OCDM transmission method based on symbol-level precoding

Abstract

The invention discloses an OCDM transmission method based on symbol-level precoding, and belongs to the technical field of communication. According to the method, on the basis of OCDM system transmission under a multipath channel, an optimization problem of power minimization is designed, an equivalent ZF precoding matrix for the OCDM system is obtained, and a corresponding SLP algorithm based on non-negative least squares is designed, so that the sending power is reduced, and a final sending signal is obtained. According to the method disclosed by the invention, symbol-level precoding is combined into the OCDM system, the interference signal is manipulated by the SLP so as to be favorably superposed at the signal receiving position, and the OCDM system is assisted to obtain the final sending signal, so that the degree of freedom of a communication system and the energy efficiency of the system are effectively improved, and the error rate performance of the system is fully improved.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to an OCDM transmission method based on symbol-level precoding. Background Art

[0002] Chirp signals have high processing gain, low power consumption, robustness against channel damage, and good autocorrelation characteristics, so they have been widely used in radar and communication fields. At the same time, Chirp signals can use their orthogonality to superimpose in the time domain or frequency domain to improve spectrum efficiency and data rate, that is, OCDM (orthogonal linear frequency modulation wavelength division multiplexing) system. Although the OCDM system has the same peak-to-average power ratio as the OFDM (orthogonal frequency division multiplexing) system, it can produce a strong performance gain compared to the OFDM system in a multipath channel. At the same time, when there is interference caused by insufficient protection interval, the OCDM system also has stronger resistance than the OFDM system.

[0003] Since the OCDM modulation system can now be digitally implemented based on discrete Fresnel transform, and the existing DFnT matrix can be implemented step by step through the Fast Fourier Transform (FFT) algorithm, OCDM modulation only needs to be simply changed based on the OFDM system to be well integrated into the current high-performance digital processing platform, reducing the cost of its research and use. Based on this, OCDM has recently begun to gain more attention in different communication systems, but there is still a lack of design research on precoding schemes for downlink OCDM systems.

[0004] In typical multi-user transmission, interference exists because the transmission data of different signals are superimposed and sent in the wireless communication channel. In traditional communication systems, interference is usually regarded as a performance limiting factor. Therefore, traditional multi-user multi-antenna precoding schemes are designed to suppress or even eliminate interference. These methods can be obtained through the instantaneous CSI in each block and are collectively referred to as BLP (Block-level Precoding). Studies have shown that SLP (Symbol-level Precoding) can manipulate the power and direction of the interference signal on the complex plane symbol by symbol, making the interference signal a useful source of the required signal power. SLP has been proven to effectively utilize the interference signal and increase the SNR (Signal to-noise Radio) of the received symbol, thereby facilitating symbol detection in the receiver and improving the overall performance of the communication system. SLP also has very important applications in multi-antenna MIMO broadband systems. At the same time, compared with the estimation and detection at the receiving end, precoding at the transmitting end has greater flexibility.

[0005] Therefore, it is of great research significance to combine the OCDM system with SLP, use the above-mentioned wide linear processing to provide new degrees of freedom for the optimization design of SLP, and assist the OCDM system to further improve its performance. Summary of the invention

[0006] The problem to be solved by the present invention is to provide an OCDM transmission method based on symbol level precoding, combining the OCDM system and the SLP coding method, so as to improve the degree of freedom of the communication system and thus fully enhance the bit error rate performance of the system.

[0007] The present invention adopts the following technical solution: an OCDM transmission method based on symbol-level precoding, comprising the following steps:

[0008] Step 1: Construct an OCDM system under a multipath channel: The OCDM system sends a number of orthogonal Chirp carriers to generate discrete time domain OCDM signals for signal transmission;

[0009] Step 2: Construct an optimization problem for minimizing the transmission power: Based on the SLP method, the transmission power of the OCDM system is minimized by using interference, and an optimization function is constructed;

[0010] Step 3: Obtain an equivalent ZF precoding matrix of the OCDM system, and select the precoding matrix according to the ZF criterion, so as to eliminate the influence of the channel;

[0011] Step 4: Obtain the final transmission signal through the SLP method based on non-negative least squares.

