Low-complexity OTFS multi-antenna detection algorithm

Abstract

The invention relates to a low-complexity OTFS multi-antenna detection algorithm, which belongs to the field of wireless communication, and is characterized in that a transmitting signal of a transmitting end reaches a multi-antenna receiving end through a time-varying multipath channel based on an orthogonal time-frequency-space OTFS modulation system; preliminarily separating received signals from different angles of arrival (AoA) at a receiving end by using a multi-antenna array and beam forming; then, starting from the angles of a time delay-Doppler (DD) domain and a low-complexity delay-time (DT) domain, according to composition of signals in beam forming branches, performing coherent combination on multipath components in each branch through maximum ratio combination (MRC), meanwhile, collecting all branches by the MRC and performing coherent combination, and performing continuous iteration to obtain an optimal estimated value; the result shows that the bit error rate performance of the provided low-complexity DT domain multi-antenna Bi-MRC detection is obviously superior to that of the existing multi-antenna MP-MRC detection, and the number of iterations required for achieving the optimal value and the time consumption of single iteration are greatly reduced.

Description

Technical Field

[0001] The invention belongs to the field of wireless communications and relates to a low-complexity OTFS multi-antenna detection algorithm. Background Art

[0002] In recent years, with the development of wireless communication technology, emerging communication modes such as Internet of Vehicles, high-speed railways, low-Earth orbit satellites and other high-speed scenarios have put forward new requirements for modulation waveforms and schemes. Traditional Orthogonal Frequency Division Multiplexing (OFDM) modulation will cause serious inter-carrier interference (ICI) in such high-mobility environments and is no longer applicable. Orthogonal Time Frequency Space (OTFS) is a two-dimensional modulation technology that modulates data information in the delay-Doppler (DD) domain, turning complex time-frequency (TF) domain channels into sparse DD domain channels. A large number of studies have shown that OTFS can achieve significant performance improvements over OFDM in high-mobility environments.

[0003] Signal detection technology is an important part of communication systems. However, most existing studies assume that the DD domain channel is sparse. In some scenarios with abundant scatterers, such as urban vehicle networks and drone swarms, the channel sparsity may not be guaranteed. The relative motion between transceivers in these scenarios will generate a large number of multipath signal components with Doppler frequency shift, which will reduce the channel sparsity and increase the complexity of detection. To this end, the existing multi-antenna-based joint message passing-maximum ratio combining (MP-MRC) detection algorithm combines multi-antenna reception and beamforming to ensure the sparsity of the channel corresponding to each branch, modify the MP algorithm, and combine MRC to obtain multi-antenna diversity gain. The results show that the error performance and convergence speed of the algorithm are improved compared with the MP algorithm. However, the MP algorithm itself still requires a certain number of iterations, and a large amount of computational complexity will be generated when the modulation scheme is 64QAM or higher. Summary of the invention

[0004] In view of this, the present invention provides a low-complexity OTFS multi-antenna detection algorithm to reduce the computational complexity and improve the convergence speed.

[0005] The above method may specifically include:

[0006] S1, based on the orthogonal time-frequency-space OTFS modulation system, the transmitting signal of the transmitter reaches the multi-antenna receiving end through the time-varying multipath channel;

[0007] S2, the receiving end passes the received signal through a multi-antenna array and a beamforming network to preliminarily separate multiple parallel branch signals with different angles of arrival (AoA);

[0008] S3, performing OTFS demodulation on each parallel branch signal to obtain a delay-Doppler (DD) domain or a time-delay (DT) domain signal;

[0009] S4. The DD domain signal or DT domain signal after demodulation of each parallel branch is passed through two dual maximum ratio combining (Bi-MRC) detectors designed in this patent for the corresponding domain, and the optimal estimation value is obtained by continuous iteration.

[0010] In S1 described in the present invention, the above-mentioned time-varying multipath channel includes: the time-varying property of the channel caused by the relative motion of the transmitting and receiving ends; and the time-varying property of the channel will bring about the Doppler frequency shift of the channel and cause the inter-carrier interference of the signal; the multipath of the channel causes the Doppler frequency shift of the channel to be very large; and the multipath effect of the channel causes the inter-symbol interference of the signal.

