM de-multiplexing 808, then an initial channelestimation (in circuit509), then FD-CDM de-spreading 802, then FD processing circuit 1004, asshown in FIG.10. (1) Input, then an initial channel estimation (in circuit 509), then FD-CDM de-spreading 802, thenFDM de-multiplexing 807, then TDM de-multiplexing 808, then FD processing circuit 1004, as shown in case 11301 of FIG.13. (2) Input, then FD-CDM de-spreading 802, then an initial channel estimation (in circuit 509), thenTDM de-multiplexing 808, then FDM de-multiplexing 807, then FD processing circuit 1004, asshown in case 21302 of FIG.13. Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final (3) Input, then FD-CDM de-spreading 802, then an initial channel estimation (in circuit 509), thenTDM de-multiplexing 808, then TDM de-multiplexing 808, as shown in case 31303 of FIG. 13,where the optional FDM de-multiplexing 807 is absent.Each of the FD-CDM de-spreading circuit 802, the FDM de-multiplexing circuit 807, and the TDM de-multiplexing circuit 808 has its own input signals (1304, 1306, and 1308, respectively) and output signals(1305, 1307, and 1309, respectively). When one of the three circuit is placed between the input 1101 and the initial channel estimation circuit 509, its input signal is formed from (also known as arepresentation of) the input 1101’s TD-CDM spread received signal 1002, and its output signal forms abasis of the initial channel estimation circuit 509’s pre-estimation signal 1304. Likewise, when one of thethree circuit is placed between the initial channel estimation circuit 509 and the FD processing circuit1004, its input signal is formed from the initial channel estimation circuit 509’s pre-estimation signal1304, and its output signal forms a basis of the FD processing circuit 1004’s first set of TD-CDM spreadestimate signal 1007.It is worth noting that the following three equivalent expressions describe situations regarding signals Aand B, when the circuit outputting signal B is placed before the circuit or circuits inputting signal A, andwhen signal A and signal B are either directly connected or linked through one or more intermediate circuits in between. ^Signal A is formed from signal B.^ Signal A is a representation of signal B.^ Signal B forms a basis of signal A.Hence, the specific illustrated locations of the FD-CDM de-spreading circuit 802, the FDM de-multiplexing circuit 807, and the TDM de-multiplexing circuit 808 in the figures are for explanatorypurposes only and should not be viewed as a strict physical location. Similarly, the FD de-noising circuit 1005 and the FD interpolation circuit 1006 inside the FD processingcircuit 1004 may equally be placed in either order in order to achieve the same aim, albeit inhandling / processing different signals. Supplementary tables The following 7 tables provide a comprehensive summary of the notations, symbols, and related information to be utilized throughout this document.Table 1 below provides a comparison between general terms and 3GPP 5GNR’s specific terms.Table 1 Comparison between general terms and 3GPP 5GNR’s specific termsName used in this document 3GPP 5GNR’s specific namePilot signal Demodulation Reference Signal (DM-RS)Pilot symbol DM-RS RESpread Code Orthogonal Covering Code (OCC)Table 2 below provides a list of index variables.Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final Table 2 List of Variables (indices)Symbol Meaning^^^ Index of FD-CDM spread code for layer ^ in the FD-CDM spread code set^^^ Index of TD-CDM spread code for layer ^ in the TD-CDM spread code set^ Index of layer, 0 ≤ ^ ≤ ^^^ Index of pilot subcarrier in a pilot OFDM symbol, 0 ≤ ^ ≤ ^^^ − 1^^ Index of subcarrier in a physical resource grid after FDM mapping, 0 ≤ ^^ ≤ ^^ − 1^^ Index of pilot subcarrier in a FD-CDM group, 0 ≤ ^^ ≤ ^^ − 1^ Index of pilot OFDM symbol in a slot, 0 ≤ ^ ≤ ^^^ − 1^^ Index of OFDM symbol in a physical resource grid for TDM mapping, 0 ≤ ^^ ≤ ^^ − 1^^ Index of pilot OFDM symbol in a TD-CDM group, 0 ≤ ^^ ≤ ^^ − 1^^ Index of FD-CDM group in a pilot OFDM symbol, 0 ≤ ^^ ≤ ^^^^^^^^^^^^^ Index of TD-CDM group in a pilot resource grid, 0 ≤ ^^ ≤ ^^^^^^^^^^^^^,^Base pilot sequence element for the ^th pilot subcarrier on the ^th pilot OFDM symbolTable 3 below provides a list of data variables.Table 3 List of Variables (Data)Symbol Meaning^^^^The FD-CDM and TD-CDM spread coded pilot for the ^th’s ^th pilot subcarrier in its ^th pilot ^,^ OFDM symbol ^^^^^^^^^^ ,^^^^,^mapped to its corresponding location on the ^^ th subcarrier of the ^^th OFDM symbol inthe physical