Delay-doppler based channel estimation method and apparatus

Abstract

Embodiments of the present invention provides a delay-Doppler based channel estimation method and apparatus for OFDM systems. Embodiments may include determining a time-frequency response of the channel based on pilot symbols contained in a received signal, dividing the time-frequency response of the channel into time segments, determining a first delay-Doppler coordinate pair based on the time-frequency response of the channel, estimating, for each time segment, a first coefficient, based on the time-frequency response of the channel of the respective time segments and the first delay-Doppler coordinate pair. Embodiments may also include generating a time-frequency response based on the first coefficient and updating the time-frequency response by subtracting the time-frequency response of the channel with the time-frequency response for the first delay-Doppler coordinate pair, where a second delay-Doppler coordinate pair is determined based on the updated time-frequency response of the channel.

Description

DELAY-DOPPLER BASED CHANNEL ESTIMATION METHOD AND APPARATUS CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to Australian Provisional Patent Application No. 2024900503 filed February 28, 2024, titled “DELAY-DOPPLER BASED CHANNEL ESTIMATION METHOD AND APPARATUS” which is hereby incorporated by reference in its entirety. TECHNICAL FIELD

[0002] The present invention relates to channel estimation method and apparatus. In particular, the present invention relates to delay-Doppler based channel estimation method and apparatus for OFDM systems. However, while some embodiments will be described herein with particular to that application, it will be appreciated that the invention is not limited to such a field of use, and is applicable in broader contexts. BACKGROUND

[0003] Communication is the process of conveying information from a transmitter to a receiver through a channel. The transmitter generates a signal containing the information to be sent. The signal propagates to the receiver, incurring various types of distortions caused by what is called the channel (e.g., liquid, cable, air, etc.). Common distortions include channel fading, time dispersion due to delay, frequency dispersion due to Doppler, carrier frequency offset, symbol timing offset, and additive noise. The receiver observes the distorted signal and attempts to recover the transmitted information using pilot symbols within the transmitted signal that are known at both the transmitter and receiver.

[0004] Fourth-generation (4G) and fifth-generation (5G) cellular networks use Orthogonal Frequency Division Multiplexing (OFDM) techniques to achieve high data rates in frequency selective channels. In OFDM, a channel is divided into multiple sub-channels or subcarriers, and each subcarrier is transmitted in parallel.

[0005] Fig.1 shows an OFDM communication system 100. The communication system 100 has a transmitter 110, a channel 130, and a receiver 120. 43240768_1:CHP

[0006] The transmitter 110 comprises a source 112, a source encoder 114, a channel encoder 116, and a OFDM modulator 118. In some implementations, the source 112 comprises a digital sampler for sampling digital or analog data and generating corresponding sampled data. Thesampled data generated by the source 112 is in the form of a binary sequence ^b^n^^ ൌb^0^, b^1^, … ….. The binary sequence ^b^n^^ is then provided to the source encoder 114.

[0007] The source encoder 114 transforms the received binary sequence^^^^^^^^into aninformation sequence^^^^^^^^. In some implementations, the transformation compresses thebinary sequence^^^^^^^^while reducing possible information loss. The information sequence^^^^^^^^is then provided to the channel encoder 116.

[0008] The channel encoder 116 is also known as the error control coding block. The channelencoder 116 adds redundancy to the information sequence^^^^^^^^to produce a coded sequence^^^^^^^^. The coded sequence^^^^^^^^provides resilience to channel distortion and increases thechance of successfully recovering any lost information at the receiver 120. The informationsequence^^^^^^^^is typically divided into blocks of size ^^ bits. The channel encoder 116 adds ^^redundancy bits to each block, resulting in each coded block having ^^ bits where ^^ ൌ ^^ ^ ^^and the coding rate is ^ ^. The addition of redundancy bits enables errors to be detected and corrected at the receiver 120 so that the receiver 120 can either discard the data in error or request a retransmission. The coded sequence ^^^^^^^^ is provided to the OFDM modulator 118.

[0009] The OFDM modulator 118 receives and converts the coded sequence ^^^^^^^^ into OFDM symbols for transmission over the subcarriers of the channel 130.

[0010] Figure 2 shows a block diagram of the OFDM modulator 118. The OFDM modulator 118 comprises a serial to parallel (S / P) converter 210, a subcarrier mapper 211, a pilot insertion module 212, an inverse discrete Fourier Transformer (IDFT) 214, a parallel to serial (P / S) converter 216, a cyclic prefix (CP) insertion module 218, and a transmitter filter 220. TheS / P converter 210 converts the serial coded sequence^^^^^^^^received from the channel encoder116 into parallel data streams. The subcarrier mapper 211 receives the parallel data streams from the S / P converter 210 and maps the parallel data streams onto subcarriers based on the modulation scheme selected, creating OFDM symbols that are complex values each representing a modulated subcarrier. The modulation scheme can be N-Quadrature Amplitude Modulation (N-QAM) such as 16-QAM, 64-QAM, 256-QAM, etc., N-Phase Shift Keying (N-PSK) such as 43240768_1:CHP8-PSK, 16-PSK, etc., or the like. The OFDM symbols are then provided to the pilot insertion module 212. The pilot insertion module 212 inserts one or more pilot symbols at regular intervals within the OFDM symbols. The pilot symbols carry information known to both the transmitter 110 and receiver 120 that is used for channel estimation at the receiver 120. The OFDM symbols including the pilot symbols are then provided to the IDFT 214. The IDFT 214 performs IDFT on the OFDM symbols, converting the frequency domain signals to time domain. The time domain OFDM symbols are provided to the P / S converter 216, which in turn converts the parallel time domain OFDM symbols to a serial sequence of time domain OFDM symbols^^^^^^^^. The serial sequence of OFDM symbols is then provided to the CP insertion module 218which adds a cyclic prefix to each OFDM symbol to maintain signal periodicity, preventing inter-symbol interference (ISI). Assuming that the OFDM symbol has a duration of ^^ and the CP has a duration of ^^^^, the addition of the CP to each OFDM symbol extends the duration of theOFDM symbol from ^^ to ^^ᇱ, where ^^ᇱ ൌ ^^ ^ ^^^^. The sequence of symbols is then passedthrough the transmitter filter 220 which confines the signal within the desired bandwidth. The transmitter filter 220 comprises, for example, a prototype filter or pulse shaping filter, such as a root raised cosine filter.

[0010] The filtered OFDM symbols^^^^^^^^is then converted into analog signal ^^^^^^by a digitalto analog converter (not shown) for transmission over the channel 130.

[0011] Referring back to Fig.1, the analog signal ^^^^^^travels to the receiver 120 via the channel 130. The channel 130 may be air, a wire, water, and the like. The channel 130 introduces losses to the analog signal ^^^^^^ due to reflection, diffraction, scattering, and / or multipath propagation.

[0012] The analog signal ^^^^^^is the analog signal ^^^^^^that has travelled through the channel130. The receiver 120 receives the analog signal ^^^^^^.

[0013] The receiver 120 comprises an OFDM demodulator 122, a channel decoder 124, a source decoder 126, and a sink 128.

[0014] Fig.3 is a block diagram of the OFDM demodulator 122. The OFDM demodulator 122 includes a CP remover 310, a S / P converter 312, a matched filter 314, a discrete Fourier transformer (DFT) 316, and a P / S converter 318. The OFDM demodulator 122 receives the analog signal y^t^ and converts the signal from analog to digital symbols by using an analog to 43240768_1:CHPdigital converter (not shown). The digital symbols are then matched filtered by the matched filter 314. The matched filter 314 applies the same filtering at the receiver 120 as the transmitter 120 for increasing the signal to noise ratio (SNR). For instance, if the transmitter filter 220 at the transmitter 110 is a root raised cosine filter, the matched filter 314 should also be a root raised cosine filter. The matched filtered symbols are then output to the CP remover 310. The CP remover 310 removes the cyclic prefix of the matched filtered symbols and provides the symbols to the S / P converter 312. The S / P converter 312 converts the symbols (with the cyclic prefix removed) to parallel data streams. The output of the S / P converter 312 is sampled and provided to the DFT 316. The DFT 316 performs discrete Fourier transform on the data streams andoutputs complex valued symbols ^^^^^, ^^^ each representing the amplitude and phase of thereceived signal at the respective symbol and subcarrier indices.

[0015] The OFDM demodulator 122 uses output of the DFT 316 to infer the transmitted symbols ^^^^^^^^. The inference process may include symbol and frame detection, channel estimation, frequency offset correction, data detection, or other advanced algorithms to combat the effect ofchannel distortions. After performing a sequence of sophisticated algorithms, the estimate^^^^^^^^^is then converted from parallel to a serial sequence by the P / S converter 318. The serial sequenceis then de-mapped into bit sequences^^̂^^^^^^, which are used to perform a best guess of thetransmitted bits, or to provide tentative decisions as the input to the channel decoder 124.

[0016] Referring back to Fig.1, the channel decoder 124 receives and processes the bit sequences ^^̂^^^^^^ to detect the existence of any error and produces the best possible guess of the information sequence ^^^^̂^^^^. The channel decoder 124 performs error detection by using the ^^ redundancy bits (see the discussion above relating to the channel encoder 116) and a decoding algorithm to remove errors (due to noise and distortion introduced in the channel 130). Theinformation sequence^^^^̂^^^^is then provided to the source decoder 126. In an iterative receiver,the output of the channel decoder 124 is fed back to the demodulator 122 to further improve the accuracy of demodulator output.

[0017] The source decoder 126 processes the information sequence ^^^̂^^^^^ to generate binary data ^^^^^^^^^. If no further error exists, then the binary data is equated with the binary sequence(i.e., ^^^^^^^^^ ൌ ^^^^^^^^). The transmission is then complete. However, if the error cannot becorrected, a retransmission may be required. The binary sequence ^^^^^^^^^ is then provided to the 43240768_1:CHPsink 128. The sink 128 is a device such as a computer to display a video, for example, if the binary sequence ^^^^^^^^ relates to a video.

[0018] Using orthogonal subcarriers, OFDM provides high spectral efficiency with simple channel estimation and equalisation. For low-mobility or fixed point-to-point communication systems, channel variation during the transmission period is relatively insignificant, allowing standard interpolation-based channel estimation methods to be used. However, in high-mobility scenarios, Doppler spreading can disadvantageously result in a rapidly varying channel which cannot be accurately characterised using standard interpolation-based techniques.

[0019] Delay-Doppler channel estimation schemes are known to advantageously address high- mobility environments. In such schemes, the channel response in time-frequency domain is transformed onto delay-Doppler domain typically implemented as a delay-Doppler coordinate system formed of a delay axis and a Doppler axis. The delay axis represents the time difference between the reception of the first multipath component and the subsequent path components. The Doppler axis represents the Doppler frequency shift observed in the received signal due to the relative motion between the transmitter and receiver. Each point in the delay-Doppler coordinate system represents the channel response at a specific delay and Doppler shift. The delay-Doppler coordinate system is typically implemented as a delay-Doppler grid by quantizing the delay axis and the Doppler axis into discrete bins.

