Optimal channel estimation method for spatial modulation system over frequency-selective channels

Abstract

The application discloses a kind of optimal channel estimation methods based on frequency selective channel under spatial modulation system, belong to wireless communication in channel estimation technical field, the method steps are as follows: first, a new optimal cross-correlation Z-complementary sequence set (pair) is constructed, then new training matrix is obtained.Transmission is carried out on frequency selective channel, and channel estimation information is obtained using least square method according to the received signal obtained by the receiving end.The application realizes optimal channel estimation by designing the optimization training matrix of spatial modulation system under frequency selective channel, and eliminates more interference.

Description

Technical Field

[0001] This invention relates to an optimal channel estimation method for spatial modulation systems based on frequency-selective channels, and belongs to the field of wireless communication. Background Technology

[0002] Spatial modulation is a novel type of multiple-input multiple-output (MIMO) technique. Compared to traditional MIMO techniques, the main characteristic of spatial modulation is that although multiple transmit antennas are configured, there is only one radio frequency (RF) chain. Therefore, spatial modulation systems are free from inter-channel interference and have low energy consumption and low receiver detection complexity. To achieve optimal channel estimation in spatial modulation systems with frequency-selective channels, wireless communication technology places new demands on training sequences. Traditional dense training sequences are no longer suitable for spatial modulation systems. To address this issue, the concept of cross-Z-complementary sequences has been proposed.

[0003] Golay complementary sequence pairs have gained widespread attention and application due to their good autocorrelation and low peak-to-average power ratio. Compared to traditional Golay complementary sequence pairs, cross-correlation Z-complementary sequence pairs consider both the autocorrelation and cross-correlation properties between sequences, completely eliminating interference in the zero-correlation region and achieving optimal channel estimation for spatial modulation systems under frequency-selective channels. However, unfortunately, only cross-correlation Z-complementary sequence pairs of even length exist. Therefore, to obtain sequence pairs with more flexible parameters, researchers further expanded the number of sequences to four, proposing the concept of cross-correlation Z-complementary sequence sets. While cross-correlation Z-complementary sequence pairs only exist at even lengths, cross-correlation Z-complementary sequence sets with both odd and even lengths exist. Moreover, cross-correlation Z-complementary sequence sets have a larger zero-correlation region, which can eliminate more interference and achieve better channel estimation performance when used as training matrices for spatial modulation optimization under frequency-selective channels. Therefore, to achieve optimal channel estimation, it is desirable to construct a cross-correlation Z-complementary sequence set that reaches the theoretical limit, i.e., the optimal cross-correlation Z-complementary sequence set. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides an optimal channel estimation method for spatial modulation systems under frequency-selective channels. By designing an optimized training matrix for the spatial modulation system under frequency-selective channels and constructing a new set (pairs) of optimal cross-correlation Z-complementary sequences, optimal channel estimation can be achieved, eliminating more interference.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] An optimal channel estimation method for spatial modulation systems under frequency-selective channels includes the following steps:

[0007] Step 1: Construct new optimal training sequences (2N1N2,N1N2)-CZCP and (N1N2,N1N2)-CZCS;

[0008] Step 2: Obtain a new training matrix through the constructed training sequence. and

[0009] Step 3: Assume that the number of transmit antennas in the single-carrier general MIMO transmission structure based on the training sequence is N. t The number of receiving antennas is N r If the system is in a frequency-selective channel with a delay spread of λ, then the nth (1≤n≤N) t The channel impulse response from the transmit antenna to the receiver is h. n =[h n,0 ,h n,1 ,...,h n,λ ] Τ The training sequence transmitted on the nth transmitting antenna is x. n =[x n,0 ,x n,1 ,...,x n,L-1 ], where L is the length of the training sequence; N t The multipath signals on each transmitting antenna are represented in matrix form.

[0010] Step 4: Set N t A multipath signal X is transmitted from one transmitting antenna, and the system transmission model is y = Xh + w, where w = [w0, w1, ..., w L-1 ] Τ This indicates that the mean is 0 and the variance is . Complex Gaussian white noise, y=[y0,y1,...,y L-1 ] Τ The received signal received by the receiving antenna;

[0011] Step 5: Apply least squares channel estimation (unbiased) to obtain the estimated channel state information.