[0012] Preferably, in step 1, constructing an OCDM system in a multipath channel to transmit signals includes the following sub-steps:

[0013] Step 1.1: Assume that a single-antenna OCDM system transmits N orthogonal Chirp carriers, and the transmitted symbol sequence on each Chirp carrier is s.

[0014] The transmitted symbol sequence is precoded to obtain x,

[0015] Where s(0), s(1), …, s(N-1) represent the transmitted symbol sequence, x(0), x(1), …, x(N-1) represent the precoded symbol sequence, and the superscript T represents transposition; Represents an N-dimensional complex field;

[0016] Step 1.2: The OCDM block generator generates a discrete time domain OCDM signal x of size N×1. OCDM :

[0017] x OCDM =Φ H x=Φ H W

[0018] Wherein, Φ represents a DFnT (discrete Fresnel transform) matrix, W represents a precoding matrix, and the superscript H represents a conjugate transpose.

[0019] The (m,n) elements of the discrete Fresnel transform matrix Φ are defined as follows:

[0020]

[0021] Here, j is used to represent other forms of complex signals, such as a+bj.

[0022] Preferably, in step S2, constructing an optimization problem for minimizing transmit power includes the following sub-steps:

[0023] Step 2.1, the transmission symbol of the OCDM system first passes through the SLP, and the discrete time domain OCDM signal is expressed as:

[0024] x OCDM =Φ H x=Φ H W(s+u)

[0025] in, is a disturbance vector;

[0026] The SLP method uses interference to minimize the transmission power of the OCDM system and obtains the optimal disturbance vector u. The optimization function is:

[0027]

[0028] Step 2.2: According to Parseval's theorem, the energy contained in the transmitted signal remains unchanged after IDFnT (inverse discrete Fresnel transform), and the optimization problem of minimizing the transmission power is transformed into:

[0029]

[0030] in, represents the i-th optimal perturbation vector, K represents the total number of users;

[0031] Preferably, in step 3, obtaining an equivalent ZF precoding matrix for the OCDM system includes the following sub-steps:

[0032] Step 3.1: After appending the cyclic prefix to the OCDM block, multipath propagation is combated. Assuming that the receiver obtains the channel state information synchronously through a specific channel estimation method, the received time domain signal is expressed as:

[0033] y=HxOCDM +n=HΦ H W(s+u)+n

[0034] Where H represents the channel impulse response matrix, n is the noise term;

[0035] Step 3.2, the OCDM system uses CP as the guard interval, the channel impulse response matrix H is a circulant matrix, no beamforming is performed at the receiving end, and the received signal after discrete Fresnel transform is r′:

[0036] r′=Φr

[0037] =ΦHx OCDM +Φn

[0038] =ΦHΦ H W(s+u)+Φn

[0039] =ΘW(s+u)+n

[0040] Where Θ = ΦHΦ H is the equivalent channel matrix, r represents the received observation signal;

[0041] Step 3.3: According to the ZF criterion, select the precoding matrix W ZF :

[0042] W ZF =Θ -1

[0043] Substituting the precoding matrix into the transmitted symbol expression, we get:

[0044] x=Θ -1 (s+u).

[0045] Preferably, in step 4, obtaining the final transmission signal based on the SLP method of non-negative least squares includes the following sub-steps:

[0046] Step 4.1: Introduce the equivalent symbol matrix And the diagonal matrix B, corresponding to each element of the symbol sequence s, the transmitted symbol sequence s is equivalently expressed as:

[0047]

[0048] Step 4.2: Define the real-valued perturbation vector To meet the constraint that the symbol amplitude increases while the phase remains unchanged, Every element u in i are all non-negative real numbers and satisfy This rewrites the send symbol expression as:

[0049]

[0050] Step 4.3: Construct an optimization function to minimize the antenna's transmit power and obtain the optimal perturbation vector The optimization function is expressed as:

[0051]

[0052] Step 4.4: Convert the optimization problem into a NNLS problem and introduce a temporary matrix A = Θ -1 B and vector d = -Θ -1 Bs, rewrite the optimization problem as:

[0053] min‖Au-d‖2

[0054] st u≥0

[0055] Step 4.5: Utilize the Euclidean norm duality between complex vectors And the augmented vector v = [v1,v2,…,v M ] represents the dimension of the complex vector, and any complex number in the vector is represented as and v i =[a i ,b i ], i = 1, ..., M represents the index value of the vector, a i is the real part of the vector, b i As the imaginary part of the vector, we get:

[0056]

[0057] in, as well as

[0058] Based on the standard NNLS problem, the fast NNLS algorithm is used to solve the optimal perturbation vector u * ; represents taking the real part of a complex number, It means taking the imaginary part of a complex number;

[0059] Step 4.6: The final transmission signal is:

[0060]

[0061] The technical solution of the present invention also provides: an electronic device, comprising:

[0062] one or more processors;

[0063] a storage device having one or more programs stored thereon;

[0064] When the one or more programs are executed by the one or more processors, the one or more processors implement any of the above-mentioned OCDM transmission methods based on symbol-level precoding.

[0065] The technical solution of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps in any of the above-mentioned OCDM transmission methods based on symbol-level precoding are implemented.

[0066] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0067] The present invention is based on the OCDM transmission method of symbol-level precoding, which combines symbol-level precoding into the OCDM system, manipulates the interference signal through SLP to make it beneficially superimposed on the received signal, assists the OCDM system to obtain the final transmission signal, reduces the transmission power, effectively improves the degree of freedom of the communication system and the energy efficiency of the system, and thus fully improves the bit error rate performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 The present invention is a flow chart of an OCDM transmission method based on symbol-level precoding;

[0069] Figure 2 Schematic diagram of the constellation points of the noise-free received signal of the precoder according to the embodiment of the present invention;

[0070] Figure 3 This is a comparison diagram of bit error rates of 128-subcarrier OCDM based on various precoders with a channel delay of 0.1us in an embodiment of the present invention;

[0071] Figure 4 This is a comparison diagram of bit error rates of 256-subcarrier OCDM based on various precoders with a channel delay of 0.1us in an embodiment of the present invention;

[0072] Figure 5 This is a comparison diagram of bit error rates of 128-subcarrier OCDM based on various precoders with a channel delay of 0.3us in an embodiment of the present invention;

[0073] Figure 6 This is a comparison chart of bit error rates of 256-subcarrier OCDM based on various precoders with a channel delay of 0.3us in an embodiment of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the application is further elaborated in detail below in conjunction with the accompanying drawings. The described embodiments are only a part of the embodiments involved in the present invention. All non-innovative embodiments of other researchers in the field on this embodiment belong to the protection scope of the present invention. At the same time, for the step numbering in the embodiment of the present invention, it is only set for the convenience of explanation, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0075] The OCDM transmission method based on symbol-level precoding of the present invention comprises the following steps:

[0076] Step 1, construct OCDM system transmission under multipath channel;

[0077] Step 2: Design the optimization problem of power minimization;

[0078] Step 3, obtain the equivalent ZF precoding matrix for the OCDM system;

[0079] Step 4: Design the corresponding SLP algorithm based on non-negative least squares (NNLS) to obtain the final transmission signal.

[0080] Specifically, Figure 1 As shown, the information bits are first digitally modulated after serial-to-parallel conversion to obtain the corresponding transmission symbols. Then, the transmitter performs symbol-level precoding on the symbols according to the acquired channel information and symbol information to obtain the encoded signal. Then, OCDM modulation is performed through IDFnT conversion to obtain OCDM transmission symbols. The cyclic convolution sequence is added, and the parallel-to-serial conversion and AD sampling are performed before transmission through the transmitting antenna.

[0081] In one embodiment of the present invention, for a more practical communication system, Monte Carlo simulation is used to verify the effectiveness of the OCDM transmission method based on symbol-level precoding of the present invention.

[0082] The simulation environment is set up as follows: OCDM and OFDM systems use N = 128,256 orthogonal subcarriers for superposition, and the CP length is 1 / 8 of the number of subcarriers. The transmitter uses OQAM modulation signals for mapping, and the sampling frequency of the system is set to f s =10MHz.

[0083] In addition, the channel model used is a quasi-static multipath channel, and the duration of the multipath channel used in this embodiment changes every 10 symbols, and the change law of its channel coefficient obeys the standard Gaussian distribution. The wireless communication channel through which the system passes is set with 10 reachable paths, and the noise used is additive Gaussian white noise.