resource grid ^^^Noise power ℎ^,^^^Channel gain between the ^^^th layer and the ^th receiving antenna for the ^th pilot ^,^ subcarrier of the ^th pilot OFDM symbol in the slot. ^^^Port number for layer ^ ^^^^,^,^^The covariance between the ^^th receiving antenna and the ^^th receiving antenna at the ^th pilot subcarrier of the ^th pilot OFDM symbol ^^^^ ^ The ^^th element ^(^ )in FD-CDM spread code for layer ^ ^^^^ ^ The ^^th element in TD-CDM spread code for laye ^(^ )r ^ ^De-noising weight matrix^^^^^^,^Instantaneous interference plus noise of the ^th pilot subcarrier of the ^th pilot OFDM symbol on the ^th receiving antenna ^ ^ ^^ ,^^The AWGN on the ^^th subcarrier of the ^^th OFDM symbol imposed on the ^th receiving antennaTable 4 below provides a list of frequency-domain-specific constants.Table 4 List of Frequency-Domain-Specific Constants^^^^^ Set of pilot subcarrier indices near pilot subcarrier ^ for covariance averaging purpose^^Number of pilot subcarriers in each FD-CDM group; FD-CDM spreading code codeword length Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final ^^^^^^Total number of different spread codes in the FD-CDM spread code set ^^^^^^^^^^^^^Number of FD-CDM groups per pilot OFDM symbol ^^^^Number of different FDM mappings ^^Number of subcarriers in the mapped physical resource ^^^Number of pilot subcarriers per pilot OFDM symbol ^^^Number of different spread codes in the FD-CDM spread code set ^^that are used for transmission, ^^^ ≤ ^^^^^^^^^Number of resource blocks (per resource grid)Table 5 below provides a list of time-domain-specific constants.Table 5 List of Time-Domain-Specific Constantsℒ^^^^ Set of pilot OFDM symbol indices near pilot OFDM symbol ^ for covariance averagingpurpose ^^Number of pilot OFDM symbols in each TD-CDM group; TD-CDM spreading code codeword length ^^^^^^Total number of different spread codes in the TD-CDM spread code set ^^^^^^^^^^^^^Number of TD-CDM groups per slot ^^^^^^^^^Number of pilot OFDM symbols required by the TD-interpolator’s algorithm to carry out TD-interpolation ^^Number of OFDM symbols in the mapped physical resource ^^^Number of pilot OFDM symbols per slot ^^^Number of different spread codes in the TD-CDM spread code set ^^that are used for transmission, ^^^ ≤ ^^^^^^^^Number of slots (per frame)Table 6 below provides a list of other constants.Table 6 List of Other Constants^^Number of pilot elements in each CDM group; CDM spreading code codeword length; Used as a generic form of either ^^or ^^^^Number of layers transmitted ^^^^^^ ⋅ ^^^: Maximum number of layers supported given the number of selected FD-CDM and TD-CDM spreading codes ^^Number of receiving antennas ^^^Number of pilot elements per pilot sequence; Used as a generic form of either ^^^or ^^^Table 7 below provides a list of notations.Table 7 List of NotationsNotation Example MeaningItalic lower-case letter ^ Indices of a vector or matrixBold italic letter ^, ^ Vector, matrix, or multi-dimensional arrayAccelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final Italic letter with ^^The ^th scalar element in ^ superscript or subscript Bold italic letter with ^^,:A vector or multi-dimensional array element of ^, whose superscript or subscript first-dimension index is ^ Italic letter with tilde ^^, ^^ Index or data mapped to the physical resource gridItalic letter with hat ^^ Data estimated by the receiverItalic letter with^^^^^^^^^A vector appeared in the proposed Channel Estimator 2 superscript “proposed” References [1] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; NR; Physical channels and modulations (Release 17), Valbonne, France: 3GPP, 2022-03. [2] L.-L. Yang, Multicarrier Communications, John Wiley & Sons, 2009. [3] H. J. Ryser, Combinatorial Mathematics, Mathematical Association of America, 1963. [4] R. Gold, "Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)," IEEE transactions on Information Theory, pp.154-156, Jan.1968. [5] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; NR; Multiplexing and channel coding (Release 17), Valbonne, France: 3GPP, 2022-06. [6] F. B. Hildebrand, Introduction to numerical analysis, Courier Corporation, 1987. [7] Y. Dodge, The concise encyclopedia of statistics, New York: Springer, 2008. [8] L. Hanzo, OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs and Broadcasting, Chichester: Wiley, 2003. [9] F. M. e. a. Tavares, "On the potential of interference rejection combining in B4G networks," in IEEE 78th Vehicular Technology Conference (VTC Fall), Las Vegas, NV, USA, 2013. Accelercomm Confidential Proprietary

