Method of beamforming for integrated sensing, computation and communication, and apparatus executing the method

Abstract

Determining operating parameters of precoder stages of transmitters and of combiner stages of a receiver, respectively, configured for over-the-air computing, respectively, involves determining the combiner for the OTA computing signals based on the entire received signals and determining the combiner for the communication signals based on signals from which the interference caused by the OTA computing signal components is removed. Determining the precoders and combiners comprises an iteration loop designed to maximise the sum-rate of the communication signals while maintaining an MSE ε between a targeted OTA computing function and the reconstructed OTA computing function below a predetermined upper bound ρ.

Description

[0001] 202402518

[0002] -1- METHOD OF BEAMFORMING FOR INTEGRATED SENSING, COMPUTATION AND COMMUNICATION, AND APPARATUS EXECUTING THE METHOD

[0003] FIELD OF THE INVENTION

[0004] The present invention relates to wireless communication, in particular to wireless communication in which accurately sensed information is transmitted to a base station while the communication signals are simultaneously used for over-the-air computing.

[0005] NOTATION

[0006] The following notation is used throughout this specification. Real vectors and matrices are represented in bold small and bold capital letters, respectively, like in v and V, while their complex counterparts are represented bold italic small and bold italic capital letters, respectively, like in v and V. Vector norm and the absolute value of a scalar are respectively denoted by II -II and | • |. Transposition and conjugate transposition are represented as (-)Tand (-)H, respectively, while

[0007]

[0008] ℜ{·}, ℑ{·} and min(·) denote the real part, imaginary part, and minimum operators. Finally, 풞풩(μn, σn2) denotes the complex Gaussian distribution with mean μnand variance σn2.

[0009] BACKGROUND

[0010] Integrated sensing, communication and computing (ISCC) is a technique of performing sensing surrounding environments, data communication and computing of aggregated data that integrates three crucial techniques for future wireless system’s use cases. Conventionally, these three techniques combine radar and communication standards.

[0011] With the expanding adoption of Internet-of-things (loT) applications in smart homes and industrial settings, telemedicine, and autonomous driving, the coordination of the communication of distributed loT devices and the aggregation of their sensing data and other data become increasingly important, notably for satisfying stringent requirements such as low latency, low power consumption, efficient spectral usage, reliability, and scalability, which are mandated by certain applications and certain use cases. However, conventional massive machine type of communication (mMTC) for current 5G cellular loT only emphasizes the number of connections, but does not 202402518

[0012] -2-demand real-time, reliability and high-speed. Therefore, there is a need for beyond 5G (B5G) cellular loT networks with distinct service provisions.

[0013] In the era of loT, many devices are used for some kind of environment sensing. For instance, a large number of sensors for temperature measurements and cameras for video capture are widely deployed. Especially with the development of autonomous driving every car will be equipped with numerous sensors to sense its surroundings. As a result, there is a massive amount of sensing information that needs to be transferred from the loT devices to a base station (BS). However, it is not a trivial task to transfer large amounts of highly accurate sensing information over a limited radio spectrum. Specifically, the accuracy of sensing information is mainly determined by the number of quantization bits. Due to the limited radio spectrum, traditional orthogonal multiple access (OMA) schemes cannot support high-capacity transmission of a very large number of loT devices.

[0014] Stimulated by the demands of fast data aggregation for loT scenarios, B5G cellular loT is converting from a data-centric network to a computation-centric one. Advanced information processing technologies, such as artificial intelligence (Al) and data mining, will provide ubiquitous computing and intelligent services to effectively realize analysis and processing of massive data from loT devices, which means that B5G cellular loT may be more concerned about the computation results of the data, e.g., the sum, the maximum, the minimum and etc, rather than the individual data itself. For example, an loT-based humidity monitoring system may only be interested in the average of humidity in certain region, instead of collecting all observations from sensors. For realizing massive data computation from loT devices, the conventional approach of transmit-then-compute is no longer viable for B5G cellular loT due to the excessively high latency and the low spectrum efficiency.

[0015] Aiming to allow communication and computation tasks to be performed simultaneously, over-the-air-computation (AirComp) has emerged as a promising technique for data aggregation in loT systems as an alternative to the conventional sequential communication and processing, which also lays the ground for a paradigm shift towards distributed computing over wireless systems. 202402518

[0016] -3- Figure 1 shows a simplified diagram of an AirComp system. In the system K edge devices (EDs) are wirelessly connected to an access point (AP), also referred to herein as base station. The individual wireless signals interfere on their paths from the EDs to the AP, or BS, the interference being used for computation, as will be discussed hereafter.

[0017] The basic principle of AirComp is to exploit the waveform superposition property of a wireless channel to realize over-the-air aggregation of data simultaneously transmitted by devices. The simultaneous transmission by multiple synchronised devices and the analogue-wave superposition property of such multiple-access channel results in an adding of the simultaneously transmitted signals “over-the-air“. The added signals arrive at the receiver as a weighted sum, also referred to as the “aggregated signal”, with weights being the channel coefficients. AirComp relies on linear-analogue modulation and channel pre-compensation at each transmitter. The former modulates the data values into the magnitudes of the carrier signals; the latter compensates for heterogeneous channel fading of different links. As a result, each component part of received signal is the transmitted data scaled by a pre-determined factor. Setting the factor uniform for all signals, called magnitude alignment, reduces the aggregated signal to the desired average of transmitted distributed data, realizing an averaging function through AirComp.