[0011] In S2 described in the present invention, the above-mentioned receiving end passes the received signal through a multi-antenna array and a beamforming network, including: the multipath time domain signal containing the incoming waves at various azimuth angles of the channel arriving at the receiving antenna array passes through the beamforming network; the beamforming network only receives the signal coming from the azimuth angle of the channel, and suppresses the incoming signals from other directions; and after passing through the beamforming network, multiple parallel branches with enhanced channel sparsity are formed.

[0012] In S3 described in the present invention, the above-mentioned parallel branch time domain signals are subjected to OTFS demodulation to obtain the delay-Doppler (DD) domain or time-delay (DT) domain symbol signals of each parallel branch, including: each parallel branch time domain signal is converted into a corresponding DT domain signal by row-column conversion; and each parallel branch time domain signal is converted into a corresponding DD domain signal by discrete Zak transform.

[0013] In S4 described in the present invention, the DD domain signals after demodulation of the above-mentioned parallel branches are passed through the DD domain dual maximum ratio combining (Bi-MRC) detector designed by this patent, including: using MRC to coherently combine the multipath components contained in the DD domain signals of each parallel branch; then, all branches are collected by MRC and then coherently combined; and the optimal estimate is obtained by continuous iteration.

[0014] In S4 of the present invention, the DT domain signals demodulated by the above-mentioned parallel branches are passed through the low-complexity DT domain Bi-MRC detector designed by this patent, including: the DD domain input-output relationship of each parallel branch is converted into the product of the matrix and the vector in the DD domain by redundant operation into the multiplication between elements in the DT domain; the multipath components contained in the DT domain signal of each parallel branch are coherently combined using MRC; then, all branches are collected by MRC and then coherently combined; and the optimal estimate is obtained by continuous iteration.

[0015] According to simulation verification, the low-complexity DT domain multi-antenna Bi-MRC detection bit error rate performance proposed in the present invention is significantly better than the existing multi-antenna MP-MRC detection, and the number of iterations required to reach the optimal value and the time consumption of a single iteration are greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to make the purpose, technical solution and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0017] Figure 1 This is a flow chart of a low-complexity OTFS multi-antenna detection algorithm according to an embodiment of the present invention;

[0018] Figure 2 This is a block diagram of an OTFS multi-antenna receiver according to an embodiment of the present invention;

[0019] Figure 3 A comparison diagram of the bit error rate performance between Bi-MRC and MP-MRC according to an embodiment of the present invention;

[0020] Figure 4 A comparison diagram of the average number of iterations of Bi-MRC and MP-MRC according to an embodiment of the present invention;

[0021] Figure 5 This is a comparison chart of the bit error rates of the Bi-MRC algorithm at different moving speeds according to an embodiment of the present invention.

[0022] Figure 6 This is a comparison chart of the bit error rates of the Bi-MRC algorithm under different system parameters described in an embodiment of the present invention. DETAILED DESCRIPTION

[0023] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0024] Figure 1The present invention provides a low-complexity OTFS multi-antenna detection algorithm design flow chart for some embodiments of the present invention. The present invention includes the following steps: S1: Based on the orthogonal time-frequency-space OTFS modulation system, the transmission signal of the transmitter reaches the multi-antenna receiving end through the time-varying multipath channel; S2: The receiving end passes the received signal through the multi-antenna array and the beamforming network to preliminarily separate multiple parallel branch signals with different arrival angles (AoA); S3: Each parallel branch signal is OTFS demodulated to obtain a delay-Doppler (DD) domain or time-delay (DT) domain symbol signal; S4: The DD domain signal or DT domain signal after demodulation of each parallel branch is passed through two dual maximum ratio combining (Bi-MRC) detectors designed for the corresponding domains in this patent, and the optimal estimate is obtained by continuous iteration.

[0025] Figure 2 The OTFS multi-antenna receiver block diagram of some embodiments of the present invention; wherein, at the transmitting end, the mapping table The complex information symbols (e.g., QAM symbols) in are placed on a two-dimensional delay-Doppler grid of dimension M′N to generate a delay-Doppler (DD) domain OTFS frame. Here, M represents the dimension of the delay domain, and N represents the dimension of the Doppler domain. The duration is T f =NT OTFS frame occupies a bandwidth of B = f s =1 / T s =MDf, where f s represents the Nyquist sampling rate, T s is the Nyquist sampling interval, T represents the OTFS block duration, and Df = 1 / T is the subcarrier spacing. It is assumed that the time-domain OTFS signal is critically sampled at the transmitter.