[0084] Both OCDM and OFDM use two precoders, namely ZF-SLP precoder and traditional ZF precoder, for simulation comparison. The constellation point diagram of the noise-free received signal of the precoder is as follows: Figure 2 shown.

[0085] In this embodiment, when the channel delay is set to {0.1us, 0.2us…, 1us}, the bit error rates of 128-subcarrier and 256-subcarrier OCDM are compared based on various precoders, such as Figure 3 and Figure 4 As shown in the figure; when the channel delay is set to {0.1us, 0.4us…, 2.7us}, the bit error rate comparison between 128-subcarrier and 256-subcarrier OCDM based on various precoders is shown in the figure. Figure 5 and Figure 6 shown.

[0086] The simulation results show that SLP can manipulate the interference signal so that it can be beneficially superimposed on the received signal. Therefore, compared with traditional precoding, it can reduce the transmission power and thus improve the energy efficiency of the system. Figure 2 The comparison of the average transmission power of an OCDM system using a ZF-SLP precoder and a traditional ZF precoder and sending an OQAM modulated signal is shown in Figure 1. It can be observed that the average transmission power of the system increases with the increase in the number of subcarriers. However, since SLP can save the system's transmission power by utilizing interference, the performance difference increases with the increase in the number of subcarriers. When the number of subcarriers N = 512, ZF-SLP can reduce the transmission power of the traditional ZF precoder by about 20%.

[0087] Specifically, the ZF-SLP precoder has a bit error rate of 10 -3 At this level, a 10dB performance gain can be achieved compared to the ZF precoder. Due to the characteristics of the OCDM system, its channel correspondence matrix undergoes DFnT and IDFnT at the receiving and transmitting ends respectively, resulting in its equivalent channel matrix Θ still being a circulant matrix with non-zero elements on its off-diagonal lines.

[0088] That is to say, after DFnT at the receiving end, the interference between different subcarriers of the OCDM system is not completely eliminated. Therefore, SLP can use the interference information to enhance the bit error rate effect of the OCDM system and generate performance gain.

[0089] For different numbers of subcarriers, namely N=128 and N=256, when the channel delay is {0.1us, 0.2us…, 1us}, there is no big difference between the two. However, when the channel delay is {0.1us, 0.4us…, 2.7us}, the OCDM system using 128 subcarriers cannot effectively resist the influence of channel multipath and delay, while the OCDM system using 256 subcarriers can show better bit error rate effect.

[0090] In an embodiment of the present invention, an electronic device is also provided, including: one or more processors; a storage device on which one or more programs are stored; when the one or more programs are executed by the one or more processors, the one or more processors implement the OCDM transmission method based on symbol-level precoding described in any of the above embodiments.

[0091] In an embodiment of the present invention, a computer-readable storage medium is further provided, on which a computer program is stored. When the program is executed by a processor, the steps of any one of the OCDM transmission methods based on symbol-level precoding in the above embodiments are implemented.

[0092] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An OCDM transmission method based on symbol-level precoding, characterized in that: The steps include: Step 1: Construct an OCDM system under a multipath channel: The OCDM system sends a number of orthogonal Chirp carriers to generate discrete time domain OCDM signals for signal transmission; Step 2: Construct an optimization problem of minimizing the transmission power, and minimize the transmission power of the OCDM system by using interference based on the SLP method; Step 3, obtaining an equivalent ZF precoding matrix of the OCDM system, and selecting a precoding matrix according to the ZF criterion to eliminate channel influence; Step 4: Reduce the transmission power by using the SLP method based on non-negative least squares to obtain the final transmission signal.

2. The OCDM transmission method based on symbol-level precoding according to claim 1, characterized in that: Step 1: construct an OCDM system under a multipath channel for signal transmission, including the following sub-steps: Step 1.1: Assume that a single-antenna OCDM system transmits N orthogonal Chirp carriers, and the transmitted symbol sequence on each Chirp carrier is s. The transmitted symbol sequence is precoded to obtain x, Where s(0), s(1), …, s(N-1) represent the transmitted symbol sequence, x(0), x(1), …, x(N-1) represent the precoded symbol sequence, and the superscript T represents transposition; Represents an N-dimensional complex field; Step 1.2: In the OCDM system, the OCDM block generator generates a discrete time domain OCDM signal x with a size of N×1. OCDM : x OCDM =Φ H x=Φ H Ws Wherein, Φ represents the discrete Fresnel transform matrix, W represents the precoding matrix, and the superscript H represents the conjugate transpose.