Claims

1. ACL-2022-002WO 13-Jun-2025 Specification_Final Claims1. A channel estimator circuit (1001), comprising:an input configured to receive in one slot a multiplexed representation of one or more time-domain code division multiplexed, TD-CDM, spread received signals (1002),an initial channel estimator circuit (509) configured to:process a pre-estimation signal (1018), formed from the multiplexed representation of theone or more TD-CDM spread received signals (1002), use a base pilot signal (1009) from a base pilot signal generator circuit as a reference signal,and output an initial estimate signal (1016); afrequency-domain processing circuit (1004) configured to receive and process a first set of oneor more TD-CDM spread channel estimate signals (1007), representative of the initial estimate signal(1016), and output a second set of one or more TD-CDM spread channel estimate signals (1008);an interpolation buffer (1013) operably coupled to an output of the frequency-domain processingcircuit (1004) and configured to buffer the second set of one or more TD-CDM spread channel estimatesignals (1008); anda TD-CDM de-spreading circuit (1003) operably coupled to an output of the interpolation buffer(1013) and configured to de-spread the buffered second set of one or more TD-CDM spread channelestimate signals (1008) from the interpolation buffer (1013) and output TD-CDM de-spread channelestimate signals (1015).

2. The channel estimator circuit (1001) of Claim 1, wherein the frequency-domain processing circuit(1004) comprises a frequency-domain de-noising circuit (1005) that is configured to receive an inputsignal that is representative of the first set of one or more TD-CDM spread channel estimate signals(1007), to remove noise from the input signal and to provide a de-noised output signal as the second setof one or more TD-CDM spread channel estimate signals (1008).

3. The channel estimator circuit (1001) of Claim 2, wherein the frequency-domain de-noising circuit(1005) is configured to use one of: a linear de-noising algorithm or a pseudo-linear de-noising algorithm.

4. The channel estimator circuit (1001) of claim 1, wherein the frequency-domain processing circuit(1004) comprises a frequency-domain interpolation circuit (1006) that is configured to receive an inputsignal that is representative of the first set of one or more TD-CDM spread channel estimate signals(1007), and to provide a frequency interpolated output signal as the second set of one or more TD-CDMspread channel estimate signals (1008).

5. The channel estimator circuit (1001) of any preceding claim, further comprising a frequencydomain code division multiplexing (FD-CDM) de-spreading circuit (802) configured to:receive and perform a FD-CDM de-spread operation on an input signal (1304), formed from themultiplexed representation of the one or more TD-CDM spread received signals (1002), wherein theoutput signal (1305) of the FD-CDM de-spreading circuit (802) forms a basis of the pre-estimation signal(1018) to the initial channel estimator circuit (509); orreceive from the initial channel estimator circuit (509) and perform a FD-CDM de-spreadAccelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Finaloperation on an input signal (1304), formed from the initial estimate signal (1016), wherein an outputsignal (1305) of the FD-CDM de-spreading circuit (802) forms a basis of the first set of one or more TD-CDM spread channel estimate signals (1007).

6. The channel estimator circuit (1001) of Claim 5, wherein the FD-CDM de-spreading circuit (802) isconfigured to perform a FD-CDM de-spread operation on an input signal to the FD-CDM de-spreadingcircuit (802) that uses a Walsh-Hadamard code with a length of two.