[0018] With appropriate data pre- and post-processing the capability of AirComp can go beyond averaging to computing a class of so-called nomographic functions, which can generally be expressed as a post-processed summation of multiple pre-processed data-values. Typical functions in this class include arithmetic mean, weighted sum, geometric mean, polynomial, and Euclidean norm. For example, to compute the geometric mean, the pre-processing is a logarithm function and postprocessing an exponential function. It has been proven that any function can be decomposed as a summation form of nomographic functions, indicating that any function can be computed via AirComp in general.

[0019] Somewhat counterintuitive, the accuracy of computation enabled by AirComp can be improved as the number of simultaneous loT devices increases. Compared to the 202402518

[0020] -4-approach of transmit-then-compute, AirComp can significantly decrease the data aggregation latency by a factor equal to the number of loT devices.

[0021] Figure 2 shows an exemplary simplified block diagram of a conventional AirComp transmitter 500 and a conventional AirComp receiver 600. Transmitter 500 receives data to be transmitted at separation block 510, which separates data destined for over-the-air (OTA) computing and for communication and whose output signals are provided to pre-processing block 520, which processes the data for over-the-air computing, and to pre-processing block 540, which modulates the data for communication. The pre-processed and the modulated data is provided to respective precoding blocks 530 and 550, which precode the data for transmission over the wireless channel. The precoded signals are provided to combiner 560, which outputs the signals for transmission to the AirComp receiver 600, indicated by the dashed line.

[0022] Receiver 600 provides the received signal to a combining block 610 that is configured for over-the-air computing, and to a combining block 630 that is configured for communication. The combining blocks receive respective required combiner operating parameters from a design block (not shown in the figure).

[0023] Combining block 610, which performs the actual over-the-air computing and implements the target function, provides the output of the target function to processing block 620 for further processing. Combining block 630 reconstructs the transmitted data from the received signal and provides the data to further function blocks, e.g., interfaces and the like, represented by box 640. Note that the conventional functional blocks of a wireless transmitter and receiver, e.g., radio frequency (RF) circuits, oscillators, and the like, are omitted in the figure. It is noted that the transmitter may have one or more antennas, while the receiver has multiple antennas.

[0024] Referring back to figure 1, consider an uplink system composed of K EDs each equipped with M antennas and one AP equipped with N antennas. Under perfect synchronization among all EDs, the signal y ∈ ℂN×1received at the AP subject to fading and noise is given by 202402518

[0025] -5- K

[0026] y = HkXk+ n (1)

[0027]

[0028] k=l

[0029] where Hk∈ ℂN×Mdenotes the channel matrix between the fc-th ED and the AP, and each element follows ~ 풞풩(0,1). xk∈ ℂM×1denotes a transmit signal from fc-th ED, and n ∈ ℂN×1~ 풞풩(0,σ2IN) denotes the additive white Gaussian noise (AWGN) at the AP. For the integration of communication and computing, the transmit signal can be defined as,

[0030] xk= vd,kdk+ vs,ksk(2)

[0031] where vd,k, vs,k∈ ℂM×1are the fc-th ED's precoding vector for the communication signal and the computing signal, respectively. dkand skdenote fc-th ED's symbol for communication and computing, respectively.

[0032] Eventually, the communication and computing performance of an AirComp communication system is determined by the precoding at the transmitter and the combining at the receiver.

[0033] As mentioned before, the computing in an AirComp system is determined by a target function (s), given as f(s) = φ(∑Kk=1ψk(sk)) → ∑Kk=1sk(3)

[0034]

[0035] k=l / k=l

[0036] where s = [s1,...,sK] is the each ED's signal for computing. φ and ψkare function and variables for expressing a general nomographic function. Without loss of generality, the arithmetic sum operation can be used for the target function (s). In possession of the received signal y, an estimated target function is constructed at the AP via the combiner f̂(us, Vs; H | s) = usHy = usH(∑Kk=1Hkxk+ n) (4)

[0037]

[0038] k=l 202402518

[0039] -6-where Vs≜ [vs,1, ···, vs,K]Tis a matrix containing all precoding scalars vkemployed by the EDs and us∈ ℂN×1denotes the combiner vector applied by the AP.

[0040] From the above, the mean squared error (MSE) E between the target and reconstructed functions averaged over transmissions of multiple distinct symbol vectors s and under constant channel H, precoders vsand combiners us, can be concisely expressed as

[0041] ε(us, Vs; H) ≜ 피[|f - f̂|2] (5)

[0042] where ℋ ≜ [H1, ···, HK] ∈ ℂN×M×Kis the channel tensor from all EDs to the AP and the arguments of the functions f and f̂ are omitted for simplicity of notation.

[0043] The communication performance with regard to the symbols dkVk can be evaluated by the achievable sum rate 17, which is given as,

[0044] K

[0045] η = ∑Kk=1log2(1 + γk), (6)

[0046]

[0047] k=l

[0048] with

[0049] γk= |ud,kHHkvd,k|2 / (|Σk'≠kud,kHHk'vd,k'|2+ |ΣKk'=1ud,k'HHk'vs,k'|2+ σ2)

[0050]

[0051] Interference from computing signal

[0052] where ykdenotes a signal to interference-plus-noise ratio (SINR) for fc-th ED. ud,fcis the combiner vector for the k-th ED.

[0053] The simultaneous transmission in AirComp allows each device to access all radio resources instead of only a fraction of them, unlike the conventional orthogonal multiple access schemes, thereby enabling high spectrum efficiency. The most promising feature of AirComp for wireless data acquisition and other purposes, however, is that it enables the direct computation of nomographic functions by multiplexing multiple streams of data over the wireless multi-access channel. Thanks 202402518

[0054] -7-to the parallel processing, AirComp systems can achieve low-complexity and energy-efficient data aggregation all while reducing the computation latency in cellular loT. Yet, AirComp only addresses the issue of computation. As mentioned earlier, B5G cellular loT usually has multiple tasks in addition to communication, e.g., sensing and computation. In order to realize accurate sensing and computation, B5G cellular loT has to provide efficient communication for both the sensing signals and the computation signals from a massive number of devices with limited wireless resources.