[0026] The DD domain OTFS frame X is mapped to the time domain s(t) through an inverse symplectic finite Fourier transform (ISFFT), followed by a Heisenberg transform. This process of converting the DD domain frame to a time domain signal is equivalent to an inverse discrete Zak transform (IDZT) modulator. Where q = 0, L, MN-1. Assuming that the transmitter uses a rectangular pulse, the time domain sampling vector s can be written as

[0027]

[0028] in The time-delay (DT) matrix representation of the OTFS frame.

[0029] make Representation Matrix The transpose of the mth row. Then, due to the interleaving of rows and columns, the elements of the time domain vector are the same as the DT domain vector The relationship between

[0030]

[0031] The discrete time domain samples s[q] are converted into continuous time domain signals s(t) by a digital-to-analog converter and transmitted through a multipath time-varying high mobility channel.

[0032] according to Figure 2 As shown, it is assumed that the base station is configured with N r The ULA with 1 antennas and a high-mobility multipath channel consists of L propagation paths, each with a delay and Doppler shift n. i , where i=0,...,L-1. a The expression of the DD domain channel response of the high mobility channel corresponding to antennas can be written as

[0033]

[0034] where h a,i represents the channel gain of the ath antenna and the i-th path, a=1,L,N r Then, the time domain received signal r corresponding to the ath antenna at the receiving end is a (t) is expressed as

[0035]

[0036] Where w(t) is the additive noise in the time domain, θ i represents the AoA associated with the ith path. Furthermore, the Doppler shift of the ith path can be expressed as v i =v′f c cos(β i ) / c, where v′, f c and c represent the vehicle speed, carrier frequency and light speed respectively; β i is randomly distributed between 0 and π, and is related to the vehicle's moving direction and the angle of departures (AoD, angle of departures) of the i-th path. In addition, represents the phase shift at the ath antenna. Since this paper adopts ULA, the entire antenna array has an AoA of θ i The steering vector at can be expressed as

[0037]

[0038] Where λ is the carrier wavelength and d is the spacing between antenna elements. Then Expressed as

[0039]

[0040] Next, the receiving end passes the received signal through a multi-antenna array and a beamforming network to preliminarily separate multiple parallel branch signals with different angles of arrival (AoA).

[0041] According to the Nyquist sampling theorem, the baseband equivalent representation of the time domain OTFS signal s(t) (band limited to B = 1 / T s )for

[0042]

[0043] According to formula (7), let l i =MDft i and k i =NTv i Denote the delay tap and Doppler tap respectively. a (t) at t = qT s Sampling is carried out at

[0044]

[0045] where q=0,...,MN-1. Next, let represents the channel tap, then equation (8) can be rewritten as

[0046]

[0047] The value range of p in equation (9) depends on the sinc function. i ≥0,

[0048]

[0049] For non-integer delay l i , the sinc function will interfere with some adjacent delay taps.

[0050]

[0051] This paper assumes integer delay, that is, the case of using equation (10). In this case, equation (9) can be rewritten as

[0052]

[0053] where g a (qT s ,p) represents the ath receiving antenna, and the sampling time is qT s , the discrete-time baseband DT domain channel response at the p-th tap is expressed as

[0054]

[0055] Finally, the received signal matrix of the entire antenna array at the receiving end can be obtained

[0056] Next, the multi-antenna received signals will pass through the beamforming network to separate signals with different AoA.

[0057] As mentioned above, since Doppler shift is closely related to multipath, the high spatial resolution provided by the antenna array can be used to approximately separate the Doppler shift component in the spatial domain. To this end, the goal of beamforming is to maintain only the signal from one desired direction while suppressing the signals from other directions. This paper adopts a matched filter (MF, matchedfilter) beamformer. Then, θ b Direction weight vector It is determined by the steering vector in equation (5), that is,

[0058]

[0059] Where b = 0, L, B-1 is the beamforming branch index, Nr represents the number of receiving antennas. Note that the number of beamforming branches B is proportional to the number of receiving antennas. Nr are not equal. Next, after passing through the beamforming network, it moves toward θ b The received signal in the direction can be expressed as

[0060]

[0061] Among them (×) * represents the conjugate operation. Then, the DT domain signal Convert to DD domain through discrete Zak transform (DZT, DiscreteZakTransform)

[0062]

[0063] Let vector express The transpose of the mth row. According to formula (16), we can write

[0064]

[0065] Where m=0,...,M-1, n=0,...,N-1.

