Design method for SAMP sparse channel estimation based on OFDM system

Abstract

The invention discloses a design method for SAMP sparse channel estimation based on a single-transmitting single-receiving OFDM (Orthogonal Frequency Division Multiplexing) system. According to the method, signals can be recovered under the condition of unknown sparseness, accurate reconstruction of the signals is realized, and signal reconstruction is carried out by converting a linear measurement model into a Bayesian inference problem and utilizing a sparse Bayesian model. A simulation experiment shows that compared with other algorithms, the algorithm provided by the invention can realize better channel reconstruction, and also has higher convergence speed and lower calculation complexity at the same time.

Description

Technical Field

[0001] The invention belongs to the technical field of digital signal processing and provides a design method for SAMP sparse channel estimation based on an OFDM system. Background Art

[0002] In recent years, mobile communication technology has developed rapidly, and people's demand for wireless high-speed data communication has increased day by day. The channel estimation problem in wireless communication has been studied in depth. In practical applications, wireless channels are often sparse, and the sparse characteristics of the channel are mainly manifested in the large delay spread and the small number of paths with strong energy. Sparse channel estimation algorithms can fully explore the sparsity of wireless channels and introduce compressed sensing technology into channel estimation, reducing the use of pilots and improving spectrum utilization. Sparse channel estimation algorithms have become a research hotspot in the field of communications.

[0003] In the actual application of OFDM system, the wireless channel often presents sparseness. In the actual wireless channel transmission process, there are only a small number of non-zero taps, most of which are zero or close to zero. In recent years, sparse channel estimation has become a research hotspot. The so-called sparse channel estimation is to use the sparsity of wireless channels and introduce compressed sensing technology into channel estimation. Therefore, the SAMP algorithm for sparse channel estimation of OFDM system based on compressed sensing theory is studied. Summary of the invention

[0004] The purpose of the present invention is to design a method to combat the distortion and distortion of the received signal caused by the harsh channel environment at the receiving end, occupy as few spectrum resources as possible, accurately restore the original transmitted data, reduce the complexity of the operation, and provide a new design method - a method for designing SAMP sparse channel estimation based on OFDM system.

[0005] The specific steps of the design method of SAMP sparse channel estimation based on OFDM system provided by the present invention are as follows:

[0006] First, according to the design requirements, in the OFDM system, the number of subcarriers is N, the channel length is L, and the number of pilots is P, which are located at subcarriers k1, k2, ..., k q Then the received signal vector at the receiving end is expressed as:

[0007]

[0008] In the formula, is the P×1-dimensional received signal vector, x is the transmitted signal of the transmitting antenna at the pilot position, F is the N-point discrete Fourier transform, F L is a P×L dimensional matrix consisting of the first L columns corresponding to F and the P rows corresponding to the pilot positions, is the L×1-dimensional channel time domain impulse response vector, the channel It usually presents sparse characteristics, most of the energy is distributed on a small number of taps, and the number of non-zero taps in the channel is much smaller than the channel length L, that is, K<<L, K is the non-zero position, is a P×1-dimensional additive Gaussian white noise, Then the channel estimation problem in OFDM system can be transformed into the original signal x by measuring the value Solving the optimal l0 norm problem can be expressed as:

[0009]

[0010] in, The elements of are all complex numbers, Expressed in real number form:

[0011]

[0012] extract The real and imaginary values ​​of the real number are expressed as:

[0013]

[0014] In the formula, Corresponding to The real part of Corresponding to The imaginary part of The real form of the channel estimation problem is expressed as:

[0015]

[0016] Step 2: Input vector y, measurement matrix A, step size S;

[0017] 3. Initialization, residual is r0=y, index set The number of iterations t = 1, the number of index set elements L = S;

[0018] 4. Calculate u = abs[A T r t-1 ], that is, calculate:

[0019] <r t-1 , a j >, 1≤j≤N (6)

[0020] Select the L largest values ​​in u and correspond these values ​​to the column numbers j of A to form a set S k (column number set);

[0021] No. 5. Order C k=Λ t-1 ∪S k , A t ={a j}(all j∈C k );

[0022] 6. Solve y = A t h t The least squares solution of is:

[0023]