[0055] Non-orthogonal multiple access (NOMA) is a promising contender in cellular loT to achieve high-speed transmission of larger amounts of data over a limited radio spectrum. Various methods of maximising the energy efficiency in uplink millimetre wave massive systems with NOMA are known, e.g., using appropriate power allocation. Moreover, grant-free NOMA schemes may be used for enhancing the performance of the uplink system with massive access. However, this still leaves the actual data aggregation and processing to some central unit that receives all data, and also still requires transmission of the messages carrying the data, whose size increases with the required precision.

[0056] NOMA leads to severe co-channel interference, especially in the scenario of massive loT. In fact, co-channel interference has different impacts on the performance of sensing and computation. Specifically, for sensing, the signal stream from each individual device should be separated from the superimposed received signal. Thus, co-channel interference reduces the quality of the sensing signal. For computation, multiple data streams from different devices are fused at the BS. Hence, co-channel interference can improve the accuracy of the computation. In other words, the harmful interference can be exploited to enhance the performance of the computation.

[0057] In order to mitigate the impact of co-channel interference on the sensing signal but enhance the impact of co-channel interference on the computation, transmit and receive beamformers are used for somewhat coordinating the interference. For example, in " Joint tx-rx beamforming design for multicarrier MIMO channels: A unified framework for convex optimization," IEEE Trans. Signal Process., vol. 51, no. 202402518

[0058] -8- 9, pp. 2381-2401, Sep. 2003, P. Palomar, J. M. Cioffi, and M. A. Lagunas, discuss beamforming for general MIMO communication systems. Especially in B5G cellular loT, BSs equipped with a large-scale antenna array provide ultra-high spatial degrees of freedom to mitigate co-channel interference through appropriate beamforming.

[0059] For AirComp, conventional beamformer (BF) designs adopt simple schemes, e.g., zero-forcing beamforming and uniform-forcing beamforming. However, due to the existence of co-channel interference between computation signals and communication signals, the conventional BF schemes cannot be applied to scenarios that integrate sensing, computation and communication (SCC) directly. Thus, new transmit and receive beamforming schemes for the integration of SCC in B5G cellular loT are required.

[0060] In " Integrated Sensing, Computation and Communication in B5G Cellular Internet of Things," IEEE Transactions on Wireless Communications, vol. 20, no. 1, pp. 332-344, Jan. 2021, doi: 10.1109 / TWC.2020.3024787, Q. Qi, X. Chen, C. Zhong and Z. Zhang propose a BF for a joint sensing, communication and computing (JSCC) system composed of multiple EDs and one BS that maximises the achievable sumrate under the constraint that the MSE of the computing function remains below the guaranteed MSE upper bound p. The underlying optimisation problem is formulated as

[0061] K

[0062] maximise η = ∑Kk=1log2(1 + γk), (8a)

[0063]

[0064] fc=l

[0065] subject to ε ≤ ρ (8b)

[0066] where Udand Vddenote the combiner and BF for the communication symbol. Since η and ε are not convex and defined by coupled optimisation variables of the BF, the above optimisation can be solved by convex approximation and iterative updating.

[0067] Even though the conventional beamformer design can - to some extent - mitigate the interference of communication and computing signal, the remaining interference is still considerable and limits the achievable data rate, which contradicts the prime purpose of a communication system. It is, therefore, desirable to obtain a system 202402518

[0068] -9-capable of JSCC that satisfies a guaranteed OTA computing accuracy while meeting a high data rate requirement imposed by the sensing objective.

[0069] SUMMARY OF THE INVENTION

[0070] This object is achieved by the methods of claims 1, 4 and 6, the wireless transmitter of claim 5, the wireless receiver of claim 7, and the wireless communication system of claim 8. A computer program product and a computer-readable medium are provided in claims 9 and 10, respectively. Embodiments and developments are described in respective dependent claims.

[0071] The present invention builds on the concept of successive interference cancellation (SIC) as found in in rate-splitting multiple access (RSMA) communication systems and applies this concept to OTA computing. More specifically, the OTA computing signal component is treated like the common part in RSMA communication, and the communication signal component is treated like the private part in RSMA.

[0072] The invention proposes, at the receiver side, to first combine the received signals for obtaining the OTA computing result, and subsequently eliminating the interference between the communication signal components and the OTA computing signal components from the received signals, yielding an interference-free communication signal component. To this end the present invention exemplarily proposes to apply a successive interference cancellation (SIC) process for eliminating the OTA computing signal components s from the received signal, leaving the interference-free communication signal components d. Then, the communication signal, or uplink signal, d is decoded from the then-available the interference-free communication signal components d.

[0073] Figure 3 shows an exemplary block diagram of a receiver 600 in accordance with the present invention. The received superimposed signals from all transmitters 500 (not shown in the figure) are input to a combining block 610 that is configured for over-the-air computing. The combining 610 block receives respective required combiner operating parameters from a design block (not shown in the figure), which may be implemented in the receiver 600 or part of a separate entity. Combining block 610, which performs the actual over-the-air computing and implements the target function, 202402518

[0074] -10-obtains the output of the target function in processing block 620, from which the computing output may be provided for further processing (not shown in the figure). The received superimposed signals from all transmitters 500 are also input, along with the computing output from block 620, to an interference cancellation block 625, which removes the interference in the received communication signal components caused by the computation signal components. The resulting interference-free communication signal components are provided to combining block 630 that is configured for communication. Like combining block 610 for computation, combining block 630 for communication receives respective required combiner operating parameters from a design block (not shown in the figure). The output obtained from combining the interference-free communication signal components is obtained in block 640, and may be provided to further function blocks. Note that the conventional functional blocks of a wireless transmitter and receiver, e.g., radio frequency (RF) circuits, oscillators, and the like, are omitted in the figure. It is noted that the transmitter may have one or more antennas, while the receiver has multiple antennas.