[0066] Next, each parallel branch signal is demodulated by OTFS to obtain a delay-Doppler (DD) domain or a time-delay (DT) domain symbol signal.

[0067] Using equations (2), (15) and (17), let r a [q] = r a (qT s ), we can get the input-output relationship of the DT domain on the b-th beamforming branch as

[0068]

[0069] where m = 0, ..., M-1, n = 0, ..., N-1, and

[0070]

[0071] represents the DT domain channel response. The second operation of equation (19) is to convert q in equation (13) into m+nM. In addition,

[0072]

[0073] represents the DT domain noise vector, and

[0074] make represents the DT domain receive vector on the bth beamforming branch, represents the DT domain transmitted information vector. Then equation (18) can be written in vector form as

[0075]

[0076] in Represents the Hadamard product operation.

[0077] For the DT domain receiving vector in equation (21), Perform N-point FFT to obtain the corresponding DD domain receive vector

[0078]

[0079] in is the DD-domain noise vector at the mth delay on the bth beamforming branch. In addition, is the discrete Doppler spread vector experienced by all symbols in the Doppler domain at the mpth delay in the OTFS frame of M′N. It can be written as

[0080]

[0081] By defining the circulant matrix The circular convolution operation in the DD domain in equation (22) can be simplified to matrix and vector multiplication, that is,

[0082]

[0083] Therefore, the input-output relationship in equation (22) can be rewritten as

[0084]

[0085] Next, the DD domain signal or DT domain signal demodulated by each parallel branch is passed through two dual maximum ratio combining (Bi-MRC) detectors designed in this patent for the corresponding domain, and the optimal estimation value is obtained by continuous iteration.

[0086] For the DD domain Bi-MRC detection algorithm, first, we can decompose equation (26) to obtain

[0087]

[0088] in b=0,...,B-1.

[0089] To get x m The estimate (using indicates), in b=0,...,B-1.

[0090] Using iterative MRC detection, assuming is obtained from the previous iteration. Then the estimated According to formula (27), we can get

[0091]

[0092] Then, the MRC algorithm is used to coherently combine the multipath components in the beamforming branches, and the MRC algorithm collects all branches and coherently combines them.

[0093]

[0094] in

[0095]

[0096] The output is then passed through a QAM symbol demodulator (hard decision) to obtain estimates of the DD domain samples at the mth delay tap and the nth Doppler tap:

[0097]

[0098] where a j Indicates the QAM mapping table The elements in , and j=1,L,Q.

[0099] For the DT domain signal Bi-MRC detection algorithm, each Total values, each value needs to be calculated Secondary Circular Matrix and estimated information The multiplication between , then the total required However, the number of these multiplications can be reduced by performing redundant operations. is the i-th iteration Then, the estimated value of can be The estimate can be rewritten as

[0100]

[0101] in is the residual error of the received signal due to estimation at the i-th iteration, expressed as

[0102]

[0103] Observe formula (35), we can initialize The value of Then store and update it at each iteration to simplify the computation.

[0104]

[0105] This style (34) Each value of requires only one cyclic matrix and vector multiplication, for a total of only Compared with formula (28), Reduced to times, the computational complexity is significantly reduced. Here we initialize Next, substitute equation (34) into equation (32) and use equation (31) to obtain

[0106]

[0107] Substituting equation (37) into equation (30), we get

[0108]

[0109] in

[0110]

[0111] According to formula (23), by replacing the DD domain with formula (36) and And in formula (39) and The matrix and vector product operation between them is converted to element multiplication in the DT domain and To further reduce the computational complexity [9] ,in Represents the estimated information vector in the DT domain.

[0112] Using N-point IFFT on equation (38) we get

[0113]

[0114] in

[0115]

[0116] The DT domain estimated information vector can be obtained by using hard decision in the DD domain and then applying IFFT

[0117]

[0118] Or it can be obtained by using the weighted sum of hard decision and soft decision

[0119]

[0120] When ω = 1, it is a hard estimate, and when ω = 0, it is a soft estimate. The run ends when it no longer decreases or the maximum number of iterations is reached.