[0024] No. 7. Selection The L term with the largest absolute value is recorded as Corresponding to A t The L column in is denoted as A tL , the corresponding column number of A is denoted as Λ tL , let M = Λ tL ;

[0025] 8. Update residual

[0026] 9. If the residual r tnew =0, then stop the iteration and go to step 11; if ||r tnew ||2≥||r t-1 ||2, update the step length L = L + S, return to step 4 and continue iterating; if none of them are satisfied, go to step 10;

[0027] Step 10: Update index set Λ tL =M, residual r t =r tnew , t=t+1, return to step 4 and continue iterating;

[0028] Chapter 11: Channel Estimation The last calculation

[0029] Step 12: Estimating the Channel Convert to imaginary form to get the final estimate Right now:

[0030]

[0031] The present invention has the following beneficial effects:

[0032] 1. The present invention provides for the first time a design method for SAMP sparse channel estimation based on OFDM system.

[0033] 2. The present invention utilizes the SAMP algorithm to restore the signal under the condition of unknown sparsity, thus achieving accurate reconstruction of the original signal.

[0034] 3. Simulation experiments have verified that this algorithm has good estimation performance for the channel. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the flow chart of the algorithm of the present invention;

[0036] Figure 2 This is a comparison chart of the mean square error (MSE) of the SAMP algorithm and other algorithms for OFDM system sparse channel estimation;

[0037] Figure 3 This is a comparison chart of the recovery channel accuracy of the SAMP algorithm and other algorithms for OFDM system sparse channel estimation;

[0038] Figure 4 This is a comparison chart of the recovered channel error rate of the SAMP algorithm and other algorithms for sparse channel estimation in OFDM systems. DETAILED DESCRIPTION

[0039] Embodiment 1:

[0040] The specific steps of the design method of SAMP sparse channel estimation based on OFDM system provided by the present invention are as follows:

[0041] First, according to the design requirements, the transmitting antenna N is given T =1, receiving antenna N R =1, number of subcarriers N = 512, channel length L = 100, number of pilots P = 64, and number of non-zeros Z = 10, the channel estimation problem in the single-receive and single-transmit OFDM system is expressed as:

[0042]

[0043] In the formula, is the P×1-dimensional received signal vector, x is the transmitted signal of the transmitting antenna at the pilot position, F is the N-point discrete Fourier transform, F L is a P×L dimensional matrix consisting of the first L columns corresponding to F and the P rows corresponding to the pilot positions, is the L×1-dimensional channel time domain impulse response vector, the channel It usually presents sparse characteristics, most of the energy is distributed on a small number of taps, and the number of non-zero taps in the channel is much smaller than the channel length L, that is, K<<L, K is the non-zero position, is a P×1-dimensional additive Gaussian white noise, Then the channel estimation problem in OFDM system can be transformed into the original signal x by measuring the value Solving the optimal l0 norm problem can be expressed as:

[0044]

[0045] Assume that in the OFDM system, subcarriers k1, k2, ..., k 64 The pilot signals are inserted on the 4th and 5th axes, respectively, for a total of 64 pilot signals, and the received vector signal is The transmitted signal vector composed of the symbols of the transmitting antenna on the pilot subcarrier is expressed as x, x = [x(k1), x(k2), ..., x(k 64 )] T , the noise vector in F is the N-point discrete Fourier transform, F L is a P×L dimensional matrix consisting of the first L columns corresponding to F and the P rows corresponding to the pilot positions. F can be expressed as:

[0046]

[0047] Among them, the qth row and the lth column

[0048] in, The elements of are all complex numbers, Expressed in real number form:

[0049]

[0050] extract The real and imaginary values ​​of the real number are expressed as:

[0051]

[0052] In the formula, Corresponding to The real part of Corresponding to The imaginary part of The real form of the channel estimation problem is expressed as:

[0053]

[0054] Step 2: Input vector y, measurement matrix A, step size S;

[0055] 3. Initialization, residual is r0=y, index set The number of iterations t = 1, the number of index set elements L = S;

[0056] 4. Calculate u = abs[A T r t-1 ], that is, calculate:

[0057] <r t-1 , aj >, 1≤j≤N (7)