[0020] In wireless communications, signals travel through the air may encounter various paths due to reflections and scattering. Each path may introduce a different delay and Doppler shift to a signal travelling therethrough. Accordingly, the channel response of a multi-path channel often exhibits as a sequence of discrete components, referred to as “taps,” in a delay-Doppler grid. Each tap corresponds to a particular pair of delay-Doppler coordinates (“delay-Doppler coordinate pair”) associated with a path or a multipath component in the channel. The delay- Doppler coordinate pair of a tap is indicative of the delay and Doppler shift experienced by the signal travelling through the corresponding path. Due to the limited resolution of the Doppler grid, subject to the acquisition time of the system, the actual Doppler frequency shift of the received signal may not fall exactly on one of the discrete Doppler bins. A component that does not fall exactly on a discrete Doppler bin is referred to as an “off-grid” or fractional component. The fractional Doppler components undesirably spread in the Doppler domain, i.e., distributed over more than one Doppler bin, causing interference between paths with different Doppler 43240768_1:CHPcoordinates, known as inter-Doppler-interference (IDI), in the channel model constructed based on the channel response. Some delay-Doppler channel estimation schemes are able to identify off-grid components. However, those schemes are complex and computationally intensive.

[0021] Some estimation schemes use all “on-grid” or “integer” taps to represent each path to mitigate Doppler spreading. However, such schemes are at the expense of degrading the sparsity of the channel model which is a significant factor in the design of delay-Doppler-based communication schemes.

[0022] The term “response” is used interchangeably with the term “transfer function” in some portions of the present disclosure. The term “tap” is used interchangeably with the term “component” in some portions of the present disclosure. The term “on-grid” is used interchangeably with the term “integer” in some portions of the present disclosure. The term “off-grid” is used interchangeably with the term “fractional” in some portions of the present disclosure.

[0023] The reference in this specification to any prior publication (or information derived from it), or to any matter which is known, is not, and should not be taken as, an acknowledgement or admission or any form of suggestion that that prior publication (or information derived from it) or known matter forms part of the common general knowledge in the field of endeavour to which this specification relates. SUMMARY

[0024] It is an object of the present invention to substantially overcome or at least ameliorate one or more of the above disadvantages.

[0025] Disclosed are techniques for estimating channel parameters of a channel for OFDM systems.

[0026] Some aspects of the disclosed techniques are directed to delay-Doppler based channel estimation methods that can be performed by a channel estimator of an OFDM demodulator of a receiver configured to receive signals from a transmitter in communication with the receiver via a channel. The signals contain pilot symbols that are known at both the transmitter and the receiver. 43240768_1:CHP

[0027] In one aspect of the present disclosure, there is provided a method of estimating channel parameters of a channel, the method comprising: determining a time-frequency response of the channel based on pilot symbols contained in a received signal; dividing the time-frequency response of the channel into time segments; determining a first delay-Doppler coordinate pair based on the time-frequency response of the channel; estimating, for each time segment, a first coefficient, based on the time-frequency response of the channel of the respective time segments and the first delay-Doppler coordinate pair; generating a time-frequency response for the first delay-Doppler coordinate pair based on the first coefficient; updating the time-frequency response of the channel by subtracting the time-frequency response of the channel with the time- frequency response for the first delay-Doppler coordinate pair; determining a second delay- Doppler coordinate pair based on the updated time-frequency response of the channel; estimating, for each time segment, a second coefficient, based on the time-frequency response of the channel of the respective time segments and the first and second delay-Doppler coordinate pairs; and generating an estimate of the time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs and the first and second coefficients.

[0028] In one or more examples, the generating an estimate of the time-frequency response of the channel comprises: generating a joint time-frequency response for each time segment based on the first and second delay-Doppler coordinate pairs and the first and second coefficients of each time segment; and concatenating the joint time-frequency response of each time segment.

[0029] In one or more examples, the first delay-Doppler coordinate pair comprises a) delay- Doppler coordinate pair of a first component of the time-frequency response of the channel and delay-Doppler coordinate pair of a second component of the time-frequency response of the channel, wherein the first component is the largest component of the time-frequency response of the channel with an integer Doppler coordinate and the second component is the largest neighbouring component of the first component with an integer Doppler coordinate, or b) delay- Doppler coordinate pair of the largest component of the time-frequency response of the channel.

[0030] In one or more examples, the second delay-Doppler coordinate pair comprises a) delay- Doppler coordinate pair of a first component of the updated time-frequency response of the channel and delay-Doppler coordinate pair of a second component of the time-frequency response of the channel, wherein the first component is the largest component of the updated time-frequency response of the channel with an integer Doppler coordinate and the second 43240768_1:CHPcomponent is the largest neighbouring component of the first component with an integer Doppler, and b) delay-Doppler coordinate pair of the largest component of the updated time-frequency response of the channel with an integer Doppler coordinate.

[0031] In one or more examples, estimating the first coefficient comprises: constructing, for each time segment, a first estimated time-frequency response of the channel based on the first delay-Doppler coordinate pair; and applying a first phase shift approximation to the first estimated time-frequency response of the channel of each time segment, the first phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time-frequency response of the channel of said time segment and the first estimated time- frequency response of the channel of said time segment.

[0032] In one or more examples, estimating the second coefficient comprises: constructing, for each time segment, a second estimated time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs; applying a second phase shift approximation to the second estimated time-frequency response of the channel of each time segment, the second phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time-frequency response of the channel of said time segment and the second estimated time-frequency response of the channel of said time segment; and updating the first coefficient.

[0033] In one or more examples, the coefficients are estimated using least squares regression.

[0034] In one or more examples, the first or second delay-Doppler coordinate pair is determined using a symplectic finite fourier transform.

[0035] In one or more examples, the first or second delay-Doppler coordinate pair is determined using a Direction of Arrival method.

[0036] The method of claim 10, wherein the Direction of Arrival method is Multiple Signal Classification (MUSIC) algorithm.

[0037] In one aspect of the present disclosure, there is provided a communication apparatus comprising an Orthogonal Frequency Division Multiplexing (OFDM) demodulator, the OFDM demodulator configured to perform operations comprising: determining a time-frequency 43240768_1:CHPresponse of the channel based on pilot symbols contained in a received signal; dividing the time- frequency response of the channel into time segments; determining a first delay-Doppler coordinate pair based on the time-frequency response of the channel; estimating, for each time segment, a first coefficient, based on the time-frequency response of the channel of the respective time segments and the first delay-Doppler coordinate pair; generating a time- frequency response for the first delay-Doppler coordinate pair based on the first coefficient; updating the time-frequency response of the channel by subtracting the time-frequency response of the channel with the time-frequency response for the first delay-Doppler coordinate pair; determining a second delay-Doppler coordinate pair based on the updated time-frequency response of the channel; estimating, for each time segment, a second coefficient, based on the time-frequency response of the channel of the respective time segments and the first and second delay-Doppler coordinate pairs; and generating an estimate of the time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs and the first and second coefficients.

[0038] In one or more examples, the OFDM demodulator is configured to: generate a joint time- frequency path response for each time segment based on the first and second delay-Doppler coordinate pairs and the first and second coefficients of each time segment; and concatenate the joint time-frequency path response of each time segment.

[0039] In one or more examples, the first delay-Doppler coordinate pair comprises a) delay- Doppler coordinate pair of a first component of the time-frequency response of the channel and delay-Doppler coordinate pair of a second component of the time-frequency response of the channel, wherein the first component is the largest component of the time-frequency response of the channel with an integer Doppler coordinate and the second component is the largest neighbouring component of the first component with an integer Doppler coordinate, or b) delay- Doppler coordinate pair of the largest component of the time-frequency response of the channel.

[0040] In one or more examples, the second delay-Doppler coordinate pair comprises a) delay- Doppler coordinate pair of a first component of the updated time-frequency response of the channel and delay-Doppler coordinate pair of a second component of the time-frequency response of the channel, wherein the first component is the largest component of the updated time-frequency response of the channel with an integer Doppler coordinate and the second component is the largest neighbouring component of the first component with an integer Doppler, 43240768_1:CHPand b) delay-Doppler coordinate pair of the largest component of the updated time-frequency response of the channel with an integer Doppler coordinate.

[0041] In one or more examples, the OFDM demodulator is configured to: construct, for each time segment, a first estimated time-frequency response of the channel based on the first delay- Doppler coordinate pair; and apply a first phase shift approximation to the first estimated time- frequency response of the channel of each time segment, the first phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time- frequency response of the channel of said time segment and the first estimated time-frequency response of the channel of said time segment.

[0042] In one or more examples, the OFDM demodulator is configured to: construct, for each time segment, a second estimated time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs; and apply a second phase shift approximation to the second estimated time-frequency response of the channel of each time segment, the second phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time-frequency response of the channel of said time segment and the second estimated time-frequency response of the channel of said time segment; wherein the estimating of the second coefficient updates the first coefficient.

[0043] In one or more examples, the coefficients are estimated using least squares regression.

[0044] In one or more examples, the first or second delay-Doppler coordinate pair is determined using a symplectic finite fourier transform.

[0045] In one or more examples, the first or second delay-Doppler coordinate pair is determined using a Direction of Arrival method.

[0046] In one or more examples, the Direction of Arrival method is Multiple Signal Classification (MUSIC) algorithm.

[0047] In some implementations, the disclosed methods comprise determining one or more further delay-doppler coordinate pairs and corresponding coefficients until the determining has iterated a preset number of times or until the updated time-frequency response of the channel is of a sufficiently low threshold. In each iteration, the time-frequency response of the channel is 43240768_1:CHPupdated in a similar way in order to remove the time-frequency response at the delay-doppler coordinate pair of that iteration from the next iteration. The delay-doppler coordinate pair of the next iteration is therefore determined independently of the influence of the responses at the delay-doppler coordinate pairs determined in any previous iterations.

[0048] The disclosed methods advantageously improve estimation accuracy by determining the delay-Doppler coordinate pairs of the channel in any iterations independently of the time- frequency response at the delay-Doppler coordinate pairs determined in previous iterations. Additionally, by segmenting the time-frequency response of the channel and determining the coefficients independently for each segment, the phase error accumulated over the OFDM frame can be removed, further improving the accuracy of channel estimation.