[0121] The following is a further description of the beneficial effects of the low-complexity DT domain Bi-MRC algorithm proposed in the present invention in combination with simulation experiments and results. The simulation tool for all simulation experiments is Matlab. Assume that the channel information is completely known, the channel Doppler frequency shift adopts the Jakes model, the antenna unit spacing is set to d = 0.5l, and the decision weight coefficient ω in formula (45) is 0.5. To avoid inter-frame interference, ZP is set at the end of each frame with a length of l ZP =M / 16, then the effective information position is M′=Ml ZP Assuming that AoA is randomly distributed in [0, p], other simulation parameters are shown in Table 1. Figure 3 , Figure 4 , Figure 5 and Figure 6 The results of the simulation test are shown in Figure 2. Figure 3 The bit error rate performance comparison between Bi-MRC and MP-MRC according to the embodiment of the present invention; Figure 4 Comparison of the average number of iterations of Bi-MRC and MP-MRC described in the embodiment of the present invention; Figure 5 It is the bit error rate of the Bi-MRC algorithm at different moving speeds described in the embodiment of the present invention. Figure 6It is the bit error rate of the Bi-MRC algorithm under different system parameters described in the embodiment of the present invention.

[0122] Table 1 Simulation parameters

[0123]

[0124] Figure 3 The following is a comparison of the bit error rate performance of Bi-MRC and MP-MRC described in some embodiments of the present invention: It shows the bit error rate performance comparison of the proposed DT domain Bi-MRC algorithm and the MP-MRC proposed in the literature [5] when the modulation scheme is 16QAM under different receiving antennas. When Nr=1, the two algorithms correspond to the MP and MRC algorithms respectively. The simulation results show that when Nr=2, the bit error rate performance of the proposed Bi-MRC algorithm is close to the performance of the MP-MRC algorithm when Nr=8; and when Nr=6 and Nr=8, the Bi-MRC algorithm is better than the MP-MRC algorithm when Nr=8 in BER=10 -4 The performance gains are approximately 8dB and 14dB respectively.

[0125] Figure 4 This is a comparison chart of the average number of iterations of Bi-MRC and MP-MRC according to some embodiments of the present invention: N is given. r When =8, the number of iterations of MP-MRC and DT domain Bi-MRC is compared. The results show that the number of iterations required by the proposed Bi-MRC algorithm in three different modulation modes is much smaller than that of the MP-MRC algorithm using 16QAM, and the average computational complexity is greatly reduced.

[0126] Figure 5 This is a comparison diagram of the bit error rate of the Bi-MRC algorithm at different mobile speeds according to some embodiments of the present invention: N r = 8, the BER performance of Bi-MRC detection in the DT domain of QPSK, 16QAM and 64QAM is compared when the terminal moving speed is 30, 120 and 500 km / h respectively. The results show that the BER performance gets better and better with the increase of the moving speed. This is because when the Doppler resolution of the system is constant, the higher the speed, the more Doppler paths the system can distinguish, thus obtaining more diversity gain and improving the BER performance.

[0127] Figure 6 This is a comparison chart of the bit error rate of the Bi-MRC algorithm under different system parameters according to some embodiments of the present invention: N r=8, and the BER performance comparison of Bi-MRC detection in DT domain for QPSK, 16QAM and 64QAM when N′M is 8×16, 16×32 and 64×64 respectively when the mobile speed is 500km / h. The results show that the detection performance is improved to a certain extent with the increase of N′M. This can be explained by the fact that the increase of N′M can increase the delay and Doppler resolution of the system, thereby resolving more DD domain channel paths, improving performance at the cost of increasing the amount of calculation.

