A low-complexity detection method for index-modulated orthogonal time-frequency-space systems

Abstract

The present invention belongs to the field of information and communication technology, and specifically relates to a low-complexity detection method for index-modulated orthogonal time-frequency-space systems. The purpose of the present invention is to propose a low-complexity and effective detection algorithm for index-modulated orthogonal time-frequency-space systems. The technical solution of the present invention is to propose a simplified equivalent form of a new multi-layer message passing detection (Multi-Layer Message Passing Detection, MLMPD) algorithm based on the sum-product algorithm for index-modulated orthogonal time-frequency-space systems by making full use of prior information, which improves the bit error rate performance of the system with lower computational complexity. At the same time, due to the full use of prior information, the number of message passing layers of the MLMPD algorithm is increased from 3 layers of the classical algorithm to 6 layers. Simulation results show that compared with traditional algorithms, the MLMPD algorithm has better bit error rate performance, lower computational complexity and acceptable convergence speed.

Description

Technical Field

[0001] The present invention belongs to the field of information and communication technology, and particularly relates to a low-complexity detection method for an index-modulated orthogonal time-frequency-space system. Background Art

[0002] Orthogonal Time-Frequency-Space (OTFS) modulation has emerged as a highly efficient waveform to address the challenges posed by highly dynamic channels. Specifically, in an OTFS system, all transmitted symbols are multiplexed in the Delay-Doppler (DD) domain, and similar channel gains are achieved through the Symplectic Finite Fourier Transform (SFFT) and Inverse Sinite Fourier Transform (ISFFT). Consequently, OTFS symbols achieve full diversity, resulting in superior performance compared to Orthogonal Frequency Division Multiplexing (OFDM) in dual-time and frequency selective channels.

[0003] Furthermore, to achieve more robust performance, researchers have developed an OTFS system based on index modulation (IM). Specifically, additional index bits are transmitted by indexing the activated DD-domain resource cells, which are independently and randomly selected. Building on the fundamental concepts of IM with OTFS (IM-OTFS), researchers have developed a number of IM-OTFS evolutions to better balance spectral efficiency (SE) and bit error rate (BER) performance. Among them, the Delay-IM OTFS (DeIM-OTFS) scheme achieves superior intersymbol interference (ISI) mitigation by activating multiple DD-domain resource cells simultaneously, resulting in better BER performance than IM-OTFS. Specifically, IM-OTFS can be considered a special case of DeIM-OTFS with only a single DD-domain resource cell activated. Summary of the Invention

[0004] The purpose of this invention is to propose a low-complexity, efficient detection algorithm for DeIM-OTFS. By fully leveraging prior information, the present invention proposes a simplified equivalent form of a new multi-layer message passing detection (MLMPD) algorithm based on the sum-product algorithm for DeIM-OTFS, thereby improving the system's BER performance at the cost of lower computational complexity.

[0005] Consider Figure 1 The DeIM-OTFS scheme shown in the figure. Since the DD domain is converted from the time frequency (TF) domain, Figure 1 The TF plane corresponding to the DD plane shown is denoted by Λ, and is sampled at intervals of T (seconds) and Δf = 1 / T (Hz), i.e., Λ = {(mΔf,nT), m = 0, ..., M-1, n = 0, ..., N-1}. Here, M and N are the number of subcarriers and the number of time domain symbols, respectively. At the same time, Δf and T are designed to be larger than the maximum Doppler frequency shift ν of the channel, respectively. max and the maximum channel delay width τ max .and Figure 1 The DD plane Γ is depicted as an information grid with a delay resolution of 1 / MΔf and a Doppler resolution of 1 / NT, i.e., Γ = {(l / MΔf,κ / NT),l = 0,…,M-1,κ = 0,…,N-1}. The entire DD plane Γ constitutes a frame of the OTFS system.

[0006] In DeIM-OTFS, the OTFS frame is further divided into The size is subframes, where and Meanwhile, the subframe located at the lth row and the kth column is defined as G[β], where The entire OTFS frame and each subframe are processed separately and The p information bits of each subframe are divided into two parts:

[0007]

[0008] Among them, S is a set of constellations of size |S|, is the number of activated delay blocks, that is, the number of activated rows in the subframe. Specifically, the first part of the p1 bits is used to determine the activated delay blocks (DelayBlock, DB) that constitute the activation mode, and the remaining p2 bits are mapped to the amplitude-and-phase modulation (APM) symbols on the activation resource grid. and In the case of , only 4 of the 6 activation modes are used to form the activation mode set, and the remaining 2 are not used.