[0049] By approximating the response of an actual path over which Doppler spreading occurs with the response at a fraction of the delay-Doppler coordinate pairs, the disclosed methods advantageously avoid or at least mitigate the effect of IDI while maintaining the sparse nature of the channel. The approximation also advantageously reduces computational complexity for further processing such as equalisation. BRIEF DESCRIPTION OF DRAWINGS

[0050] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0051] Fig.1 is a block diagram of an OFDM system;

[0052] Fig.2 is a block diagram of an OFDM modulator of a transmitter in the OFDM system of Fig.1;

[0053] Fig.3 is a block diagram of an OFDM demodulator of a receiver in the OFDM system of Fig.1;

[0054] Fig.4 is a block diagram of an OFDM system according to an embodiment of the present invention;

[0055] Fig.5 is a block diagram of an OFDM demodulator of the OFDM system of Fig.4; 43240768_1:CHP

[0056] Fig.6 is a flow chart of a method performed by a channel estimator of the OFDM demodulator of Fig.5;

[0057] Fig.7 depicts graphs 70a-70d illustrating symbolwise normalised mean square errors (NMSE) and graphs 72a-72d illustrating average NMSE against signal-noise-ratio (SNR) of the method of Fig.6; and

[0058] Fig.8 is a flow chart of another method performed by the channel estimator of the OFDM demodulator of Fig.5; and

[0059] Fig.9A and 9B form a schematic block diagram of a general purpose computer system upon which the transmitter or the receiver of the communication system of Figures 4 to 5 can be practiced. DETAILED DESCRIPTION

[0060] Fig.4 shows a communication system 400. The communication system 400 comprises a transmitter 110, a receiver 420, and a channel 130. The communication system 400 has the same structure as the communication system 100 of Fig.1, except that the receiver 420 of the communication 400 uses a different OFDM demodulator as discussed in more detail below with reference to Fig.5.

[0061] The transmitter 110 is the same as the transmitter 110 in the communication system 100 discussed above with reference to Figs.1 through 3. The transmitter 110 is configured to generatean OFDM signal ^^^^^^ by modulating symbol data ^^^^^, ^^^ onto the subcarriers. The modulationcomprises applying, by the IDFT 214, an inverse discrete Fourier transform (IDFT) and, applying by the transmitter filter 220, a prototype filter or pulse shaping filter. In some implementations, the IDFT 214 is configured to compute the IDFT of an input by applying a fast Fourier transform to the input. The OFDM signal ^^^^^^ comprises an OFDM frame including ^^ OFDM symbols each having a duration of ^^ for transmission over ^^ OFDM subcarriers. TheOFDM symbols comprise one or more pilot symbols ^^൫^^^^^^௧, ^^^^^^௧൯. The characteristics of thepilot symbols ^^൫^^^^^^௧, ^^^^^^௧൯ are known at both the transmitter 110 and the receiver 420. Thetime-frequency domain representation of the generated OFDM signal ^^^^^^ is given by 43240768_1:CHPwhere ^^^^^, ^^^ denotes the ^^௧^ OFDM symbol transmitted at the ^^௧^ subcarrier, ^^^^⋅^ denotesthe prototype filter or pulse shaping filter for the ^^௧^subcarrier, encoding the data onto the subcarrier ^^ and windowing the signal in the time domain using the rectangular function Rect, ^^^^denotes the duration of the cyclic prefix, ^^ is the imaginary unit.

[0062] The OFDM signal ^^^^^^ travels to the receiver 420 via the channel 130. The channel 130 may be air, a wire, water, and the like. The channel 130 may exhibit multiple paths. For example, the channel 130 is a doubly selective channel. The channel 130 introduces losses to the analog signal ^^^^^^due to reflection, diffraction, scattering, multipath propagation, or the like.

[0063] The analog signal ^^^^^^is the analog signal ^^^^^^that have travelled through the channel130. The receiver 420 receives the analog signal ^^^^^^.

[0064] The receiver 420 comprises an OFDM demodulator 422, a channel decoder 124, a source decoder 126, and a sink 128. The channel decoder 124, source decoder 126, and sink 128 are the same as the channel decoder 124, source decoder 126, and sink 128 of the receiver 120 in communication system 100 discussed above with refence to Figs.1 through 3.

[0065] Fig.5 is a block diagram of the OFDM demodulator 422. The OFDM demodulator 422 comprises a CP remover 310, a S / P converter 312, a matched filter 314, a discrete Fourier transformer (DFT) 316, a P / S converter 318, a channel estimator 510, and a channel equaliser 512. The OFDM demodulator 422 receives the analog signal ^^^^^^and converts the signal from analog to digital symbols ^^^^^^by an analog to digital converter (not shown). The CP remover 310, S / P converter 312, matched filter 314, discrete Fourier transformer (DFT) 316, and P / S converter 318 are the same as CP remover 310, S / P converter 312, matched filter 314, discrete Fourier transformer (DFT) 316, P / S converter 318 of Fig.3. The digital symbols ^^^^^^ are then matched filtered by the matched filter 314. The matched filter 314 applies the same match filtering at the receiver 420 as the transmitter 110 for increasing the SNR. For instance, if the transmitter filter 220 at the transmitter 110 is a root raised cosine filter, the matched filter 314 should also be a root raised cosine filter. The matched filtered symbols are then output to the CP 43240768_1:CHPremover 310. The CP remover 310 removes the cyclic prefix from the matched filtered symbols and provide the symbols to the S / P converter 312. The S / P converter 312 converts the symbols which have had the cyclic prefix removed to parallel data streams. 66] The output of the S / P converter 312 is sampled at sampling points ^ெ ᇲ [00்(^^ ൌ 0,1, … , ^^் െ 1) and provided to the DFT 316. The DFT 316 performs discrete Fourier transform on the sampled streams. In some implementations, DFT 316 is configured to compute the DFT of an input by applying FFT to the input. The output of the DFT 316 is an array of complex valuedsymbols ^^^^^, ^^^ each representing the amplitude and phase of the received signal at the ^^௧^subcarrier and the ^^௧^ symbol, where ^^ ൌ 0,1, … , ^^ െ 1 and ^^ ൌ 0,1, … ,^^. The output of theDFT 316 is provided to the channel estimator 510 for estimation of the time-frequency response of channel 130 characterising how the channel 130 affects the transmitted signal.

[0067] Channel estimation is a process of estimating the characteristics of a channel. In delay- Doppler channel estimation schemes, the process typically involves using a channel model to quantify the characteristics of the channel in terms of both delay and Doppler frequency shift with parameters and fitting the channel model with observed channel response by an estimation method, such as least squares, to find the parameters of best fit. In instances where channel 130 exhibits multiple paths, the parameters can include path coefficients of the multiple paths of the channel. For example, in estimating the channel response for an OFDM signal in delay-Doppler domain, each path of a multipath channel can be represented in delay-Doppler domain as a complex coefficient ℎ^at delay-Doppler-shift pair ^^^^,^^^). The delay and Doppler shifts are subjected to the environment and accordingly remain relatively stationary compared to time- frequency response. In the present disclosure, the delay and Doppler shifts are assumed to be stationary for the transmitted OFDM frame. In some implementations, the received signal ^^^^^^ can be represented by a time domain signal model dictated by the following equation:where ^^ denotes the total number of paths, ^^^^^^denotes noise.

[0068] Based on the above signal model, channel 130 can be characterised by a channel model dictated by the following equation (3) in delay-Doppler domain in the form of a delay-Doppler 43240768_1:CHPgrid. The grid has a delay axis and a Doppler shift axis with resolutions of ^ and ^ ேᇲ,்respectively, where Δ^^ is the subcarrier spacing given by^்,where parameters ^^ఔ^and ^^ఛ^denote the Doppler shift coordinate and delay coordinate of path ^^, respectively, terms ^^ି^ଶగ^ ^ ಾ^ഓ^and ^^^ଶగಿ^ഌ^denote the phase vectors of path ^^.

[0069] The delay and Doppler shift ^^^^,^^^) can be obtained from the delay and Doppler shift coordinates by the following equations,

[0070] Channel estimation in the context of the present disclosure comprises establishing the ^ ^ delay-Doppler coordinates ^^^^,^^ఔ^^and corresponding path parameters ^ℎ^, ^^^, ^^^^

[0071] Fig.6 shows a channel estimation method 600 that can be carried out by the channel estimator 510. Method 600 starts from step 620. At step 602, the channel estimator 510determines a time-frequency response of the channel 130 based on the symbols ^^^^^, ^^^ at pilotindices

[0072] In one or more implementations, inter-symbol interference (ISI) is ignored due to thepresence of the cyclic prefix. In other words, the received symbol at indices ^^^, ^^^ is simplifiedas the convolution of the corresponding transmitted symbol and the time frequency response of the channel 130 expressed by

[0073] If intercarrier interference (ICI) is also ignored, the received symbol ^^^^^, ^^^ can befurther simplified into ^^^^^, ^^^ ൌ ^^^^^, ^^^^^^^^, ^^^. (6)43240768_1:CHP

[0074] Therefore, the transfer function ^^^^^, ^^^ can be determined from the above equation (6),if both the received symbols ^^^^^, ^^^ and the transmitted symbols ^^^^^, ^^^ are known. Asdiscussed above, the characteristics of the transmitted pilot symbols ^^൫^^^^^^௧,thetransmitted symbols at pilot indices, are known at both the transmitter 110 and the receiver 420.Accordingly, at step 602, the time frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130 isobtained based on ^^^^^, ^^^ at pilot indices ൫^^^^^^௧, ^^^^^^௧൯ and the known pilot symbols^^൫^^^^^^௧, ^^^^^^௧൯ using equation (6). In one or more portions of the following description, thetime frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130 is interchangeably denoted as^^^,^ or ^^^^^, ^^^ for the sake of illustration simplicity. The method 600 proceeds from step 602to step 604.

[0075] At step 604, the channel estimator 510 divides the time-frequency response^^൫^^ ^^^^^௧, ^^^^^^௧൯ of the channel 130 into time segments ^^ ൫^^^^^^௧, ^^^^^^௧൯. In one or moreportions of the following description, the time frequency response ^^^൫^^^^^^௧ , ^^^^^^௧൯ of thechannel 130 is interchangeably denoted as^or ^^ ^^^, ^^^ for the sake of illustrationIn one implementation, the time segments comprise a total of 2 time segments. In another implementation, the time segments comprise a total of 4 time segments. In another implementation, the time segments comprise a total of 10 time segments. In yet another implementation, the time segments comprise a total of 20 time segments. The number of time segments can range from 2 to 20. However, as would be appreciated, the number of time segments is not limited to the examples provided herein.

[0076] Assuming the time segments comprise a total of S time segments, the time-frequencyresponse ^^^^^, ^^^ to the channel 130 is represented by the time-frequency response ^^^^^^, ^^^ ofeach segment from time segment 0 through time segment ^^ െ 1 as shown by equation (7) below:

[0077] Thus, the time-frequency response of the sthtime segment can be obtained by applying arectangular function ^^^^^^^^the time-frequency response ^^^^^, ^^^ of the channel 130.Similarly, the time-frequency response for the sthtime segment can be represented by a segmentwise channel model dictated by the following equation, 43240768_1:CHP

[0078] Method 600 proceeds from step 604 to step 606. Whilst step 606 is described to occur after step 604, the scope of the present disclosure is not limited to such an order. In some implementations, step 606 occurs before step 604 or concurrently with step 604 without departing from the scope of the present disclosure.