[0058] Select the L largest values ​​in u and correspond these values ​​to the column numbers j of A to form a set S k (column number set);

[0059] No. 5. Order C k =Λ t-1 ∪S k , A t ={a j}(all j∈C k );

[0060] 6. Solve y = A t h t The least squares solution of is:

[0061]

[0062] No. 7. Selection The L term with the largest absolute value is recorded as Corresponding to A t The L column in is denoted as A tL , the corresponding column number of A is denoted as Λ tL , let M = Λ tL ;

[0063] 8. Update residual

[0064] 9. If the residual r tnew =0, then stop the iteration and go to step 11; if ||r tnew ||2≥||r t-1 ||2, update the step length L = L + S, return to step 4 and continue iterating; if none of them are satisfied, go to step 10;

[0065] Step 10: Update index set Λ tL =M, residual r t =r tnew , t=t+1, return to step 4 and continue iterating;

[0066] Chapter 11: Channel Estimation The last calculation

[0067] Step 12: Estimating the Channel Convert to imaginary form to get the final estimate Right now:

[0068]

[0069] In order to verify the performance of the algorithm, the method was simulated by computer. The design of SAMP sparse channel estimation based on OFDM system was realized by using pycharm software, and the mean square error MSE of several channel estimation algorithms was simulated and calculated with the change of signal-to-noise ratio SNR, accuracy and error rate performance, as shown below Figure 2 , 3 As shown in Figure 4, after simulation calculation, it can be seen that compared with several other algorithms, the SAMP algorithm has better channel reconstruction accuracy and can better improve the accuracy of channel estimation.

Claims

1. A design method for SAMP sparse channel estimation based on OFDM system, characterized in that The SAMP algorithm can be used to restore the signal in the case of unknown sparsity to achieve accurate reconstruction of the original signal. The method is carried out in the following steps: First, according to the design requirements, in the OFDM system, the number of subcarriers is N, the channel length is L, and the number of pilots is P, which are located at subcarriers k1, k2, ..., k q Then the received signal vector at the receiving end is expressed as: In the formula, is the P×1-dimensional received signal vector, x is the transmitted signal of the transmitting antenna at the pilot position, F is the N-point discrete Fourier transform, F L is a P×L dimensional matrix consisting of the first L columns corresponding to F and the P rows corresponding to the pilot positions, is the L×1-dimensional channel time domain impulse response vector, the channel It usually presents sparse characteristics, most of the energy is distributed on a small number of taps, and the number of non-zero taps of the channel is much smaller than the channel length L, that is, K<<L, K is the non-zero position, is a P×1-dimensional additive Gaussian white noise, Then the channel estimation problem in OFDM system can be transformed into the original signal x by measuring the value Solving the optimal l0 norm problem can be expressed as: in, The elements of are all complex numbers, Expressed in real number form: extract The real and imaginary values ​​of the real number are expressed as: In the formula, Corresponding to The real part of Corresponding to The imaginary part of The real form of the channel estimation problem is expressed as: Second, input vector y, measurement matrix A, step size S; 3. Initialization, residual is r0=y, index set The number of iterations t = 1, the number of index set elements L = S; 4. Calculate u = abs[A T r t-1 ], that is, calculate: <r t-1 ,a j >,1≤j≤N (6) Select the L largest values ​​in u and correspond these values ​​to the column numbers j of A to form a set S k (column number set); No.

5. Order C k =A t-1 ∪S k , A t ={a j }(all j∈C k ); 6. Solve y = A t h t The least squares solution of is: No.

7. Selection The L term with the largest absolute value is recorded as Corresponding to A t The L column in is denoted as A tL , the corresponding column number of A is denoted as Λ tL , let M = Λ tL ; 8. Update residual 9. If the residual r tnew =0, then stop the iteration and go to step 11; if ||r tnew ||2≥||r t-1 ||2, update the step length L = L + S, return to step 4 and continue iterating; if none of them are satisfied, go to step 10; Step 10: Update index set Λ tL =M, residual r t =r tnew , t=t+1, return to step 4 and continue iterating; Chapter 11: Channel Estimation The last calculation Step 12: Estimating the Channel Convert to imaginary form to get the final estimate Right now:

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