[0009] Assume that the channel consists of L paths, and the channel gain, delay and Doppler shift corresponding to the i-th path are h i , τ i and v i , given as follows

[0010]

[0011] Where u = 0, ..., MN-1, p = 0, ..., P-1, T s is the sampling period. rc (t) is the impulse response of the raised cosine filter equivalent to the root raised cosine filter at the transmitting and receiving ends. At the same time, the channel beat number P is determined by the maximum multipath delay and the overall filter response P rc The duration of (t) is determined. Then, the received signal in the DD domain can be expressed as

[0012]

[0013] Among them, e=0,…,M, κ=0,…,N, In the above formula, Y[e,κ] and X[l,κ]∈{0,S} are the signals at the lth row and the kth column of the receiving DD plane Y and the transmitting DD plane X, respectively. Z[l,κ] is the Gaussian white noise at the lth row and the kth column of the noise matrix Z on the DD plane, with a mean of 0 and a variance of at the same time, is defined as

[0014]

[0015]

[0016] Finally, Equation (3) can be expressed in vector form as

[0017] y=Hx+z,y=vec(Y),x=vec(X),z=vec(Z) (6)

[0018] The element H[d,c] at the dth row and cth column of H, d = κ1M + l1, c = κ2M + l2 can be expressed as

[0019]

[0020] Here, δ(·) is the Dirac function.

[0021] As can be seen from Equation (6), the inter-symbol interference at the receiving end is severe and the equivalent channel matrix H is dimensional, which greatly increases the detection complexity and reduces the detection performance of traditional algorithms. Furthermore, traditional algorithms do not fully utilize prior information. Specifically, traditional algorithms assume that the probability of selecting zero and each APM symbol on each resource grid is equal, but this does not conform to the actual modulation scheme. Furthermore, traditional algorithms cannot handle the interference caused by non-selected activation modes during the iteration process. Therefore, this article will provide a low-complexity MLMPD algorithm to solve this problem, which is also the core of the present invention.

[0022] According to equation (6), the theoretically optimal maximum a posteriori probability detector of the transmitted signal can be expressed as

[0023]

[0024] At the same time, the posterior probability of the above formula can be decomposed into

[0025]

[0026] Where x[c] is the cth element of x, and a[f] is the fth element of the activation state vector a of all DBs. is the index set of x[c], a j Defined as And b[j] is the jth element of the activation mode index vector b of all subframes. Specifically, b[j]∈[1,…,p1] is the activation mode index of the jth subframe. At the same time, the set of legal activation modes for each subframe is defined as

[0027] like Figure 2 As shown in Figure 1, the system model is interpreted as a multi-layer factor graph (FG) consisting of variable nodes (VN) represented by ovals and factor nodes (FN) represented by rectangles. In the factor graph, the first-layer factor nodes are Pr(y[d]|x,b,H), d=1,…,MN, the first-layer variable nodes are x[c], c=1,…,MN, and the second-layer factor nodes are Pr(x[c]|a[f]), c=1,…,MN. The second layer variable node is a[f], and the third layer factor node is Pr(a j |b[j]), the third layer variable node is b[j], j=1,…,J, and the last layer factor node is Pr(b[j]). For simplicity, let and Represents the index set of non-zero elements in the d-th row and c-th column of H. For the posterior probability Pr(x,b|y,H), each element of the variables x, b and latent variable a is a variable node in the factor graph, and each probability factor is a factor node.

[0028] First, before the MLMPD algorithm starts to iterate, it is necessary to input the prior information Pr(x[c]|a[f]), Pr(a j |b[j]), Pr(b[j]) and input parameters Specifically, the above prior information and parameters are initialized as follows

[0029]

[0030]

[0031]

[0032] Afterwards, according to the sum-product algorithm, the process of the proposed MLMPD algorithm in the equivalent simplified form at the tth iteration is as follows.

[0033] 1) For any d and Calculating intermediate variables and as follows

[0034]

[0035]

[0036] 2) For any d and Calculating intermediate variables and as follows

[0037]

[0038]

[0039] 3) Calculate the message from VN Pr(y[d]|x,H) to VN x[c] c=1,…,MN, and d=1,…,MN, as follows

[0040]

[0041] Among them, s m is the mth element in the set {S,0}.