[0075] Based on this signal processing in the receiver a BF design for both, improved OTA computing with a guaranteed minimum accuracy and communication having the best achievable sum rate, is enabled, as will be discussed in the following.

[0076] Assuming perfect SIC the computing signal s can be eliminated from the received signal y as

[0077] ŷ = SIC(y, f̂(s)) (9a)

[0078]

[0079] K

[0080] = ∑Kk=1Hk· vd,kdk+ n. (9b)

[0081]

[0082] k=i

[0083] The corresponding SINR γ̂kis given as

[0084] Kk^d,fe|2

[0085] (10)

[0086]

[0087] ud,kHk'Vdlk' \2+ (T2 202402518

[0088] -11- Thanks to the SIC, the optimisation problem for the proposed BF design can be given as

[0089] K

[0090] maximise fj = ) log2(1 + yfc). (11a) uss,ud d4— i

[0091] / c=i

[0092] subject to ε ≤ ρ (11b)

[0093] As the above optimisation cannot be solved directly, the present invention suggests approximately solving it using an iterative method as summarised below and as exemplarily represented in the flow diagram of figure 4.

[0094] Inputs to the method 100 are the channel matrix HkG CNXMYk, i.e., from all transmitters to the receiver, and the termination criterion, e.g., a number of iterations or a targeted accuracy range. Outputs of the method are the precoder matrix Vsand the combiner vector usfor OTA computing and the corresponding precoder matrix Vdand the combiner matrix Udfor communication. After receiving the inputs in step 110, in accordance with the present invention initial precoder matrices Vsand Vdfor communication signal components and computing signal components, respectively, are computed in step 120. The initial matrices are then used as input to the subsequent iterative sub-process, represented in the dashed-line box 101.

[0095] In the iterative sub-process 101 the combiner vector usfor OTA computing and the combiner matrix Udfor communication are computed in steps 130 and 140, respectively, by appropriate closed-form update. The expression closed-form in this context refers to any suitable mathematical function or operation from a generally accepted set, including, in this case, solving the optimisation problem using a minimum mean squared error (MMSE) approach. Then, in step 150, for the optimisation of the beamformers, equation (11) is solved for Vsand Vdwith fixed values for usand Ud. The resulting precoder matrices Vsand Vdare used as input for a next iteration, “no”-branch of checking step 160, as long as the termination criterion is not met. If the termination criterion is met, “yes”-branch of checking step 160, the optimised precoder matrix Vsand the combiner vector usfor OTA computing and the corresponding precoder matrix Vdand the combiner matrix Udfor communication are output in step 180, e.g., for communicating to and use in the respective transmitters 500 / ED and the receiver 600 / AP in step 190. 202402518

[0096] -12-

[0097] The performance of the proposed method is shown hereafter in comparison to the conventional approach discussed in " Integrated Sensing, Computation and Communication in B5G Cellular Internet of Things" (full citation further above). As mentioned above, both methods target to maximise the achievable sum rate while preserving the best possible MSE for the computing objective. Thus, the performance of both methods can be compared in terms of the achievable sum rate under the same MSE constraint. Since the both methods solve the underlying optimisation problem with an iterative algorithm, the convergence behaviour of the achievable sum rate shows the improvement achieved in the proposed method by applying the SIC.

[0098] The convergence behaviour of the achievable sum rate over the number of iterations is illustrated in figure 5. Since the proposed method assumes a perfect SIC, it can eliminate interference from the computing signal and provides superior performance in the communication signal over the conventional method (SotA) used for comparison, as is readily apparent from the figure.

[0099] In light of the foregoing, in accordance with a first aspect of the invention a method of determining operating parameters of precoder stages of transmitters configured for over-the-air computing, and of combiner stages of a receiver configured for over-the-air computing, respectively, is presented. The method determines separate sets of operating parameters, Vs, us, for computation signals and Vd, Ud, for communication signals, respectively. The operating parameters

[0100]

[0101] Ud, Vdare determined in a way targeting to maximise the communication sum rate rj while maintaining an MSE E between a targeted OTA computing function and an OTA computing function reconstructed at the receiver below a predetermined upper bound p. The method comprises receiving channel matrices Hkfrom all transmitters to the receiver, a targeted upper bound p for the MSE E, and a termination criterion for a computing loop. The method further comprises computing, based on the respective channel matrix Hk, initial operating parameters of the precoder stages of the transmitters for the computation signals

[0102]

[0103] and the communication signals Vd, respectively. The initial operating parameters are computed under the condition that the maximum transmit power constraint of each transmitter be respected. 202402518

[0104] -13-

[0105] Next, an iteration loop is executed, in which iteration loop the sum rate η̂ for an assumed received signal ŷ that comprises superimposed signals from all transmitters from which the received computation signals are eliminated is maximised over the operating parameters

[0106]

[0107] Ud, Vdof the precoder and combiner stages, respectively, while maintaining the MSE E of the OTA computing function below the predetermined upper bound p.