7. The channel estimator circuit (1001) of any preceding claim, wherein the TD-CDM de-spreadingcircuit (1003) is configured to perform a TD-CDM de-spread operation on the buffered second set of oneor more TD-CDM spread channel estimate signals (1008) that uses a Walsh-Hadamard code with alength of two.

8. The channel estimator circuit (1001) of any preceding claim further comprising an FDM de-multiplexing circuit (807) configured to:receive and perform a FDM de-multiplex operation on an input signal (1306), formed from themultiplexed representation of the one or more TD-CDM spread received signals (1002) wherein anoutput signal of the FDM de-multiplexing circuit (807) forms a basis of the pre-estimation signal (1018),or receive and perform a FDM de-multiplex operation on the representation of the initial estimatesignal (1016), wherein an output signal (1307) of the FDM de-multiplexing circuit (807) forms a basis ofthe first set of one or more TD-CDM spread channel estimate signals (1007).

9. The channel estimator circuit (1001) of any preceding claim, further comprising a TDM de-multiplexing circuit (808) configured to: receive and perform a TD-de-multiplex operation on an input signal (1308), formed from themultiplexed representation of the one or more TD-CDM spread received signals (1002), wherein anoutput signal (1309) of the TDM de-multiplexing circuit (808) forms a basis of the pre-estimation signal(1018), or receive and perform a TD-de-multiplex operation on the representation of the initial estimatesignal (1016) from the initial channel estimation circuit (509), wherein an output signal (1309) of theTDM de-multiplexing circuit (808) forms a basis of the first set of one or more TD-CDM spread channel estimate signals (1007).

10. The channel estimator circuit (1001) of any preceding claim further comprising a channel matrixTD processing circuit (815) operably coupled to an output of the TD-CDM de-spreading circuit (1003) andcomprising at least one of the following:a time-domain interpolation circuit (814) configured to perform time-domain interpolation on theTD-CDM de-spread channel estimate signals (1015),a time-domain filtering circuit (819) configured to perform a time-domain smoothing operation onthe TD-CDM de-spread channel estimate signals (1015), atiming compensation circuit (821) configured to perform phase error compensation on TD-CDMde-spread channel estimate signals (1015). Accelercomm Confidential Proprietary ACL-2022-002WO 13-Jun-2025 Specification_Final11. The channel estimator circuit (1001) of any preceding claim, wherein each of a plurality of themultiplexed representation of the one or more TD-CDM spread received signals (1002) is a vector havinga length equal to a number of receive antenna ports ^^, wherein each of the first set of one or more TD-CDM spread channel estimate signals (1007) and each of the second set of one or more TD-CDM spreadchannel estimate signals (1008) is a matrix having a first dimension equal to a number of layers ^^ ^ divided by a TD-CDM spreading factor ^^^ , and having a second dimension equal to the number ofreceive antenna ports ^^.

12. The channel estimator circuit (1001) of Claim 11, wherein the number of receive antenna ports^^, the number of layers ^^^, and the TD-CDM spreading factor ^^^ are configured to vary from slot toslot.

13. A method for channel estimation performed by a channel estimator circuit (1001), the methodcomprising: receiving in one slot a multiplexed representation of one or more time-domain code divisionmultiplexed, TD-CDM, spread received signals (1002), processing a pre-estimation signal (1018), by an initial channel estimator circuit (509), formedfrom the multiplexed representation of the one or more TD-CDM spread received signals (1002) andusing a base pilot signal (1009) provided by a base pilot signal generator circuit (502) as a referencesignal; outputting an initial estimate signal (1016) by the initial channel estimator circuit (509);receiving and processing by a frequency-domain processing circuit (1004) a first set of one ormore TD-CDM spread channel estimate signals (1007), representative of the initial estimate signal(1016), and outputting a second set of one or more TD-CDM spread channel estimate signals (1008);buffering, by an interpolation buffer (1013), the second set of one or more TD-CDM spreadchannel estimate signals (1008); and de-spreading, by a TD-CDM de-spreading circuit (1003), the buffered second set of one or moreTD-CDM spread channel estimate signals (1008) and outputting TD-CDM de-spread channel estimatesignals (1015). Accelercomm Confidential Proprietary

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