[0079] At step 606, the channel estimator 510 determines a delay-Doppler coordinate pair basedon the time frequency response ^^൫^^^^^^௧ , ^^^^^^௧൯. The delay-Doppler coordinate pair is anapproximation of the true delay-Doppler coordinate pair of a path of channel 130. As the true delay-Doppler coordinate pair is unknown, the delay-Doppler coordinate pair is used in further processing such as coefficient estimation or channel equalisation as the true delay-Doppler coordinate pair of that path.

[0080] In some implementations, the delay-Doppler coordinate pair is determined from a delay-Doppler representation of the time frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130. Inone example, the delay-Doppler representation of the time frequency response ^^൫^^^^^^௧ , ^^^^^^௧൯of the channel 130 is generated by applying a projection operation that transforms the timefrequency response ^^൫^^^^^^௧ , ^^^^^^௧൯ of the channel 130 from time-frequency domain to delay-Doppler domain. In some implementations, the projection operation is performed by a symplectic finite fourier transform (SFFT). In one example, the time-frequency response^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130 is input into the SFFT which calculates the projection of thetime-frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ onto aset of predetermined “test” vectors representedas the delay-Doppler grid. Each grid point at coordinate pair ^^^,^^^ in the delay-Doppler grid,where ^^ ∈ ^0,1, …^^ െ 1^ and ^^ ∈ ^0,1, …^^ െ 1^, represents a ‘test’ vector with delay τ ൌ ^and Doppler frequency ν ൌ ^For example, the grid point at coordinate pair^^^,^^^represents a ‘test’ vector with delay ^^^^and Doppler frequency ν ൌThe output of the SFFT is a power spectrum for each of the ‘test’ vectors. The magnitude of the projection onto a ‘test’ vector is indicative of the likelihood of the coordinate pair of that ‘test’ vector corresponding to the delay- Doppler coordinate pair of one of the actual paths of channel 130. For example, the coordinate 43240768_1:CHPpair with the largest magnitude has the highest likelihood of corresponding to the delay-Doppler coordinate pair of one of the actual paths of channel 130. The delay-Doppler representation ofthe time frequency response ^^൫^^^^^^௧ , ^^^^^^௧൯ of the channel 130 comprises the power spectrumof each of the “test” vectors.

[0081] In some implementations, the delay-Doppler coordinate pair is determined by a Direction of Arrival (DOA) method, such as Multiple Signal Classification (MUSIC) algorithm, compressed sensing, orthogonal matching pursuit or the like. DOA methods are known to estimate the directions of arrival of signals received by a uniform rectangular array (URA) or a uniform linear array (ULA) by tracking phase changes in elements of the URA or ULA. In application of a DOA method to determining the delay-Doppler representation of the time frequency response of the channel, the channel is regarded as a time-invariant uniformrectangular array (URA) of antennas and the channel response at index ^^^, ^^^ as an arrayelement in the URA. Based on the time frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130,the DOA method outputs a power spectrum for each of the ‘teste’ vectors with the value of the power spectrum indicating the likelihood of the coordinate pair of that ‘test’ vector corresponding to the delay-Doppler coordinate pair of one of the actual paths of channel 130.The delay-Doppler representation of the time frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel130 comprises the power spectrum of each of the “test” vectors.

[0082] Due to limitations in the bandwidth and time period of observation, the true Doppler shift coordinates may not correspond with integer multiples of the resolution of the Doppler shift axis, in which case the peak would appear to spread out over a multitude of on-grid taps. Accordingly, the output of the SFFT or DOA method represents an equivalent channel model of the channel 130 where the response of one actual path is spread over many on-grid taps.

[0083] In the equivalent channel model, the time frequency response ^^^^^, ^^^ is the sum of thetime-frequency response of each tap expressed by equation (9) below:where ^^^ఔ^̃ denotes the on-grid Doppler coordinate and ℎ^̃ denotes the coefficient for tap ^^^.43240768_1:CHP

[0084] The number of taps ^^^ of the delay Doppler representation is ^^ time as large as thenumber of actual paths of the channel 130, i.e., ^^^ ൌ ^^ ൈ ^^. This is due to the actual channelresponse being ^^ sparse in the delay domain and non-sparse in the Doppler domain, hence ^^ taps are used to represent the time-varying response of each actual path. In contrast, the actual channel model is ^^ times sparse in both the delay and Doppler domains. Therefore, modelling the channel using the equivalent channel model is at the expense of loss of sparsity of the channel model. In some circumstances, there may be only a few paths and the paths could be separated, meaning there are only a few significant signal components at specific time delays and Doppler shifts. Such a characteristic is referred to as “sparsity.” When a wireless channel is sparse, it is easier for communication systems to construct an estimated time-frequency response using a relatively small number of paths. In contrast, loss of sparsity increases the complexity of channel estimation and equalisation as the coefficients of each Doppler tap must be estimated correctly to ensure correct equalisation and detection. Modulation schemes, such as Orthogonal Time Frequency Space (OTFS) and Orthogonal Delay-Doppler Division Multiplexing (ODDM), that encode data in the delay-Doppler domain may efficiently handle a sparse channel, making communication more reliable and computationally simpler. When sparsity is lost, the performance of delay-Doppler-based modulation schemes such as OTFS and ODDM, which rely on sparsity, may be limited. Additionally, it is likely that such an equivalent channel model may not capture all the components due to noise.

[0085] To maintain sparsity, a sparse approximation can be applied to the multiple on-grid taps over which spreading occurs. The sparse approximation uses a fraction of the multiple on-grid taps to represent the response of each path. Accordingly, the sparse approximation approximates the true delay-Doppler coordinates of the path with the delay-Doppler shift coordinates of the fraction of the multiple taps.

[0086] In the example of Fig.6, the sparse approximation comprises a “one-tap-on-grid” approximation. The “one-tap-on-grid” approximation uses a single on-grid tap to represent the response of an actual path. For instance, in determining the delay-Doppler coordinate pair that approximates the true delay-Doppler coordinate pair of a path in step 606, the “one-tap-on-grid” approximation assumes that the on-grid tap having the largest magnitude (“the largest on-grid tap”) is the closest approximation to the response of the path. As discussed above, the largest on- grid tap has the highest likelihood of corresponding with one of the actual paths of the channel, 43240768_1:CHPi.e., having the smallest error between the approximated value and the actual coordinates of the path.

[0087] Applying the “one-tap-on-grid” approximation comprises identifying the largest on-grid tap and the corresponding delay Doppler coordinate pair. The delay-Doppler coordinate pair, i.e., the “one-tap-on-grid” approximation of the true delay-Doppler coordinate pair of the path, is the delay Doppler coordinate pair of the largest on-grid tap. In some implementations, the largest magnitude is determined through the use of a maximum operation. In some implementations, the search of the largest on-grid tap is restricted to taps within the maximum delay in order to reduce the likelihood of selecting an incorrect coordinate pair.

[0088] The application of the one-tap-on-grid approximation may create a fractional component due to the potential difference between the actual coordinate pair of the actual path and the one- tap-on-grid approximation, thereby resulting in a linear time-phase rotation error between the estimated time-frequency response constructed using the one-tap-on-grid approximation and the ‘true’ time-frequency response.

[0089] Referring to Fig.7, graphs 70a-70d illustrate the symbolwise normalised mean square errors (NMSE) of the “one-tap-on-grid” approximation and graphs 72a-72d illustrate the average NMSE against SNR of the “one-tap-on-grid” approximation. As can be seen, the error varies over the signal, being smallest at the centre of the OFDM frame and largest at the edges of the OFDM frame. The fractional component in the “one-tap-on-grid” approximation can be reduced by increasing the acquisition time, although this increases latency.

[0090] It will be appreciated that the sparse approximation is not limited to comprising the “one- tap-on-grid” approximation discussed above. In some implementations, the sparse approximation can comprise other forms of approximation where a path is approximated by, for example, two or more on-grid taps without departing from the scope of the present invention.

[0091] By representing the response of each path using a fraction of the multiple on-grid taps over which spreading occurs and which are most likely to correspond to the actual delay and Doppler shift of the path, the application of the sparse approximation avoids or at least mitigates channel estimation and equalisation complexity. The method 600 proceeds from step 606 to step 608. 43240768_1:CHP

[0092] At step 608, the channel estimator 510 estimates a coefficient for the delay-Doppler coordinate pair based on the time-frequency response of channel 130.

[0093] Various coefficient estimation methods can be used to determine the coefficient for a delay-Doppler coordinate. In one example, the estimating uses least squares regression. The least squares linear regression aims to find the coefficient that minimises the difference between the time-frequency response ^^^,^of the channel 130 determined at step 602 and an estimated time- frequency response ^^^^,^of the channel 130. The estimated time-frequency response is constructed based on the delay-Doppler coordinate pair using the channel model dictated by equation (3) above. In one example, the estimated time-frequency response ^^^^,^of the channel 130 is a function of variable ^^^representing the coefficient of each path,where ^^^ఔ^denotes the delay-Doppler coordinate pair, i.e., the one-tap-on-grid approximation of the delay-Doppler coordinate pair of path ^^.

[0094] In some implementations, the phase rotation induced by Doppler shift is approximated as a constant for each OFDM symbol, i.e.,

[0095] The estimated transfer function can therefore be approximated as43240768_1:CHPwherein ^^^,^denotes a phase response vector, also referred to as a steering vector in URA, ofpath ^^, denotes a phase response matrix, also referred to as a steering matrix in URA,of path ^^.

[0096] Due to the fractional Doppler components created by sparse approximation, the accuracy of the determination can vary over the frame. To minimize error variation, the channel estimator 510 can be configured to determine the coefficient for each time-segment independently, i.e., segmentwise, whereby the coefficient of each time segment is determined based on the time- frequency response of channel 130 of the corresponding time segment.

[0097] In some implementations, the estimation of the path coefficients comprises applying a phase shifted integer approximation to the estimated time-frequency response of the channel 130 of each time segment to further minimise the overall estimation error of each segment. The segmentwise phase shifted integer approximation is given bywhere ^^^ఔ^is the one-tap-on-grid approximation of the delay-Doppler coordinate pair of the path, ℎ^denotes the complex coefficient at delay-Doppler-shift pair ^^^^,^^^), ^^^^denotes the phase shift variable for the ^^௧^segment.

[0098] In one example, estimation error is measured by normalised mean square error (NMSE). Accordingly, ^^^^^is chosen to minimise the NMSE of the phase-shifted approximation according to the following equation, ಿ^ೞశభ^ ^̂^^^ ൌ arg min ∑ೄ^^ಿೞ ห^^^,^ െ ^̂^^,^ห. (14) ^̂^ೞ^ୀೄis a ^^ ൈ 1 vector of the variable ^^^^ .