[0042] 4) For any c, compute the message from VN x[c] to FN Pr(x[c]|a[f]) as follows

[0043]

[0044] 5) For any c and Compute the message FN Pr(x[c]|a[f]) to VN a[f] as follows

[0045]

[0046] 6) For any f and Calculate VN a[f] to FN Pr(a j |b[j])'s message as follows

[0047]

[0048] 7) For any j, calculate the intermediate variable as follows

[0049]

[0050] 8) For any j and Calculate FN Pr(a j |b[j]) to VN a[f] as follows

[0051]

[0052] 9) For any f and Calculating intermediate variables and as follows

[0053]

[0054] And calculate the message from VN a[f] to FN Pr(x[c]|a[f]) as follows

[0055]

[0056] 10) For any c, compute the message from FN Pr(x[c]|a[f]) to VN x[c] as follows

[0057]

[0058] 11) For any c and Calculating intermediate variables Intermediate variables and the message from VN x[c] to FN Pr(y[d]|x,b,H) as follows

[0059]

[0060]

[0061] 12) Calculate the convergence indicator η (t) , used to determine whether the algorithm converges, as follows

[0062]

[0063] Among them, II(·) is an indicator function, which is 1 when the logical judgment in the brackets is met, and 0 otherwise. is a small positive real number, and At the same time, if η (t) >η (ι) , ι=1,…,t-1, then at this time and Assign the values to temporary variables and

[0064] 13) Finally, when η (t) = 1 or the maximum number of iterations t is reached max When , stop the algorithm. Otherwise, return to step 2). After the algorithm terminates, you can and Determine the activation mode of each subframe and the modulation signal on each activated resource grid. First, let the function Then the activation pattern index of the jth subframe can be detected as in

[0065]

[0066] in, At the same time, the factor node Pr(a j b[j]) is passed to the variable node b[j] and the variable node b[j] is passed to the factor node Pr(b[j]), Pr(b[j]) is also the factor node Pr(b[j]) passed to the variable node b[j] and the variable node b[j] passed to the factor node Pr(a[j]). j |b[j]). Secondly, according to and the prior probability Pr(a j |b[j]), activated Finally, the modulation signal on each activated resource grid can be detected as At this point, the algorithm ends.

[0067] The above key technical solution steps basically correspond to Figure 2 The arrows on the left and right indicate

[0068] The present invention proposes a low-complexity MLMPD algorithm for detecting IM-OTFS systems. By fully leveraging prior information, the MLMPD algorithm increases the number of message layers from three in the classic algorithm to six, while avoiding a loss in BER performance. Simulation results demonstrate that, compared to traditional algorithms, the proposed MLMPD algorithm achieves superior BER performance, lower complexity, and sufficiently rapid convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Schematic diagram of the modulation scheme of OTFS-DeIM.

[0070] Figure 2 This is a diagram of the message passing process of the MLMPD algorithm.

[0071] Figure 3 This is a comparison chart of the complexity of each iteration of the MLMPD algorithm and the traditional algorithm.

[0072] Figure 4 This is a comparison chart of the convergence performance of the MLMPD algorithm and the traditional algorithm in the DeIM-OTFS scheme, where (a) is L=5 and (b) is L=7.

[0073] Figure 5 : This is a comparison chart of the BER performance of the DeIM-OTFS scheme and the traditional scheme under different detectors, where (a) is L=5 and (b) is L=7. DETAILED DESCRIPTION

[0074] The steps and performances of the present invention are described in detail below with reference to the accompanying drawings so that those skilled in the art can better understand the present invention.

[0075] Figure 1 and Figure 2The following are a general system diagram and an algorithm message transmission flow diagram for the present invention. The purpose of this communication system is to improve the BER performance of the OTFS system by introducing index modulation in the delay domain, thereby enhancing communication reliability in high-speed mobile scenarios. Under this system model, the specific implementation steps of the present invention are as follows:

[0076] a) Input the channel matrix H between the transmitter and receiver, the receive vector y, and the noise power at the receiver And initialize the prior information Pr(x[c]|a[f]), Pr(a j |b[j]), Pr(b[j]) and parameters

[0077] b) Calculate according to formula (13) and formula (14) and

[0078] c) Calculate according to formula (15) and formula (16) and

[0079] d) Calculate according to formula (17) and

[0080] e) Calculate according to formula (18)

[0081] f) Calculate according to formula (19) and formula (20) and And according to formula (21)