3. The OCDM transmission method based on symbol-level precoding according to claim 1, characterized in that: The (m,n) elements of the discrete Fresnel transform matrix Φ are defined as follows: Among them, j is used to represent complex signals.

4. The OCDM transmission method based on symbol-level precoding according to claim 2, characterized in that: Step 2 constructs an optimization problem for minimizing transmit power, including the following sub-steps: Step 2.1, the transmission symbol of the OCDM system first passes through the SLP, and the discrete time domain OCDM signal is expressed as: x OCDM =Φ H x=Φ H W(s+u) in, is a disturbance vector; The SLP method uses interference to minimize the transmission power of the OCDM system and obtains the optimal disturbance vector u. The optimization function is: min||x OCDM ||2 Step 2.2: According to Parseval's theorem, the energy contained in the transmitted signal remains unchanged after passing through the IDFnT, and the optimization problem of minimizing the transmission power is transformed into: my || x||2。 5. The OCDM transmission method based on symbol-level precoding according to claim 3, characterized in that: Step 3 obtains the equivalent ZF precoding matrix for the OCDM system, including the following sub-steps: Step 3.1: After appending the cyclic prefix to the OCDM block, multipath propagation is combated. Assuming that the receiver obtains the channel state information synchronously through a specific channel estimation method, the received time domain signal is expressed as: y=Hx OCDM +n=HΦ H W(s+u)+n Where H represents the channel impulse response matrix, n is the noise term; Step 3.2: The OCDM system uses CP as the guard interval, and the channel impulse response matrix H is a circulant matrix. No beamforming is performed at the receiving end. The received signal after discrete Fresnel transform is r ′ : r′=Φr =ΦHx OCDM +Φn =ΦHΦ H W(s+u)+Φn = ΘW(s+u)+n Where Θ = ΦHΦ H is the equivalent channel matrix, r represents the received observation signal; Step 3.3: According to the ZF criterion, select the precoding matrix W ZF : W ZF =Θ -1 Substituting the precoding matrix into the transmitted symbol expression, we get: x=Θ -1 (s+u).

6. The OCDM transmission method based on symbol-level precoding according to claim 5, characterized in that: Step 4 is based on the SLP method of non-negative least squares to obtain the final transmission signal, including the following sub-steps: Step 4.1: Introduce the equivalent symbol matrix And the diagonal matrix B, corresponding to each element of the symbol sequence s, the transmitted symbol sequence s is equivalently expressed as: Step 4.2: Define the real-valued perturbation vector To meet the constraint that the symbol amplitude increases while the phase remains unchanged, Each element are all non-negative real numbers and satisfy Rewrite the send symbol expression as: Step 4.3: Construct an optimization function to minimize the antenna's transmit power and obtain the optimal perturbation vector The optimization function is expressed as: Where K represents the total number of users; Step 4.4: Convert the optimization problem into a NNLS problem and introduce a temporary matrix A = Θ -1 B and vector The optimization problem can be rewritten as: min‖Au-d‖2 st u≥0 Step 4.5: Utilize the Euclidean norm duality between complex vectors And the augmented vector v = [v1,v2,…,v M ] represents the dimension of the complex vector, and any complex number in the vector is represented as and v i =[a i ,b i ], i = 1, ..., M represents the index value of the vector, a i is the real part of the vector, b i As the imaginary part of the vector, we get: in, as well as represents taking the real part of a complex number, It means taking the imaginary part of a complex number; Based on the standard NNLS problem, the fast NNLS algorithm is used to solve the optimal perturbation vector u * ; Step 4.6: The final transmission signal is:

7. An electronic device, characterized in that: include: one or more processors; a storage device having one or more programs stored thereon; When the one or more programs are executed by the one or more processors, the one or more processors implement the OCDM transmission method based on symbol-level precoding as described in any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the steps in the OCDM transmission method based on symbol-level precoding described in any one of claims 1 to 6 are implemented.

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