[0099] The phase difference between the time-frequency response determined based on the pilot symbols and the response from the phase-shifted approximation for each path in each segment r OFDM symbol ^^ within ^ே^^ ^ foே^ା^ ௌ,ௌ ] is given by, 43240768_1:CHP

[0100] The NMSE of the phase-shifted approximation is proportional to the absolute phase difference ห^^^^^^^ห. The phase difference linearly increases with ^^. As such, ^^^^^can bechosen such that ห^^ ^^^ห ^ 0 at the centre of each segment where ^^ ൌௌ ,

[0100] Substituting equation (16) into (15), the phase difference is simplified as,

[0101] Assuming |^^ఔ^ െ ^^^ఔ^| ^ 0.5, the maximum phase difference will occur at the edges ofthe segment where ^^ ∈ ^ே^^ା^^ ^ ^ ௌ, ே^ௌ]. Substituting ^^ ൌ ே^ା^ ௌ into equation (17), the phase difference is simplified as,

[0102] As can be seen from equation (18) above, the number of segments determines the maximum phase difference or error within each segment. Accordingly, increasing the number of segments can result in a more accurate estimation.

[0103] With the phase shifted integer approximation, the response of a path ^^ of each time segment can be approximated as,

[0104] where ^^^^is a variable representing the complex path coefficient for the ^^௧^segmentwhich incorporates the phase shift term ^^^^and ^^^ఔ^ denotes the one-tap-on-grid approximationof the delay-Doppler coordinate pair of path ^^. 43240768_1:CHP

[0105] An estimated transfer function of channel 130 of each time segment can therefore be constructed according to the following equation

[0106] In determining the coefficient for the delay-Doppler coordinate pair at step 608, the number of paths ^^ is set to 1. If determining the coefficient for a second and further delay- Doppler coordinate pair, the number of paths ^^ is correspondingly set to the number of delay- Doppler coordinate pairs (iterations) that have been determined. With ^^ set to 1, the response of the path of each time segment is accordingly approximated as

[0107] where ^^^^is a variable representing the complex path coefficient for each segment which incorporates the phase shift term ^^^^.

[0108] With ^^ set to 1, the estimated transfer function of channel 130 of each time segment can therefore be constructed segmentwise according to the following equation,

[0109] Based on the segmentwise time frequency responseof the channel 130 determined at step 602 and the segmentwise estimated time-frequency response ^̂^୫^,୧^^^^^^ of the channel 130, the channel estimator 510 estimates complex coefficient ^^^^^segmentwise using least squares linear regression according to the equation below, ^^^^^^^ ൌ^a∥^^ೞrg minభ^

[0110] By determining the complex coefficients for each time segment independently, the accumulated channel estimation error can be reduced or removed, improving the accuracy of the estimation. 43240768_1:CHP

[0111] Returning to method 600, the method proceeds from step 608 to step 610. At step 610,the channel estimator 510 generates a time-frequency path responsefor the delay-Doppler coordinate pair based on the coefficient ^^^^, where ^^^^ is a vector of size ^^ ൈ 1containing the complex coefficients for each segment. In some implementations, the generating comprises generating a time-frequency path response for the delay-Doppler coordinate for each time segment based on the coefficient of that time segment according to equation (22) and concatenating the time-frequency path response of each time segment according to equation (7). The time-frequency path response ^^^^,^^^^^^ fordelay-Doppler coordinate pair represents the path influence of the path. The method proceeds from step 610 to step 612.

[0112] At step 612, the channel estimator 510 updates the time-frequency response of the channel 130 determined based on the pilot symbols by subtracting the time-frequency response of the channel 130 with the time-frequency response for the delay-Doppler coordinate according to the following equations,

[0113] The update step removes the path influence of the path on the determination any further delay-Doppler coordinate pairs which approximate the true delay-Doppler coordinate pairs of corresponding further paths that may exist in the channel 130. The method 600 proceeds from step 612 to a check step 614.

[0114] At check step 614, the channel estimator 510 determines whether one or more criteria have been met. In some implementations, the one or more criteria comprise a criterion that the updated time-frequency response,^of the channel 130 is of an energy lower than a threshold energy. In one example, the threshold energy is related to the energy of the noise in the channel. In some implementations, the one or more criteria comprise a criterion that step 606 to step 612 have been iterated a preset number of times. In one example, the maximum number of iterations is 7, for example, for an EVA channel model with a subcarrier spacing of 15 kHz.

[0115] In response to determining that at least one of the one or more criteria has been met, the method 600 proceeds to step 616. Otherwise, the method 600 returns to step 606. In any subsequent iteration of step 606 through to step 614 after the first iteration, a delay-Doppler coordinate pair and a corresponding coefficient are determined. The delay-Doppler coordinate 43240768_1:CHPpair of any subsequent iteration is determined in the same way as the delay-Doppler coordinate pair of the first iteration was determined, except the SFFT or DOA method uses the updated time-frequency response,^of the channel 130 as the input, rather than the initial time- frequency response ^^^,^of the channel 130 determined at step 602. The one-tap-on-grid approximation assumes that the largest on-grid tap of the output from the SFFT or DOA method of any subsequent iteration is the closest approximation of the response of the path of that subsequent iteration. The delay-Doppler coordinate pair of any subsequent iteration is accordingly the delay-Doppler coordinate pair of the largest on-grid tap from the output of the SFFT or DOA method of that iteration. As the path influence of the path of any previous iteration has been removed in the updated time-frequency response,^of the channel 130 in each subsequent iteration, the largest on-grid tap in step 606 of each subsequent iteration is different from that of any previous iteration. Similarly, the coefficient for the delay-Doppler coordinate pair of any subsequent iteration can be determined in the same way as the coefficients of the delay-Doppler coordinate of the first iteration were determined, except the number of paths ^^ is set to the number of iterations so that the estimated transfer function of channel 130 is constructed based on the delay-Doppler coordinate pairs of the present and all previous iterations. It is important to note that in step 608 of each iteration equation (23) uses the same time- frequency response of channel 130 determined at step 602 for the termIn one implementation, each subsequent iteration of determining the coefficient at step 608 comprises updating the coefficients of previous iterations.

[0116] At step 616, the channel estimator 510 generates an estimate of the time-frequency response of channel 130 based on the delay-Doppler coordinate pairs and corresponding coefficients from all iterations. In some implementations, the generating comprises generating a joint time-frequency response for each time segment based on the delay-Doppler coordinate pairs and coefficients from all iterations of that time segment according to equation (20) and concatenating the joint time-frequency response of each time segment according to equation (7). The method 600 ends at step 616.

[0117] As the delay-Doppler coordinate pair of each iteration is determined based on an updated time frequency response of the channel 130 which has excluded the time frequency path responses of previous paths, each path is estimated independently with reduced inter-path interference. 43240768_1:CHP

[0118] Fig.8 shows another channel estimation method 800 that can be carried out by the channel estimator 510. Method 800 starts from step 820. At step 802, the channel estimator 510determines a time-frequency response of the channel 130 based on the symbols ^^^^^, ^^^ outputfrom the DFT 316 at pilot indices ൫^^^^^^௧, ^^^^^^௧൯.

[0119] In one or more implementations, inter-symbol interference (ISI) is ignored due to thepresence of the cyclic prefix. In other words, the received symbol at indices ^^^, ^^^ is simplifiedas the convolution of the corresponding transmitted symbol and the time frequency response of the channel 130 as shown by equation (5) above.

[0120] If intercarrier interference (ICI) is also ignored, the received symbol ^^^^^, ^^^ can befurther simplified into equation (6) above.

[0121] Therefore, the transfer function ^^^^^, ^^^ can be determined from the above equation (6),if both the received symbols ^^^^^, ^^^ and the transmitted symbols ^^^^^, ^^^ are known. Asdiscussed above, the characteristics of the transmitted pilot symbols ^^൫^^^^^^௧, ^^^^^^௧൯, i.e., thetransmitted symbols at pilot indices, are known at both the transmitter 110 and the receiver 420.Accordingly, at step 802, the time frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130 isobtained based on ^^^^^, ^^^ at pilot indices ൫^^^^^^௧, ^^^^^^௧൯ and the known pilot symbols^^൫^^^^^^௧, ^^^^^^௧൯ using equation (6). The method 600 proceeds from step 802 to step 804.

[0122] At step 804, the channel estimator 510 divides the time-frequency response^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130 into time segments. In one implementation, the timesegments comprise a total of 2 time segments. In another implementation, the time segments comprise a total of 4 time segments. In another implementation, the time segments comprise a total of 10 time segments. In yet another implementation, the time segments comprise a total of 20 time segments. The number of time segments can range from 2 to 20. However, as would be appreciated, the number of time segments is not limited to the examples provided herein.

[0123] Assuming the time segments comprise a total of S time segments, the time-frequencyresponse ^^^^^, ^^^ to the channel 130 is the sum of the time-frequency response ^^^^^^, ^^^ of eachsegment from time segment 0 through time segment ^^ െ 1 as shown by equation (7) above.43240768_1:CHP

[0101] Thus, the time-frequency response of the sthtime segment can be obtained byapplying a rectangular function ^^^^^^^^ െ ^^^ to the time-frequency response ^^^^^, ^^^ of thechannel 130. Similarly, the time-frequency response for the sthtime segment can be represented by a segmentwise channel model dictated by equation (8) above. Method 600 proceeds from step 804 to step 806. Whilst step 806 is described to occur after step 804, the scope of the present disclosure is not limited to such an order. In some implementations, step 806 occurs before step 804 or concurrently with step 804 without departing from the scope of the present disclosure.

[0124] At step 806, the channel estimator 510 determines a delay-Doppler coordinate pair basedon the time frequency response ^^൫^^^^^^௧ , ^^^^^^௧൯. The delay-Doppler coordinate pair is anapproximation of the true delay-Doppler coordinate pair of a path of channel 130. As the true delay-Doppler coordinate pair is unknown, the delay-Doppler coordinate pair is used in further processing such as coefficient estimation or channel equalisation as represent the true delay- Doppler coordinate pair of that path.

[0125] In some implementations, the delay-Doppler coordinate pair is determined from a delay-Doppler representation of the time frequency response8 ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130. Inone example, the delay-Doppler representation of the time frequency response ^^൫^^^^^^௧ , ^^^^^^௧൯of the channel 130 is generated by applying a projection operation that transforms the timefrequency response ^^൫^^^^^^௧ , ^^^^^^௧൯ of the channel 130 from time-frequency domain to delay-Doppler domain). In one example, the time-frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel130 is input into the SFFT which calculates the projection of the time-frequency response^^൫^^^^^^௧, ^^^^^^௧൯ onto a set of predetermined “test” vectors represented as the delay-Doppler grid.Each grid point at coordinate pair ^^^,^^^ in the delay-Doppler grid, where ^^ ∈ ^0,1, …^^ െ1^ and ^^ ∈ ^0,1, …^^ െ 1^, represents a ‘test’ vector with delay τ ൌ ^and Doppler frequencyν ൌ ே்ᇲ. For example, the grid point at coordinate pair ^^^,^^^ represents a ‘test’ vector with delay ^and Doppler frequency ν ൌ ^The output of the SFFT is a power spectrum for each of the ‘test’ vectors. The magnitude of a ‘test’ vector is indicative of the likelihood of the coordinate pair of that ‘test’ vector corresponding to the delay-Doppler coordinate pair of one of the actual paths of channel 130. For example, the coordinate pair with the largest magnitude has the highest likelihood of corresponding to the delay-Doppler coordinate pair of one of the actual 43240768_1:CHPpaths of channel 130. The delay-Doppler representation of the time frequency response^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130 comprises the power spectrum of each of the “test” vectors.