[0082] g) Calculate according to formula (22)

[0083] h) Calculated according to formula (23) and And according to formula (24)

[0084] i) Calculate according to formula (25) And calculate according to formula (26) and

[0085] j) Calculate according to formula (27)

[0086] k) Calculate the convergence indicator according to formula (28). If η (t) >η (ι) , ι=1,…,t-1, then and Assign the values to temporary variables and

[0087] 1) When η (t) = 1 or the maximum number of iterations t is reached max When , stop the algorithm. Otherwise, go back to b);

[0088] After the algorithm terminates, the activation pattern index of the jth subframe can be detected as Among them, Pr j (e) is shown in formula (29). Then, according to and Pr(a j |b[j]) confirms the activated Finally, the modulation signal on each activated resource grid can be detected as

[0089] Figure 3 , Figure 4 and Figure 5 China E b / N0 and spectral efficiency are defined as and Meanwhile, the carrier frequency is 4 GHz and the roll-off factor of the raised cosine filter is 0.5. Unless otherwise specified, the sizes of OTFS frames and subframes are (M×N)=(64×16) and The subcarrier spacing is set to 15kHz and the user moving speed is set to 500 kilometers per hour. In addition, the Doppler shift is given by the function ν i =ν max cos(q i ), -p≤q i ≤p, generate. Among them, is the speed of light. In addition, the various parameters in MLMPD are set as: ρ x =0.4,ρ a =0.8 and Finally, P is set to

[0090] Figure 3 The computational complexity comparison of the proposed MLMPD algorithm and the traditional algorithm is given. Although the computational complexity of the Customized Message Passing Detection (CMPD) algorithm is theoretically lower than that of the Multi-Layer Joint Symbol and Activation Pattern Detection (MLJSAPD) algorithm, Figure 3As can be seen from the figure, the complexity difference between the two is not significant. This is because the CMPD algorithm and the MLJSAPD algorithm have the same complexity order and the coefficient of the highest-order complexity term is also the same. At the same time, due to the smaller coefficient of the highest-order complexity term, the complexity of the unsimplified MLMPD algorithm is slightly lower than that of the MLJSAPD algorithm and the CMPD algorithm. At the same time, the complexity of the simplified MLMPD algorithm is the lowest. When M = 64, N = 16, and Quadrature Phase Shift Keying (QPSK) is used, the complexity of the simplified MLMPD algorithm is reduced by more than 99% compared to that of MLJSAPD, which proves the effectiveness of the simplification. In addition, the 16QAM in the figure refers to 16-order Quadrature Amplitude Modulation (QAM).

[0091] Figure 4 The convergence performance of the MLMPD algorithm and the traditional algorithm when using QPSK is demonstrated. Specifically, in E b Under the conditions of / N0 = 10dB and L = 5, the CMPD algorithm, MLJSAPD algorithm, and the proposed MLMPD algorithm converged after an average of 9, 9, and 7 iterations, respectively. However, compared with CMPD and MLJSAPD, the MLMPD algorithm achieved a lower BER after convergence. This phenomenon indicates that due to the full utilization of prior information, the MLMPD algorithm converges closer to the optimal point compared to CMPD and MLMPD. Furthermore, the higher the signal-to-noise ratio, the faster the MLMPD algorithm converges. Furthermore, when L = 7, the MLMPD algorithm's BER performance improves while converging at a speed similar to that when L = 5.

[0092] At a spectral efficiency of 1.125 bits per second per Hertz, Figure 5 The BER performance comparison between the DeIM-OTFS scheme and the traditional scheme using different detectors is shown. It should be noted that the OTFS and Orthogonal Frequency Division Multiplexing (OFDM) schemes in the figure use both Binary Phase Shift Keying (BPSK) and QPSK symbols to achieve the same BER as in The spectrum efficiency is the same as that of the DeIM-OTFS scheme under the condition of |S|=4. Figure 5 As shown in (a), among all the schemes, the DeIM-OTFS scheme using the MLMPD algorithm has the best BER performance. Specifically, when L = 5 and BER = 10 -4When , the performance of MLMPD algorithm is improved by more than 1dB compared with MLJSAPD algorithm. Figure 5 In (a), the CMPD algorithm has the worst BER performance among the MLJSAPD algorithm, CMPD algorithm and MLMPD algorithm. This is because the CMPD algorithm only uses the relevant and the prior information of H. Similar phenomena can also be seen when L=7 Figure 5 Observed in (b).