[0108] The iteration loop comprises computing, based on the channel matrices Hkand the operating parameters Vsof the precoder stages of the transmitters for the computation signals as provided initially or from a previous iteration, operating parameters for the combiner stage usfor the computation signal, targeted to provide an MSE E between the targeted OTA computing function and the reconstructed OTA computing function below the received upper bound p. In a further step of the iteration loop the operating parameters the combiner stage Udfor the communication signals are computed based on the respective channel matrix Hk, the operating parameters of the precoder stages for the communication signals Vd, and assuming a received signal y that comprises superimposed communication signals from all transmitters and is free from interference with the computation signals from any transmitter. In yet another step of the iteration loop corresponding operating parameters of the precoder stages for the computation signals Vsand the communication signals Vdare determined for each transmitter. The determining step is based on the respective channel matrix Hkand the previously computed operating parameters for the combiner stages us, Udfor the computation signals and for the communication signals, respectively. The determining step is targeting to maintain an MSE E between the targeted OTA computing function and the reconstructed OTA computing function below the received upper bound p, while maximising the sum-rate fj of the assumed interference-free received signal that comprises superimposed communication signals from all transmitters.

[0109] The iteration loop is executed until the termination criterion is met, and the operating parameters us, Vs, Ud, Vdassociated with the maximised the sum rate η̂ are output. 202402518

[0110] -14- The termination criterion may comprise a predetermined number of iterations, a difference between the sum rates η̂ in subsequent iterations falling below a predetermined threshold, or the like. Combinations of termination criteria are likewise conceivable, e.g., a minimum number of iterations may be required before a difference-between-iteration results criterion can be applied.

[0111] The so-determined operating parameters are then provided to the corresponding transmitters and the receiver. As the channel matrices Hkmay change over time, determining the operating parameters may be repeated at predetermined intervals or whenever the sum rate η of the actual received signals drops by a predetermined value, e.g., over sum rates from previous transmissions or over an expected sum rate. In the latter case the repetition may be triggered by a communication rate supervision process, which may be implemented in the receiver.

[0112] In accordance with a second aspect of the invention a method of transmitting wireless signals for joint over-the-air computation and communication is presented. The method comprises receiving operating parameters for an OTA computing precoder stage and for a communication precoder stage, the operating parameters being determined through the method in accordance with the first aspect of the invention. The method further comprises receiving communication data and OTA computing data to be transmitted, or receiving combined communication and OTA computing data to be transmitted and separating the respective data components. The OTA computing data is then processed for implementing a targeted computing function, and the communication data is modulated in preparation for the transmission. Next, the processed OTA computing data is precoded using the received OTA computing precoding parameters, and the modulated communication data is precoded using the received communication precoding parameters. Prior to transmitting the precoded computing and communication data components are combined into a transmission signal, which is eventually provided to a transmission block, for wireless transmission thereof.

[0113] In accordance with a third aspect of the invention a transmitter configured for transmitting wireless signals for joint over-the-air computation and communication is presented. The transmitter comprises one or more microprocessors, volatile and non- 202402518

[0114] -15-volatile memory, and wireless interface circuitry configured for transmitting electromagnetic signals via one or more antennas. The various elements are communicatively connected via one or more data or signal lines or buses. The nonvolatile memory stores computer program instructions which, when executed by the microprocessor, configure the transmitter to execute the method in accordance with the second aspect of the invention as presented above.

[0115] In accordance with a fourth aspect of the invention a method of receiving wireless signals for joint over-the-air computation and communication is presented. The method comprises receiving operating parameters for an OTA computing combiner stage and for a communication combiner stage, the operating parameters being determined through the method in accordance with the first aspect of the invention. The method further comprises receiving, at a plurality of antennas, wireless signals comprising superimposed transmissions from a plurality of transmitters, each transmission carrying an OTA computing signal component and a communication signal component. Next, the received wireless signals are combined in the OTA computing combiner stage using the corresponding received operating parameters, thereby obtaining an OTA computing result. Once the OTA computing result is available, an interference cancellation is performed on the received signal, using the previously obtained OTA computing result, for removing the corresponding superimposed OTA computing signal component and yielding interference-free received signals representing the superimposed communication signal components of the superimposed transmissions. The interference cancellation may be performed jointly on the signals received at all antennas or individually for signals received at each antenna. The method then proceeds to combining the interference-free signals in the communication combiner stage, using the corresponding received operating parameters, for obtaining the respective communication signal components from the plurality of transmitters. The communication signals and the computing result can then be output for further processing, storing, or other purposes.

[0116] In accordance with a fifth aspect of the invention a receiver configured for receiving wireless signals joint over-the-air computation and communication is presented. The receiver comprises one or more microprocessors, volatile and non-volatile memory, and wireless interface circuitry configured for receiving electromagnetic signals via a 202402518

[0117] -16-plurality of antennas. The various elements are communicatively connected via one or more data or signal lines or buses. The non-volatile memory stores computer program instructions which, when executed by the microprocessor, configure the receiver to execute the method in accordance with the fourth aspect of the invention as presented above.

[0118] In accordance with a sixth aspect of the invention a wireless communication system configured for joint over-the-air computation and communication is presented. The system comprises two or more transmitters 500 in accordance with the third aspect of the invention and at least one receiver 600 in accordance with the fifth aspect of the invention.

[0119] In accordance with a further aspect of the invention a method of operating an apparatus configured for providing operating parameters to one or more transmitters 500 in accordance with the third aspect of the invention and / or a receiver 600 in accordance with the fifth aspect of the invention is provided. The apparatus may comprise one or more microprocessors, associated volatile and non-volatile memory, and one or more communication interfaces adapted for receiving channel matrices Hkfrom all transmitters 500 to the receiver 600, a targeted upper bound p for the MSE E, and a termination criterion for a computing loop. The method comprises determining operating parameters by executing the method 100 in accordance with the first aspect of the invention or receiving operating parameters determined through execution of said method, and transmitting the determined or received operating parameters to the transmitters 500 and / or the receiver 600.