[0126] In some implementations, the delay-Doppler coordinate pair is determined by a Direction of Arrival (DOA) method, such as Multiple Signal Classification (MUSIC) algorithm, compressed sensing, orthogonal matching pursuit or the like. DOA methods are known to estimate the directions of arrival of signals received by a uniform rectangular array (URA) or a uniform linear array (ULA) by tracking phase changes in elements of the URA or ULA. In application of a DOA method to determining the delay-Doppler representation of the time frequency response of the channel, the channel is regarded as a time-invariant uniformrectangular array (URA) of antennas and the channel response at index ^^^, ^^^ as an arrayelement in the URA. Based on the time frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel 130,the DOA method outputs a power spectrum for each of the ‘test’ vectors with the value of the power spectrum indicating the likelihood of the coordinate pair of that ‘test’ vector corresponding to the delay-Doppler coordinate pair of one of the actual paths of channel 130.The delay-Doppler representation of the time frequency response ^^൫^^^^^^௧, ^^^^^^௧൯ of the channel130 comprises the power spectrum of each of the “test” vectors.

[0127] As discussed above, the true Doppler coordinates may not correspond with integer multiples of the resolution of the Doppler shift axis due to limitations in the bandwidth and time period of observation, in which case the peak would appear to spread out over a multitude of on- grid taps. Accordingly, the output of the SFFT or DOA method represents an equivalent channel model of the channel 130 where the response of one actual path is spread over many on-grid taps.

[0128] In the equivalent channel model, the time frequency response ^^ is the sum of the time- frequency response of each tap given by equation (9) above.

[0129] To maintain sparsity, a sparse approximation can be applied to the multiple on-grid taps over which spreading occurs. The sparse approximation uses a fraction of the multiple on-grid taps to represent the response of each path. Accordingly, the sparse approximation approximates the true delay-Doppler coordinates of the path with the delay-Doppler shift coordinates of the fraction of the multiple taps. 43240768_1:CHP

[0130] In the example of Fig.7, the sparse approximation comprises a “two-tap-on-grid” approximation. The “two-tap-on-grid” approximation uses two neighbouring on-grid taps to represent the response of an actual path. In determining the delay-Doppler coordinate pair in step 806, the “two-tap-on-grid” approximation assumes that the largest on-grid tap and its largest neighbouring on-grid tap are the closest approximations to the response of the path.

[0131] Applying the “two-tap-on-grid” approximation comprises identifying the largest on-grid tap and its largest neighbouring on-grid tap and the corresponding delay-Doppler coordinate pairs. The delay-Doppler coordinate pair, i.e., the “two-tap-on-grid” approximation of the delay- Doppler coordinate pair of the path, comprises the delay Doppler coordinate pairs of the largest on-grid tap and its largest on-grid tap’s largest neighbouring on-grid tap. In some implementations, the largest magnitude is determined through the use of a maximum operation. In some implementations, the search of the largest on-grid tap is restricted to taps within the maximum delay in order to reduce the likelihood of selecting an incorrect coordinate pair.

[0132] It will be appreciated that the sparse approximation is not limited to comprising the “one- tap-on-grid” approximation or “two-tap-on-grid” approximation discussed above. In some implementations, the sparse approximation can comprise other forms of approximation where a path is approximated by, for example, more than two on-grid taps without departing from the scope of the present invention.

[0133] As discussed above, the application of the sparse approximation avoids or at least mitigates channel estimation and equalisation complexity. Using two neighbouring taps to represent the response of an actual path further improves the accuracy of estimation as two taps allow for fine-tuning of the Doppler frequency using coefficients. The method 800 proceeds from step 806 to step 808.

[0134] At step 808, the channel estimator 510 estimates the coefficients for the delay-Doppler coordinate pairs, based on the time-frequency response of channel 130.

[0135] Various coefficient estimation methods can be used to determine the coefficients for a delay-Doppler coordinate pair. In one example, the estimating uses least squares regression. The least squares regression aims to find the coefficients that minimise the difference between the time-frequency response ^^^,^of the channel 130 determined based on pilot symbols and an 43240768_1:CHPestimated time-frequency response ^^^^,^of the channel 130. The estimated time-frequencyresponse ^^^^,^ is constructed based on the delay-Doppler coordinate pairs using channel modeldictated by equation (3) above. In one example, the estimated time-frequency response ^^^^,^of the channel 130 is a function of variables ^^^and ^^^representing the coefficients of each delay- Doppler coordinate pair,

[0136] where the ceiling and floor operators^ and ^^^^^ denote the delay- coordinate pair, i.e., the two-tap-on-grid approximation of the delay-Doppler coordinate pair of path ^^.

[0137] Due to the fractional Doppler components created by sparse approximation, the accuracy of the determination can vary over the frame. To minimize error variation, the channel estimator 510 can be configured to determine the coefficients segmentwise whereby the coefficients of each time segment is determined based on the time-frequency response of channel 130 of the corresponding time segment.

[0138] In some implementations, the channel estimator 510 is configured to apply a phase shifted integer approximation to each time segment of the estimated time-frequency response of the channel 130 to further minimise the overall estimation error of each segment. The application of the phase shifted integer approximation is the same as that of method 600.

[0139] With the phase shifted integer approximation, the response of a path ^^ of each time segment can be approximated as,

[0140] where ^^^^and ^^^^are variables representing the complex path coefficients for each segment which incorporate the phase shift term ^^^^. 43240768_1:CHP

[0141] As can be seen from equation (26) above, the two-tap-on-grid approximation allows for fine-tuning of the Doppler frequency using the complex coefficients ^^^^and ^^^^.

[0142] An estimated transfer function of channel 130 of each time segment can therefore be constructed according to the following equation,

[0143] In determining the coefficients for the delay-Doppler coordinate pair at step 808, the number of paths ^^ is set to 1. If determining the coefficients for a second and further delay- Doppler coordinate pair, the number of paths ^^ is correspondingly set to the number of delay- Doppler coordinate pairs (iterations) that have been determined. With ^^ set to 1, the response of the path is accordingly approximated as

[0144] where ^^^^and ^^^^are variables representing the complex path coefficients for each segment which incorporate the phase shift term ^^^^.

[0145] The estimated transfer function of channel 130 can therefore be constructed segmentwise with ^^ set to 1 according to the following equation,

[0146] Based on the segmentwise time frequency response of the channel 130 determined at step 802 and the segmentwise estimated time-frequency response of the channel 130, the channel estimator 510 estimates the coefficients ^^^^^and ^^^^^segmentwise using least squares regression according to the equation below, 43240768_1:CHP^^^^, ^^^^൯ ൌ argೞ mೞin ∥^^^୫,୧ െ ^̂^୫^^,୧^^^, ^^^^ଶ ൫^^∥^ ^∥∥. (30) ൫^^భ ,^^భ൯

[0147] By determining the complex coefficients independently for each segment, the accumulated channel estimation error can be reduced or removed, improving the accuracy of the estimation.

[0148] Returning to method 800, the method proceeds from step 808 to step 810. At step 810,the channel estimator 510 generates a time-frequency path responsefor the delay-Doppler coordinate pair based on the coefficients ^^^^and ^^^^, where ^^^^and ^^^^are vectors of size^^ ൈ 1 containing the complex coefficients for each time segment. In some implementations, thegenerating comprises generating a time-frequency path response for each time segment based on the delay-Doppler coordinate pair and the coefficients of that time segment according to equation (29) and concatenating the time-frequency path response of each time segment according toequation (7). The time-frequency path responsefor the delay-Doppler coordinaterepresents the path influence of the path. The method proceeds from step 810 to step 812.

[0149] At step 812, the channel estimator 510 updates the time-frequency response of the channel 130 by subtracting the time-frequency response of the channel 130 with the time- frequency path response for the delay-Doppler coordinate pair according to the following equations,

[0150] The update step removes the path influence of the path on the determination of any further delay-Doppler coordinate pair that approximates the true delay-Doppler coordinate pairs of corresponding further paths that may exist in the channel 130. The method 800 proceeds from step 812 to step 814.

[0151] At step 814, the channel estimator 510 determines whether one or more criteria have been met. In some implementations, the one or more criteria comprise a criterion that the updated time-frequency response ^^^ᇱ,^of the channel 130 is of an energy lower than a threshold energy. In one example, the threshold energy is related to the energy of the noise in the channel. In some implementations, the one or more criteria comprise a criterion that step 806 to step 812 have 43240768_1:CHPbeen iterated a preset number of times. In one example, the maximum number of iterations is 7, for example, for an EVA channel model for a system with 15 kHz subcarrier spacing.

[0152] In response to determining that at least one of the one or more criteria has been met, the method 800 proceeds to step 816. Otherwise, the method 800 returns to step 806. In any subsequent iteration of step 806 through to step 814 after the first iteration, a delay-Doppler coordinate pair and corresponding coefficient are determined. The delay-Doppler coordinate pair of the path of any subsequent iteration is determined in the same way as the delay-Doppler coordinate pair of the first iteration was determined, except the SFFT or DOA method uses the updated time-frequency response,^of the channel 130 as the input, rather than the initial time-frequency response ^^^,^of the channel 130 determined at step 802. The two-tap-on-grid approximation assumes that the largest on-grid tap of the output from the SFFT or DOA method of any subsequent iteration and the largest neighbouring on-grid tap of the largest on-grid tap are the closest approximations of the response of the path of that subsequent iteration. The delay- Doppler coordinate pair of any subsequent iteration accordingly comprises the delay-Doppler coordinate pair of the largest on-grid tap from the output of the SFFT or DOA method of that iteration and the delay-Doppler coordinate pair of the largest neighbouring on-grid tap of the largest on-grid tap. As the path influence of the path of any previous iteration has been removed in the updated time-frequency response,^of the channel 130 in each subsequent iteration, the largest on-grid tap in step 806 of each iteration is different from that of any previous iteration. Similarly, the coefficients for the delay-Doppler coordinate of any subsequent iteration can be determined in the same way as the coefficients for the delay-Doppler coordinate pair of the first iteration were determined, except the number of paths ^^ is set to the number of iterations so that the estimated transfer function of channel 130 is constructed based on the delay-Doppler coordinate pairs of the present and all previous iterations. It is important to note that in step 808 of each iteration equation (30) uses the same time-frequency response of channel 130 determined at step 802 for the termIn one implementation, each subsequent iteration of determining the coefficients at step 808 comprises updating the coefficients of previous iterations.