[0128] The complexity of each iteration of the proposed low-complexity DT domain Bi-MRC algorithm will be analyzed from the perspective of complex multiplication. As shown in lines 7-18 of Algorithm 2, the complexity of each iteration of all symbols is calculated. and Total required Complex multiplication operations, where M′=Ml ZP In addition, calculate The hard decision part in needs to perform two Fourier transforms, and each symbol corresponds to 2Nlog2(N) complex multiplication operations. So each iteration requires a total of Complex multiplication operations, the complexity is The complexity of each iteration of the multi-antenna MP-MRC algorithm in reference [5] is Where S represents the sparsity of the DD domain channel matrix H, that is, the number of discrete DD domain paths; represents the order of the modulation scheme, for example, for QPSK, Table 2 Comparison of total computational complexity

[0129]

[0130] Table 2 compares the total complexity and computational effort of three different detection algorithms when M = 32, M′ = 30, N = 16, B = 5, P = 9, S = 5, and the modulation mode is 64QAM. Figure 3 , for MRC and Bi-MRC, the average number of iterations N iter Take it as 5; for MP-MRC, N iter Take it as 45. Combining Table 2 and Figure 2 Through comparison, it is found that the proposed DT domain multi-antenna Bi-MRC algorithm only requires a part of the additional computational effort compared to the single-antenna MRC algorithm to achieve a significant performance improvement; compared to the multi-antenna MP-MRC algorithm, the computational effort is reduced by two orders of magnitude, the iteration time is greatly reduced, and the performance is also improved to a certain extent.

[0131] The above description is only an example of the present invention and is not intended to limit the present invention. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A low-complexity OTFS multi-antenna detection algorithm. It is characterized by: The method comprises: S1, the transmission signal of the transmitter reaches the multi-antenna receiving end through the time-varying multipath channel; S2, the receiving end passes the received signal through a multi-antenna array and a beamforming network to preliminarily separate multiple parallel branch signals with different angles of arrival (AoA); S3, performing OTFS demodulation on each parallel branch signal to obtain a delay-Doppler (DD) domain or a time-delay (DT) domain symbol signal; S4. The DD domain signal or DT domain signal after demodulation of each parallel branch is passed through two dual maximum ratio combining (Bi-MRC) detectors designed in this patent for the corresponding domain, and the optimal estimation value is obtained by continuous iteration.

2. The low-complexity OTFS multi-antenna detection algorithm according to claim 1, characterized in that: The time-varying multipath channel in S1 includes: The channel time-variability caused by the relative motion of the transmitting and receiving ends; and the channel time-variability will bring about the Doppler frequency shift of the channel and cause the inter-carrier interference of the signal; the multipath of the channel causes the Doppler frequency shift of the channel to be very large; and the multipath effect of the channel causes the inter-symbol interference of the signal.

3. The low-complexity OTFS multi-antenna detection algorithm according to claim 1, characterized in that: The receiving end in S2 receives the signal through a multi-antenna array and a beamforming network, including: The multipath time domain signals arriving at the receiving antenna array, which contain the waves from all azimuth angles of the channel, pass through the beamforming network; the beamforming network only receives the signals from the azimuth angle of the channel, and suppresses the signals from other directions; and after passing through the beamforming network, multiple parallel branches with enhanced channel sparsity are formed.

4. The low-complexity OTFS multi-antenna detection algorithm according to claim 1, characterized in that: The time domain signals of each parallel branch in S3 are subjected to OTFS demodulation to obtain a delay-Doppler (DD) domain or time-delay (DT) domain symbol signal of each parallel branch; including: Each parallel branch time domain signal is converted into a corresponding DT domain signal through row-column conversion; and each parallel branch time domain signal is converted into a corresponding DD domain signal through discrete Zak transformation.

5. The low-complexity OTFS multi-antenna detection algorithm according to claim 1, characterized in that: The DD domain signals demodulated by each parallel branch in S4 are subjected to two dual maximum ratio combining (Bi-MRC) detectors designed in this patent for the corresponding domains, including: The multipath components contained in the DD domain signals of each parallel branch are coherently combined using MRC; at the same time, all branches are collected by MRC and then coherently combined; the optimal estimate is obtained by continuous iteration.

6. The low-complexity OTFS multi-antenna detection algorithm according to claim 1, characterized in that: The DT domain signal after demodulation of each parallel branch in S4 passes through the low-complexity DT domain Bi-MRC detector designed by this patent, including: The DD domain signal input and output relationship of each parallel branch is converted into the multiplication between the matrix and the vector in the DD domain by redundant operation. The multipath components contained in the DT domain signal of each parallel branch are coherently combined using MRC. At the same time, all branches are collected by MRC and then coherently combined. The optimal estimate is obtained by continuous iteration.

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