[0120] As will be appreciated by one skilled in the art, aspects of the embodiments may be embodied as a system, apparatus, method, or program product. Accordingly, embodiments may take the form of an entirely hardware embodiment, an entirely software-implemented embodiment, including firmware, resident software, microcode, etc., or an embodiment combining software and hardware aspects.

[0121] For example, the disclosed embodiments may be implemented as a hardware circuit comprising custom very-large-scale integration (VLSI) circuits or gate arrays, off-the-shelf semiconductors such as logic chips, transistors, or other discrete components. 202402518

[0122] -17- The disclosed embodiments may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices, or the like. As another example, the disclosed embodiments may include one or more physical or logical blocks of executable code which may, for instance, be organised as an object, procedure, or function.

[0123] The method presented hereinbefore may be represented by computer program instructions. Accordingly, in accordance with a further aspect of the invention, a computer program product comprises computer program instructions which, when executed by a microprocessor of a computer, of a transmitter in accordance with the third aspect of the invention, or of a receiver in accordance with the fifth aspect of the invention, respectively, cause the microprocessor to execute the method in accordance with the first aspect, the second aspect, or the fourth aspect of the present invention, respectively, and to accordingly control hardware and / or software blocks or modules of the computer, the transmitter, or the receiver, respectively.

[0124] Computer program instructions, or code, for carrying out operations for embodiments may be any number of lines and may be written in any combination of one or more programming languages including an object- oriented programming language such as Python, Ruby, Java, Smalltalk, C++, or the like, and conventional procedural programming languages, such as the “C” programming language, or the like, and / or machine languages such as assembly languages. The code may execute entirely on the user’s computer, partly on the user’s computer, as a stand-alone software package, partly on the user’s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user’s computer through any type of network, including a local area network (LAN), wireless LAN (WLAN), or a wide area network (WAN), or the connection may be made to an external computer, for example, through the Internet using an Internet Service Provider (ISP).

[0125] The computer program instructions may be retrievably stored or transmitted on a computer-readable medium or data carrier. The medium or the data carrier may by tangibly or physically embodied, e.g., in the form of a hard disk, solid state disk, flash memory device or the like. However, the medium or the data carrier may also 202402518

[0126] -18-comprise a modulated electro-magnetic, electrical, or optical signal that is received by the computer by means of a corresponding receiver, and that is transferred to and stored in a memory of the computer.

[0127] The described features, structures, or characteristics of the embodiments may be combined in any suitable manner. In this description, numerous specific details are provided, such as examples of programming, software modules, user selections, network transactions, database queries, database structures, hardware modules, hardware circuits, hardware chips, etc., to provide a thorough understanding of embodiments. One skilled in the relevant art will recognize, however, that embodiments may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of an embodiment. Reference throughout this specification to “one embodiment,’’ “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment, but mean “one or more but not all embodiments” unless expressly specified otherwise. The terms “including,” “comprising,” “having,” and variations thereof mean “including but not limited to,” unless expressly specified otherwise. An enumerated listing of items does not imply that any or all of the items are mutually exclusive, unless expressly specified otherwise. The terms “a,” “an,” and “the” also refer to “one or more” unless expressly specified otherwise.

[0128] Where aspects of the embodiments are described in this specification with reference to schematic flowchart diagrams and / or schematic block diagrams of methods, apparatuses, systems, and program products according to embodiments it will be understood that each block of the schematic flowchart diagrams and / or schematic block diagrams, and combinations of blocks in the schematic flowchart diagrams and / or schematic block diagrams, can be implemented by code. This code may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that 202402518

[0129] -19-the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart diagrams and / or block diagrams.

[0130] It should be noted that, in some implementations or embodiments, the functions noted in the exemplary embodiments shown in the figures may occur out of the order shown in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. Other steps and methods may be conceived that are equivalent in function, logic, or effect to one or more blocks, or portions thereof, shown in the figures.

[0131] The present invention applies a concept previously linked to RSMA to the OTA computing and communication problem, by separating the data for computing and communication, treating each data component in accordance with its purpose, and merging the treated data components prior to transmission as one combined signal. This departs from conventional modulation and access schemes, effectively implementing a NOMA scheme that enhances the spectral efficiency for communication and reducing the latency for the OTA computing objective. It should be noted, however, that the novel way of determining beamformers can be used in any JSCC system that has a high data rate requirement and needs a guaranteed computing performance.

[0132] The present invention can be used in various contexts, including massive loT sensor arrangements, indoor location, connected vehicles communicating with each other and with stationary road side units, and the like.

[0133] BRIEF DESCRIPTION OF THE DRAWING

[0134] In the following section the invention will be described with reference to the drawings, in which

[0135] Fig. 1 shows a simplified diagram of an AirComp system,

[0136] Fig. 2 shows an exemplary simplified block diagram of a conventional AirComp transmitter and AirComp receiver, 202402518

[0137] -20- Fig. 3 shows an exemplary block diagram of an AirComp receiver in accordance with the present invention,

[0138] Fig. 4 shows a schematic flow diagram of the method of determining operating parameters of precoder stages of transmitters configured for over-the-air computing, and of combiner stages of a receiver configured for over-the-air computing, respectively, in accordance with the invention,

[0139] Fig. 5 shows the convergence behaviour of the achievable sum rate over the number of iterations,

[0140] Fig. 6 shows an exemplary flow diagram of a method of transmitting wireless signals for joint over-the-air computation and communication in accordance with the second aspect of the invention,

[0141] Fig. 7 shows an exemplary flow diagram of a method of receiving wireless signals for joint over-the-air computation and communication in accordance with the fourth aspect of the invention, and

[0142] Fig. 8 shows an exemplary block diagram of a transmitter or a receiver, respectively, in accordance with the third or fifth aspects of the present invention, respectively.