[0153] At step 816, the channel estimator 510 generates an estimate of the time-frequency response of channel 130 based on the delay-Doppler coordinate pairs and corresponding coefficients from all iterations. In some implementations, the generating comprises generating a joint time-frequency response for each time segment based on the delay-Doppler coordinate pairs and coefficients from all iterations of that time segment according to equation (27) and 43240768_1:CHPconcatenating the joint time-frequency response of each time segment according to equation (7). The method 600 ends at step 816.

[0154] As the delay-Doppler coordinate pair of each iteration is determined based on an updated time frequency response of the channel 130 which has excluded the time frequency path responses of previous paths, each path is estimated independently with reduced inter-path interference.

[0155] By dividing the received OFDM frame into time segments and independently estimating coefficients and generating time-frequency response for each time segment, the error variation over the frame is limited. The addition of the phase shift errorreduces the estimation error further by minimising the estimation error in the centre of each segment.

[0156] The estimate of the time-frequency response of channel 130 is provided to the channel equaliser 512.

[0157] The channel equaliser 512 is configured to inverse the estimate of time-frequency response of channel 130 and convolute the received data symbols with the inversed estimate of the time-frequency response of channel 130 to recover the transmitted data symbols. The channel equaliser 512 can apply a direct inverse or an equalisation method such as Minimum Mean Squared Error (MMSE) equalization or the like.

[0158] The P / S converter 320 and channel decoder 124 are the same as the P / S converter 320 and channel decoder 124 of the communication system 100 discussed above with reference to Figs.1 through 3. The P / S converter converts the equalised data symbols from parallel to a serial sequence ^^^^^^^^^ which is then de-mapped into bit sequences ^^̂^^^^^^. The bit sequences ^^̂^^^^^^ can be used to perform a best guest of the transmitted bits, or to provide tentative decisions as the input to the channel decoder 124.

[0159] The channel decoder 124, source decoder 126, and sink 128 are the same as the channel decoder 124, source decoder 126, and sink 128 of the receiver 120 discussed above with refence to Fig.1. Computer Description 43240768_1:CHP

[0160] Figs.9A and 9B depict a general-purpose computer system 900, upon which the transmitter 110 (and its corresponding components) or the receiver 420 (and its corresponding components) described can be practiced.

[0161] As seen in Fig.9A, the computer system 900 includes: a computer module 901; input devices such as a keyboard 902, a mouse pointer device 903, a scanner 926, a camera 927, and a microphone 980; and output devices including a printer 915, a display device 914 and loudspeakers 917. An external Modulator-Demodulator (Modem) transceiver device 916 may be used by the computer module 901 for communicating to and from a communications network 920 via a connection 921. The communications network 920 may be a wide-area network (WAN), such as the Internet, a cellular telecommunications network, or a private WAN. Where the connection 921 is a telephone line, the modem 916 may be a traditional “dial-up” modem. Alternatively, where the connection 921 is a high capacity (e.g., cable) connection, the modem 916 may be a broadband modem. A wireless modem may also be used for wireless connection to the communications network 920.

[0162] The computer module 901 typically includes at least one processor unit 905, and a memory unit 906. For example, the memory unit 906 may have semiconductor random access memory (RAM) and semiconductor read only memory (ROM). The computer module 901 also includes a number of input / output (I / O) interfaces including: an audio-video interface 907 that couples to the video display 914, loudspeakers 917 and microphone 980; an I / O interface 913 that couples to the keyboard 902, mouse 903, scanner 926, camera 927 and optionally a joystick or other human interface device (not illustrated); and an interface 908 for the external modem 916 and printer 915. In some implementations, the modem 916 may be incorporated within the computer module 901, for example within the interface 908. The computer module 901 also has a local network interface 911, which permits coupling of the computer system 900 via a connection 923 to a local-area communications network 922, known as a Local Area Network (LAN). As illustrated in Fig.9A, the local communications network 922 may also couple to the wide network 920 via a connection 924, which would typically include a so- called “firewall” device or device of similar functionality. The local network interface 911 may comprise an Ethernet circuit card, a Bluetooth®wireless arrangement or an IEEE 802.11 wireless arrangement; however, numerous other types of interfaces may be practiced for the interface 911. 43240768_1:CHP

[0163] The I / O interfaces 908 and 913 may afford either or both of serial and parallel connectivity, the former typically being implemented according to the Universal Serial Bus (USB) standards and having corresponding USB connectors (not illustrated). Storage devices 909 are provided and typically include a hard disk drive (HDD) 910. Other storage devices such as a floppy disk drive and a magnetic tape drive (not illustrated) may also be used. An optical disk drive 912 is typically provided to act as a non-volatile source of data. Portable memory devices, such optical disks (e.g., CD-ROM, DVD, Blu-ray DiscTM), USB-RAM, portable, external hard drives, and floppy disks, for example, may be used as appropriate sources of data to the system 900.

[0164] The components 905 to 913 of the computer module 901 typically communicate via an interconnected bus 904 and in a manner that results in a conventional mode of operation of the computer system 900 known to those in the relevant art. For example, the processor 905 is coupled to the system bus 904 using a connection 918. Likewise, the memory 906 and optical disk drive 912 are coupled to the system bus 904 by connections 919. Examples of computers on which the described arrangements can be practised include IBM-PC’s and compatibles, Sun Sparcstations, Apple MacTMor like computer systems.

[0165] The methods performed by the channel estimator 510 may be implemented using the computer system 900 (when implemented as the receiver 420) wherein the processes of Figs.6 and 8, described above, may be implemented as one or more software application programs 933 executable within the computer system 900. In particular, the steps of methods 600 and 800 of Figs.6 and 8 are effected by instructions 931 (see Fig.9B) in the software 933 that are carried out within the computer system 900. The software instructions 931 may be formed as one or more code modules, each for performing one or more particular tasks. The software may also be divided into two separate parts, in which a first part and the corresponding code modules performs the methods described above and a second part and the corresponding code modules manage a user interface between the first part and the user. Similarly, other components may be implemented using the computer system 900 as described above.

[0166] The software may be stored in a computer readable medium, including the storage devices described below, for example. The software is loaded into the computer system 900 from the computer readable medium, and then executed by the computer system 900. A computer readable medium having such software or computer program recorded on the computer 43240768_1:CHPreadable medium is a computer program product. The use of the computer program product in the computer system 900 (either implemented as the transmitter 210 or the receiver 220) preferably effects an advantageous apparatus for wireless communication.

[0167] The software 933 is typically stored in the HDD 910 or the memory 906. The software is loaded into the computer system 900 from a computer readable medium, and executed by the computer system 900. Thus, for example, the software 933 may be stored on an optically readable disk storage medium (e.g., CD-ROM) 925 that is read by the optical disk drive 912. A computer readable medium having such software or computer program recorded on it is a computer program product. The use of the computer program product in the computer system 900 (either implemented as the transmitter 210 or the receiver 220) preferably effects an apparatus for wireless communication.

[0168] In some instances, the application programs 933 may be supplied to the user encoded on one or more CD-ROMs 925 and read via the corresponding drive 912, or alternatively may be read by the user from the networks 920 or 922. Still further, the software can also be loaded into the computer system 900 from other computer readable media. Computer readable storage media refers to any non-transitory tangible storage medium that provides recorded instructions and / or data to the computer system 900 for execution and / or processing. Examples of such storage media include floppy disks, magnetic tape, CD-ROM, DVD, Blu-rayTMDisc, a hard disk drive, a ROM or integrated circuit, USB memory, a magneto-optical disk, or a computer readable card such as a PCMCIA card and the like, whether or not such devices are internal or external of the computer module 901. Examples of transitory or non-tangible computer readable transmission media that may also participate in the provision of software, application programs, instructions and / or data to the computer module 901 include radio or infra-red transmission channels as well as a network connection to another computer or networked device, and the Internet or Intranets including e-mail transmissions and information recorded on Websites and the like.

[0169] The second part of the application programs 933 and the corresponding code modules mentioned above may be executed to implement one or more graphical user interfaces (GUIs) to be rendered or otherwise represented upon the display 914. Through manipulation of typically the keyboard 902 and the mouse 903, a user of the computer system 900 and the application may manipulate the interface in a functionally adaptable manner to provide controlling commands 43240768_1:CHPand / or input to the applications associated with the GUI(s). Other forms of functionally adaptable user interfaces may also be implemented, such as an audio interface utilizing speech prompts output via the loudspeakers 917 and user voice commands input via the microphone 980.

[0170] Fig.9B is a detailed schematic block diagram of the processor 905 and a “memory” 934. The memory 934 represents a logical aggregation of all the memory modules (including the HDD 909 and semiconductor memory 906) that can be accessed by the computer module 901 in Fig.9A.

[0171] When the computer module 901 is initially powered up, a power-on self-test (POST) program 950 executes. The POST program 950 is typically stored in a ROM 949 of the semiconductor memory 906 of Fig.9A. A hardware device such as the ROM 949 storing software is sometimes referred to as firmware. The POST program 950 examines hardware within the computer module 901 to ensure proper functioning and typically checks the processor 905, the memory 934 (909, 906), and a basic input-output systems software (BIOS) module 951, also typically stored in the ROM 949, for correct operation. Once the POST program 950 has run successfully, the BIOS 951 activates the hard disk drive 910 of Fig.9A. Activation of the hard disk drive 910 causes a bootstrap loader program 952 that is resident on the hard disk drive 910 to execute via the processor 905. This loads an operating system 953 into the RAM memory 906, upon which the operating system 953 commences operation. The operating system 953 is a system level application, executable by the processor 905, to fulfil various high level functions, including processor management, memory management, device management, storage management, software application interface, and generic user interface.

[0172] The operating system 953 manages the memory 934 (909, 906) to ensure that each process or application running on the computer module 901 has sufficient memory in which to execute without colliding with memory allocated to another process. Furthermore, the different types of memory available in the system 900 of Fig.9A must be used properly so that each process can run effectively. Accordingly, the aggregated memory 934 is not intended to illustrate how particular segments of memory are allocated (unless otherwise stated), but rather to provide a general view of the memory accessible by the computer system 900 and how such is used. 43240768_1:CHP

[0173] As shown in Fig.9B, the processor 905 includes a number of functional modules including a control unit 939, an arithmetic logic unit (ALU) 940, and a local or internal memory 948, sometimes called a cache memory. The cache memory 948 typically includes a number of storage registers 944 - 946 in a register section. One or more internal busses 941 functionally interconnect these functional modules. The processor 905 typically also has one or more interfaces 942 for communicating with external devices via the system bus 904, using a connection 918. The memory 934 is coupled to the bus 904 using a connection 919.