Claims

1. A low-complexity detection method for index-modulated orthogonal time-frequency-space systems, where the received signal in the system is defined as: y=Hx+z,y=vec(Y),x=vec(X),z=vec(Z) in, Y is the receive DD plane, X is the transmit DD plane, Z is the noise matrix, the DD plane is the delay-Doppler plane, and the element H[d,c] at the dth row and cth column on H, d = κ1M + l1, c = κ2M + l2, is expressed as: Where l = 0,…,M,κ = 0,…,N, M and N are the number of subcarriers and the number of time domain symbols respectively, h i is the channel gain corresponding to the i-th path, δ(·) is the Dirac function, P is the number of channel beats, L is the number of paths, T = 1 / △f, △f is the subcarrier spacing in the time-frequency domain, τ i is the delay corresponding to the i-th path, v i is the Doppler shift corresponding to path i, P rc (t) is the impulse response of the raised cosine filter equivalent to the root raised cosine filter at the transmitting and receiving ends, T s is the sampling period, is defined as: Characterized in that, the detection method is: S1. Define the maximum a posteriori probability detector as: Where S is a constellation set of size |S|, and the posterior probability is decomposed into: Where x[c] is the cth element of x, a[f] is the fth element of the activation state vector a of all activated delay blocks, is the index set of x[c], is the number of subframes divided by the OTFS frame, and the size of each subframe is a j Defined as b[j] is the jth element of the activation mode index vector b of all subframes, that is, b[j]∈[1,…,p1] is the activation mode index of the jth subframe; S2. Definition and Denotes the index set of non-zero elements in the dth row and cth column of H. The set of legal activation modes for each subframe is The posterior probability Pr(x,b|y,H) is represented by a factor graph. Each element of the variables x, b and the latent variable a is a variable node in the factor graph, and each probability factor is a factor node. Based on the factor graph, a multi-layer message passing detection algorithm based on the sum-product algorithm is designed for detection. Specifically, the following steps are performed: The prior information of the input Pr(x[c]|a[f]), Pr(a j |b[j]), Pr(b[j]) and input parameters Initialize: in, is the number of activated delay blocks; according to the sum-product algorithm, the process of the t-th iteration of the multi-layer message passing detection algorithm is as follows: S21, for any d and Calculating intermediate variables and S22, for any d and Calculating intermediate variables and in is the variance of the Gaussian white noise in the noise matrix; S23. Calculate the message from the factor node Pr(y[d]|x,H) to the variable node x[c] and Among them, s m is the mth element in the set {S,0}; S24. For any c, calculate the message from the variable node x[c] to the factor node Pr(x[c]|a[f]) S25, for any c and Calculate the message from the factor node Pr(x[c]|a[f]) to the variable node a[f] S26、For any f and Calculate the variable node a[f] to the factor node Pr(a j |b[j])'s message S27. For any j, calculate the intermediate variable S28, for any j and Calculation factor node Pr(a j |b[j]) to the variable node a[f] S28、For any f and Calculating intermediate variables and And calculate the message from variable node a[f] to factor node Pr(x[c]|a[f]) S29. For any c, calculate the message from the factor node Pr(x[c]|a[f]) to the variable node x[c] S210, for any c and Calculating intermediate variables Intermediate variables and the message from the variable node x[c] to the factor node Pr(y[d]|x,b,H) S211, calculation convergence indicator η (t) , used to determine whether the algorithm converges: in, is an indicator function, which is 1 when the logical judgment in the brackets is met, otherwise it is 0; is a small positive real number, and If η (t) >η (ι) , ι=1,…,t-1, then at this time and Assign the values to temporary variables and S212, when η (t) = 1 or the maximum number of iterations t is reached max When , stop the algorithm and go to S3; otherwise, return to step S22; S3, obtained through and Determine the activation mode of each subframe and the modulation signal on each activated resource grid: let the function Then the activation pattern index of the jth subframe is detected as e∈[1,…,p1], where in, At the same time, the factor node Pr(a j b[j]) is passed to the variable node b[j] and the variable node b[j] is passed to the factor node Pr(b[j]), Pr(b[j]) is also the factor node Pr(b[j]) passed to the variable node b[j] and the variable node b[j] passed to the factor node Pr(a[j]). j |b[j]) message; according to and the prior probability Pr(a j |b[j]), activated It was further determined that The modulated signal on each activated resource grid is detected as

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