[0143] In the figures identical or similar elements may be referenced using the same reference designators.

[0144] DETAILED DESCRIPTION OF EMBODIMENTS

[0145] Figures 1 to 5 have been described further above and will not be discussed again.

[0146] Figure 6 shows an exemplary flow diagram of a method 200 of transmitting wireless signals for joint over-the-air computation and communication in accordance with the second aspect of the invention. In step 210 operating parameters for an OTA computing precoder stage and a communication precoder stage determined using the method in accordance with the first aspect of the invention are received. In step 220 communication data and OTA computing data to be transmitted are received. Alternatively, as indicated by the dashed arrows, in step 220a, combined communication and OTA computing data to be transmitted are received, and the respective data components are separated in step 220b. Next, in step 230, the OTA computing data is processed for implementing a targeted computing function, and in 202402518

[0147] -21-step 240 the processed OTA computing data is precoded using the received OTA computing precoding parameters. In step 250 the communication data is modulated, and in step 260 the modulated communication data is precoded using the received communication precoding parameters. Note that while steps 230, 240 and 260, 260 are shown as sequential in the figure, only steps 230 and 240, as well as steps 250 and 260 must be executed sequentially. The respective two-step sequences 230, 240 and 250, 260 may be executed in reverse order or in parallel. In step 270 the precoded data components are combined into a transmission signal, and in step 280 the transmission signal is provided to a transmission block of a transmitter 500 executing the method, for wireless transmission.

[0148] Figure 7 shows an exemplary flow diagram of a method 300 of receiving wireless signals for joint over-the-air computation and communication in accordance with the fourth aspect of the invention. In step 310 operating parameters for an OTA computing combiner stage and a communication combiner stage determined using the method in accordance with the first aspect of the invention are received. In step 320 wireless signals y comprising superimposed transmissions are received from a plurality of transmitters 500, at a plurality of antennas 502. Each transmission carries an OTA computing signal component and a communication signal component. In step 330 the received wireless signals y are combined in the OTA computing combiner stage using the corresponding received operating parameters, thereby obtaining, in step 340, an OTA computing result. In step 350 an interference cancellation is performed on the received signal y of each antenna, using the previously obtained OTA computing result, for removing the corresponding superimposed OTA computing signal component and yielding interference-free received signals y representing the superimposed communication signal components of the superimposed transmissions. In step 360, the interference-free signals y are combined in the communication combiner stage, for obtaining the respective communication signal components from the plurality of transmitters 500. The OTA computing result and the obtained communication signals may be output in step 370.

[0149] Figure 8 shows an exemplary block diagram of a transmitter 500 or a receiver 600, respectively, configured for carrying out methods in accordance with the present invention. While the transmitter 500 comprises at least one antenna 502, the receiver 202402518

[0150] -22- 600 comprises two or more antennas 502. Both apparatus further comprise circuitry 504 for processing radio frequency signals, one or more microprocessors 506, volatile memory 508 and non-volatile memory 510. Both apparatus may comprise one or more further communication interfaces 512. The aforementioned components or elements are connected via one or more data and / or signal lines or buses 514. The non-volatile memory 510 stores computer program instructions which, when executed by the one or more microprocessors 506, configure components of the transmitter 500 to implement or carry out a method in accordance with the third aspect of the invention, or configure components of the receiver 600 to implement or carry out a method in accordance with the fifth aspect of the invention, respectively. 202402518

[0151] -23- LIST OF REFERENCE NUMERALS (PART OF THE DESCRIPTION)

[0152] 100 method 310 receive operating parameters 101 iterative loop 320 receive wireless signals 110 receive input 330 combine received signals for 120 compute initial operating computing

[0153] parameters 340 obtain computing result 130 compute combiner operation 350 perform interference parameters cancellation

[0154] 140 compute precoder operation 360 combine interference-free parameters signals

[0155] 150 determine maximised operation 370 output results parameters

[0156] 160 termination criterion met? 500 transmitter

[0157] 180 output operating parameters 502 antenna

[0158] 190 transmit operating parameters 504 RF circuitry

[0159] 506 microprocessor

[0160] 200 method 508 volatile memory

[0161] 210 receive operating parameters 510 non-volatile memory 220 receive data 512 communication interface 230 process OTA computing data 514 data / signal line / bus