[0174] The application program 933 includes a sequence of instructions 931 that may include conditional branch and loop instructions. The program 933 may also include data 932 which is used in execution of the program 933. The instructions 931 and the data 932 are stored in memory locations 928, 929, 930 and 935, 936, 937, respectively. Depending upon the relative size of the instructions 931 and the memory locations 928-930, a particular instruction may be stored in a single memory location as depicted by the instruction shown in the memory location 930. Alternately, an instruction may be segmented into a number of parts each of which is stored in a separate memory location, as depicted by the instruction segments shown in the memory locations 928 and 929.

[0175] In general, the processor 905 is given a set of instructions which are executed therein. The processor 905 waits for a subsequent input, to which the processor 905 reacts to by executing another set of instructions. Each input may be provided from one or more of a number of sources, including data generated by one or more of the input devices 902, 903, data received from an external source across one of the networks 920, 902, data retrieved from one of the storage devices 906, 909 or data retrieved from a storage medium 925 inserted into the corresponding reader 912, all depicted in Fig.9A. The execution of a set of the instructions may in some cases result in output of data. Execution may also involve storing data or variables to the memory 934.

[0176] The disclosed arrangements use input variables 954, which are stored in the memory 934 in corresponding memory locations 955, 956, 957. The disclosed arrangements produce output variables 961, which are stored in the memory 934 in corresponding memory locations 962, 963, 964. Intermediate variables 958 may be stored in memory locations 959, 960, 966 and 967. 43240768_1:CHP

[0177] Referring to the processor 905 of Fig.9B, the registers 944, 945, 946, the arithmetic logic unit (ALU) 940, and the control unit 939 work together to perform sequences of micro- operations needed to perform “fetch, decode, and execute” cycles for every instruction in the instruction set making up the program 933. Each fetch, decode, and execute cycle comprises:

[0178] a fetch operation, which fetches or reads an instruction 931 from a memory location 928, 929, 930;

[0179] a decode operation in which the control unit 939 determines which instruction has been fetched; and

[0180] an execute operation in which the control unit 939 and / or the ALU 940 execute the instruction.

[0181] Thereafter, a further fetch, decode, and execute cycle for the next instruction may be executed. Similarly, a store cycle may be performed by which the control unit 939 stores or writes a value to a memory location 932.

[0182] Each step or sub-process in the processes of Figs.6 and 8 is associated with one or more segments of the program 933 and is performed by the register section 944, 945, 947, the ALU 940, and the control unit 939 in the processor 905 working together to perform the fetch, decode, and execute cycles for every instruction in the instruction set for the noted segments of the program 933.

[0183] The methods performed by the transmitter 110 or the receiver 420 may alternatively be implemented in dedicated hardware such as one or more integrated circuits performing the functions or sub functions described above, in particular the functions or sub functions of Figs.8 and 9. Such dedicated hardware may include graphic processors, digital signal processors, FPGA and ASCI chipsets, or one or more microprocessors and associated memories.

[0184] Approximating the response of each path in the multipath channel 130 to a fraction of the ‘on-grid’ taps in the delay-Doppler domain, the above described methods and apparatus allow for simplification of channel estimation while maintaining the sparsity of the channel. The “two- tap-on-grid” approximation additionally improves estimation accuracy by capturing fractional frequency components while maintaining the sparsity of the channel. 43240768_1:CHP

[0185] Additionally, by generating path coefficients independently for each segment, the accumulated channel estimation error can be reduced, increasing the accuracy of the estimation.

[0186] The arrangements described are applicable to the wireless communication and radar industry.

[0187] Although specific embodiments of the invention are illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternative and / or equivalent implementations exist. It should be appreciated that the exemplary embodiment or exemplary embodiments are examples only and are not intended to limit the scope, applicability, or configuration in any way. Rather, the foregoing summary and detailed description will provide those skilled in the art with a convenient road map for implementing at least one exemplary embodiment, it being understood that various changes may be made in the function and arrangement of elements described in an exemplary embodiment without departing from the scope as set forth in the appended claims and their legal equivalents. Generally, this application is intended to cover any adaptations or variations of the specific embodiments discussed herein. 43240768_1:CHP

Claims

CLAIMS 1. A method of estimating channel parameters of a channel, the method comprising: determining a time-frequency response of the channel based on pilot symbols contained in a received signal; dividing the time-frequency response of the channel into time segments; determining a first delay-Doppler coordinate pair based on the time-frequency response of the channel; estimating, for each time segment, a first coefficient, based on the time-frequency response of the channel of the respective time segments and the first delay-Doppler coordinate pair; generating a time-frequency response for the first delay-Doppler coordinate pair based on the first coefficient; updating the time-frequency response of the channel by subtracting the time-frequency response of the channel with the time-frequency response for the first delay-Doppler coordinate pair; determining a second delay-Doppler coordinate pair based on the updated time-frequency response of the channel; estimating, for each time segment, a second coefficient, based on the time-frequency response of the channel of the respective time segments and the first and second delay-Doppler coordinate pairs; and generating an estimate of the time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs and the first and second coefficients.

2. The method of claim 1, wherein the generating an estimate of the time-frequency response of the channel comprises: generating a joint time-frequency response for each time segment based on the first and second delay-Doppler coordinate pairs and the first and second coefficients of each time segment; and concatenating the joint time-frequency response of each time segment.

3. The method of claim 1 or 2, wherein the first delay-Doppler coordinate pair comprises a) delay-Doppler coordinate pair of a first component of the time-frequency response of the channel and delay-Doppler coordinate pair of a second component of the time-frequency response of the channel, wherein the first component is the largest component of the time-frequency response of 42780798_2the channel with an integer Doppler coordinate and the second component is the largest neighbouring component of the first component with an integer Doppler coordinate, or b) delay- Doppler coordinate pair of the largest component of the time-frequency response of the channel.

4. The method of any one of claims 1-3, wherein the second delay-Doppler coordinate pair comprises a) delay-Doppler coordinate pair of a first component of the updated time-frequency response of the channel and delay-Doppler coordinate pair of a second component of the time- frequency response of the channel, wherein the first component is the largest component of the updated time-frequency response of the channel with an integer Doppler coordinate and the second component is the largest neighbouring component of the first component with an integer Doppler, and b) delay-Doppler coordinate pair of the largest component of the updated time- frequency response of the channel with an integer Doppler coordinate.

5. The method of any one of claims 1-4, wherein estimating the first coefficient comprises: constructing, for each time segment, a first estimated time-frequency response of the channel based on the first delay-Doppler coordinate pair; and applying a first phase shift approximation to the first estimated time-frequency response of the channel of each time segment, the first phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time-frequency response of the channel of said time segment and the first estimated time-frequency response of the channel of said time segment.

6. The method of any one of claims 1-5, wherein estimating the second coefficient comprises: constructing, for each time segment, a second estimated time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs; applying a second phase shift approximation to the second estimated time-frequency response of the channel of each time segment, the second phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time-frequency response of the channel of said time segment and the second estimated time-frequency response of the channel of said time segment; and updating the first coefficient.

7. The method of any one of claims 1-6, wherein the coefficients are estimated using least squares regression. 42780798_28. The method of any one of claims 1-7, wherein the first or second delay-Doppler coordinate pair is determined using a symplectic finite fourier transform.

9. The method of any one of claims 1-7, wherein the first or second delay-Doppler coordinate pair is determined using a Direction of Arrival method.

10. The method of claim 10, wherein the Direction of Arrival method is Multiple Signal Classification (MUSIC) algorithm.

11. A communication apparatus comprising an Orthogonal Frequency Division Multiplexing (OFDM) demodulator, the OFDM demodulator configured to perform operations comprising: determining a time-frequency response of the channel based on pilot symbols contained in a received signal; dividing the time-frequency response of the channel into time segments; determining a first delay-Doppler coordinate pair based on the time-frequency response of the channel; estimating, for each time segment, a first coefficient, based on the time-frequency response of the channel of the respective time segments and the first delay-Doppler coordinate pair; generating a time-frequency response for the first delay-Doppler coordinate pair based on the first coefficient; updating the time-frequency response of the channel by subtracting the time-frequency response of the channel with the time-frequency response for the first delay-Doppler coordinate pair; determining a second delay-Doppler coordinate pair based on the updated time-frequency response of the channel; estimating, for each time segment, a second coefficient, based on the time-frequency response of the channel of the respective time segments and the first and second delay-Doppler coordinate pairs; and generating an estimate of the time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs and the first and second coefficients.

12. The apparatus of claim 11, wherein the OFDM demodulator is configured to: 42780798_2generate a joint time-frequency path response for each time segment based on the first and second delay-Doppler coordinate pairs and the first and second coefficients of each time segment; and concatenate the joint time-frequency path response of each time segment.

13. The apparatus of any one of claims 11 or 12, wherein the first delay-Doppler coordinate pair comprises a) delay-Doppler coordinate pair of a first component of the time-frequency response of the channel and delay-Doppler coordinate pair of a second component of the time- frequency response of the channel, wherein the first component is the largest component of the time-frequency response of the channel with an integer Doppler coordinate and the second component is the largest neighbouring component of the first component with an integer Doppler coordinate, or b) delay-Doppler coordinate pair of the largest component of the time-frequency response of the channel.

14. The apparatus of any one of claims 11-13, wherein the second delay-Doppler coordinate pair comprises a) delay-Doppler coordinate pair of a first component of the updated time- frequency response of the channel and delay-Doppler coordinate pair of a second component of the time-frequency response of the channel, wherein the first component is the largest component of the updated time-frequency response of the channel with an integer Doppler coordinate and the second component is the largest neighbouring component of the first component with an integer Doppler, and b) delay-Doppler coordinate pair of the largest component of the updated time-frequency response of the channel with an integer Doppler coordinate.

15. The apparatus of any one of claims 11-14, wherein the OFDM demodulator is configured to: construct, for each time segment, a first estimated time-frequency response of the channel based on the first delay-Doppler coordinate pair; and apply a first phase shift approximation to the first estimated time-frequency response of the channel of each time segment, the first phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time-frequency response of the channel of said time segment and the first estimated time-frequency response of the channel of said time segment. 42780798_216. The apparatus of any one of claims 11-15, wherein the OFDM demodulator is configured to: construct, for each time segment, a second estimated time-frequency response of the channel based on the first and second delay-Doppler coordinate pairs; and apply a second phase shift approximation to the second estimated time-frequency response of the channel of each time segment, the second phase shift approximation of each time segment minimises normalised mean square error (NMSE) between the time-frequency response of the channel of said time segment and the second estimated time-frequency response of the channel of said time segment; wherein the estimating of the second coefficient updates the first coefficient.

17. The apparatus of any one of claims 11-16, wherein the coefficients are estimated using least squares regression.

18. The apparatus of any one of claims 11-17, wherein the first or second delay-Doppler coordinate pair is determined using a symplectic finite fourier transform.

19. The apparatus of any one of claims 11-17, wherein the first or second delay-Doppler coordinate pair is determined using a Direction of Arrival method.

20. The apparatus of claim 19, wherein the Direction of Arrival method is Multiple Signal Classification (MUSIC) algorithm. 42780798_2

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