[0162] 240 precode OTA computing data

[0163] 250 modulate communication data 600 receiver

[0164] 260 precode communication data

[0165] 270 combine precoded data AP receiver

[0166] 280 provide transmission signal ED transmitter

[0167] 300 method

Claims

202402518-24- CLAIMS1. Method (100) of determining operating parameters (Vs, Vd; us, Ud) of precoder stages of transmitters (500) configured for over-the-air computing, and of combiner stages of a receiver (600) configured for over-the-air (OTA) computing, respectively, separate sets of operating parameters being determined for computation signals (Vs,us) and communication signals (Vd, Ud), respectively, the operating parameters (us, Vs, Ud, Vd) being targeted to maximise the communication sum rate (η) while maintaining a mean square error (MSE; E) between a targeted OTA computing function and a reconstructed OTA computing function below a predetermined upper bound (p), the method comprising:i) receiving (110) or determining channel matrices (Hk) from all transmitters (500) to the receiver (600), a targeted upper bound (p) for the MSE (ε), and a termination criterion for a computing loop,ii) computing (120), based on the respective channel matrix (Hk), for each transmitter (500), initial operating parameters of the precoder stages for the computation signals (Vs) and the communication signals (Vd), respectively, the initial operating parameters respecting the maximum transmit power constraint of each transmitter,iii) executing an iteration loop (101) until the termination criterion is met, the iteration loop comprising:a) computing (130), based on the channel matrices (Hk) and the operating parameters (Vs) of the precoder stages of the transmitters (500) for the computation signals as provided initially or from a previous iteration, operating parameters for the combiner stage (us) for the computation signal, targeted to provide an MSE (E) between the targeted OTA computing function and the reconstructed OTA computing function below the received upper bound (p),b) computing (140), based on the channel matrices (Hk), the operating parameters of the precoder stages for the communication signals (Vd), and assuming a received signal (y) that comprises superimposed communication signals from all transmitters (500) while being free from interference with the computation signals from any transmitter (500),202402518-25- operating parameters for the combiner stage (Ud) for the communication signals,c) determining (150) for each transmitter (500), based on the respective channel matrix (Hk) and the previously computed operating parameters for the combiner stages (us, Ud) for the computation signals and for the communication signals, respectively, corresponding operating parameters of the precoder stages for the computation signals (Vs) and the communication signals (Vd), targeted, together with the previously computed operating parameters for the combiner stages (us, Ud) for the computation signals and for the communication signals, to maintain an MSE (ε) between the targeted OTA computing function and the reconstructed OTA computing function below the received upper bound (p), while maximising the sum-rate (η̂) of the assumed interference-free received signal (y) that comprises superimposed communication signals from all transmitters (500),d) repeating (160) the iteration if the termination criterion is not met or terminating the iteration otherwise, and- outputting (180) the operating parameters (Vs, Vd; us; Ud) associated with the maximised sum rate (η̂)..

2. The method of claim 1, wherein computing (130) operating parameters for the combiner stage (us) for the computation signal and for the combiner stage (Ud) for the communication signal comprises invoking / executing a convex optimisation and solving process, including but not limited to a minimum mean squared error (MMSE) solving process.

3. The method of claim 1 or 2, wherein determining (140) operating parameters (Vs, Vd) for the computation and communication precoder stages, respectively, comprises an eigenvalue decomposition and / or a matrix inversion.

4. A method (200) of transmitting wireless signals for joint over-the-air computation and communication, comprising:- receiving (210) operating parameters for an OTA computing precoder stage and a communication precoder stage determined in accordance with the202402518-26- method of one or more of claims 1 to 3,- receiving (220) communication data and OTA computing data to be transmitted, or receiving combined communication and OTA computing data to be transmitted and separating the respective data components,- processing (230) the OTA computing data for implementing a targeted computing function,- precoding (240) the processed OTA computing data using the received OTA computing precoding parameters,- modulating (250) the communication data,- precoding (260) the modulated communication data using the received communication precoding parameters,- combining (270) the precoded data components into a transmission signal, and- providing (280) the transmission signal to a transmission block () of a transmitter executing the method, for wireless transmission.

5. A transmitter (500) configured for transmitting wireless signals for joint over- the-air computation and communication, comprising one or more microprocessors (350), volatile (352) and non-volatile (354) memory, wireless interface circuitry (356) configured for transmitting electromagnetic signals via one or more antennas (306), wherein the non-volatile memory (354) stores computer program instructions which, when executed by the one or more microprocessor (352), configure the transmitter (500) to execute the method of claim 4.

6. A method (300) of receiving wireless signals for joint over-the-air computation and communication, comprising:- receiving (310) operating parameters for an OTA computing combiner stage and a communication combiner stage determined in accordance with the method of one or more of claims 1 to 3,- receiving (320), at a plurality of antennas (502) wireless signals (y) comprising superimposed transmissions from a plurality of transmitters (500), each transmission carrying an OTA computing signal component and a communication signal component,202402518-27- - combining (330) the received wireless signals (y) in the OTA computing combiner stage using the corresponding received operating parameters, thereby obtaining (340) an OTA computing result,- performing (350) an interference cancellation on the received signal (y), using the previously obtained OTA computing result, for removing the corresponding superimposed OTA signal component and yielding interference-free received signals (y) representing the superimposed communication signal components of the superimposed transmissions, - combining (360) the interference-free signals (y) in the communication combiner stage for obtaining the respective communication signal components from the plurality of transmitters (500).

7. A receiver (600) configured for receiving wireless signals for over-the-air computation and communication, comprising one or more microprocessors (350), volatile (352) and non-volatile (354) memory, wireless interface circuitry (356) configured for receiving electromagnetic signals via a plurality of antennas (306), wherein the non-volatile memory (354) stores computer program instructions which, when executed by the one or more microprocessor (352), configure the transmitter (500) to execute the method of claim 6.

8. Wireless communication system configured for joint over-the-air computation and communication, comprising two or more transmitters (500) in accordance with claim 5 and at least one receiver (600) in accordance with claim 7.

9. Computer program product comprising computer program instructions which, when executed by a microprocessor (506) of a computer, of a transmitter (500) in accordance with claim 5, or of a receiver (600) in accordance with claim 7, respectively, cause the microprocessor (506) to execute the method (100, 200, 300) in accordance with claim 1, claim 4, or claim 6, respectively, and to accordingly control hardware and / or software blocks or modules of the computer, the transmitter (500), or the receiver (600), respectively.202402518-28- 10. Computer readable medium or data carrier retrievably transmitting or storing the computer program product of claim 9.

Images