[0012] Step 6: If the training matrix and When the length of the zero-correlation region Z of the selected training sequence is greater than or equal to λ, then and It can achieve minimum MSE when used for channel estimation in spatial modulation systems.

[0013]

[0014] At this point, the optimal channel estimation has been achieved.

[0015] A further improvement to the technical solution of the present invention is that the specific construction method of step 1 is as follows:

[0016] Step 1-1:

[0017] Let (a,b) be a pair of Golay complementary sequences of length N1, and (c,d) be a pair of Golay complementary sequences of length N2. The following construction...

[0018]

[0019] The optimal cross-correlation Z-complementary sequence pair with parameters (2N1N2,N1N2)-CZCP can be obtained, denoted as (e,f);

[0020] Steps 1-2:

[0021] Let (a,b) be a pair of Golay complementary sequences of length N1, and (c,d) be a pair of Golay complementary sequences of length N2. The following construction...

[0022]

[0023] The optimal cross-correlation Z-complementary sequence set with parameters (N1N2,N1N2)-CZCS can be obtained, denoted as C={c0,c1,c2,c3};

[0024] Where a||b represents the horizontal cascade of sequences a and b; a * Indicates the conjugate of sequence a; Let represent the inversion of sequence 'a'; 'a' and 'b' represent two sequences of length N1 and N2, respectively. Let Kronecker product be represented, then The length is N1N2; N1N2 has 2 α 10 β 26 γ (α,β,γ)≥0 or 2 α+μ 3 β 5 γ 11 η 13 ζ (α,β,γ,η,ζ,μ≥0,β+γ+η+ζ≤α+2μ+1,μ≤γ+ζ) form.

[0025] A further improvement to the technical solution of the present invention is that the new training matrix in step 2 is constructed through the following steps:

[0026] Step 2-1: Design a training matrix based on (N,Z)-CZCP As shown below:

[0027]

[0028] Where a and b are subsequences of CZCP obtained in step 2-1, and "0" represents a vector of length N with all elements being 0. t " " represents the number of transmitting antennas, L = 2N t N;

[0029] Step 2-2:

[0030] Design a training matrix based on (4,N,Z)-CZCS As shown below:

[0031]

[0032] Where c0, c1, c2, and c3 are subsequences of CZCS obtained in step 2-2, and "0" represents a vector of length N with all elements being 0. t " " indicates the number of transmitting antennas, L = 4N t N.

[0033] A further improvement to the technical solution of the present invention lies in: the training sequence x transmitted on the nth transmitting antenna in step 3. n =[x n,0 ,x n,1 ,...,x n,L-1 They have equal energy E, and

[0034] A further improvement to the technical solution of the present invention lies in: the multipath signal X in step 3. n (1≤n≤N t It has the following form:

[0035]

[0036] A further improvement to the technical solution of the present invention is that h in step 4 has the following form:

[0037]

[0038] A further improvement to the technical solution of the present invention lies in: the training sequence x transmitted on the nth transmitting antenna. n =[x n,0 ,x n,1 ,...,x n,L-1 [The newly obtained training matrix] and The training sequence in.

[0039] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0040] (1) The construction of the training sequence proposed in this invention can simultaneously obtain the optimal cross-correlation Z-complementary sequence set (pair) in binary and quaternary, which makes the design of the training matrix more flexible and improves the applicability of channel estimation.

[0041] (2) The construction of the training sequence proposed in this invention has a new sequence length form compared with the existing construction methods. This not only enriches the existing training sequence construction methods, but also provides more training sequence options for the design of training matrices.

[0042] (3) The cross-correlation Z-complementary sequence set (pair) obtained by this invention is optimal, that is, the width Z of the zero correlation region reaches the theoretical maximum value. When used to design the optimization training matrix of the spatial modulation system under frequency selection channel, more interference can be eliminated, thereby ensuring the performance of channel estimation. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0044] Figure 2 This is a simulation diagram showing the distribution of the autocorrelation function calculation results of (e,f) in the embodiment;

[0045] Figure 3 This is a simulation diagram showing the distribution of the cross-correlation function calculation results of (e,f) in the embodiment;

[0046] Figure 4 This is a simulation diagram showing the distribution of the autocorrelation function calculation results of C={c0,c1,c2,c3} in the embodiment;

[0047] Figure 5 This is a simulation diagram showing the distribution of the cross-correlation function calculation results of C={c0,c1,c2,c3} in the embodiment. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to embodiments:

[0049] This invention proposes an optimal channel estimation method for spatial modulation systems under frequency-selective channels. By selecting binary and quaternary Golay complementary sequence pairs of different lengths as base sequences, and combining this with the Turing method, a Golay complementary sequence pair of length N1N2 is obtained. Based on the generated Golay complementary sequence pairs, optimal cross-correlation Z-complementary sequence pairs of length 2N1N2 and optimal cross-correlation Z-complementary sequence sets of length N1N2 can be obtained through a special concatenation method. For the optimal cross-correlation Z-complementary sequence pair (e,f) of length 2N1N2, when 1≤τ≤2N1N2-1, its autocorrelation function and ρ... e (τ)+ρ f(τ)=0. When N1N2≤τ≤2N1N2-1, its cross-correlation function and ρ e,f (τ)+ρ f,e (τ) = 0. For the optimal cross-correlation Z-complementary sequence set C = {c0, c1, c2, c3} of length N1N2, when 1 ≤ τ ≤ N1N2-1, its autocorrelation function and When 0≤τ≤N1N2-1, its cross-correlation function and Therefore, the sequence set parameters obtained by the construction method proposed in this invention can reach the theoretical limit, and are suitable for designing the optimization training matrix of a spatial modulation system under frequency-selective channel, thereby achieving optimal channel estimation.

[0050] like Figure 1 The diagram shown is a flowchart of the implementation of the present invention, and the specific implementation methods are as follows:

[0051] Step 1:

[0052] Let (a, b) be a binary Golay complementary sequence pair of length N1 = 2, where a = (1-1) and b = (11). Let (c, d) be a quaternary Golay complementary sequence pair of length N2 = 3, where c = (1j 1) and d = (jj -j). Through the construction of this invention...

[0053]

[0054] The optimal cross-correlation Z-complementary sequence pair with parameters (12,6)-CZCP can be obtained, denoted as (e,f).

[0055] Defined by the aperiodic cross-correlation function The sum of the aperiodic autocorrelation functions of (e,f) can be obtained as follows: The sum of the aperiodic cross-correlation functions of (e,f) is: Figure 2-3 A simulation diagram of the distribution of the correlation function calculation results of (e,f) is given. It can be seen from the figure that the width of the zero correlation region of (e,f) reaches the theoretical upper limit, which is the optimal cross-correlation Z-complementary sequence pair with a length of 12.

[0056] Let (a, b) be a binary Golay complementary sequence pair of length N1 = 8, where a = (111-111-11) and b = (111-1-1-11-1). Let (c, d) be a binary Golay complementary sequence pair of length N2 = 2, where c = (1-1) and d = (11). Through the construction of this invention...

[0057]

[0058] The optimal cross-correlation Z-complementary sequence set with parameters (4,16,16)-CZCS can be obtained, denoted as C={c0,c1,c2,c3}. From the correlation function calculation formula, the sum of the aperiodic autocorrelation functions of C={c0,c1,c2,c3} is... The sum of the aperiodic cross-correlation functions of C = {c0, c1, c2, c3} is: Figure 4-5 Simulation results of the correlation function calculation for C = {c0, c1, c2, c3} are given. As can be seen from the figure, the width of the zero correlation region of C = {c0, c1, c2, c3} reaches the theoretical upper limit, which is the optimal cross-correlation Z-complementary sequence set with a length of 16.

[0059] Step 2:

[0060] Substituting the optimal cross-correlation Z-complementary sequence set (pairs) generated in step 1 into the framework for constructing the training matrix, the training matrices Ω and Λ are respectively

[0061]

[0062]

[0063] Step 3:

[0064] The training sequence x in the training matrix Ω and Λ obtained in step 2 n =[x n,0 ,x n,1 ,...,x n,L-1 [Through N] t Each transmitting antenna transmits. N t The multipath signals on each transmitting antenna are represented in matrix form. Among them, multipath signal X n (1≤n≤N t It has the following form:

[0065]

[0066] Step 4:

[0067] A multipath signal X is delayed and spread to a frequency-selective channel of λ, where the channel impulse response from the nth transmit antenna to the receiver is h. n =[h n,0 ,h n,1 ,...,h n,λ ] Τ The system transmission model is y = Xh + w, where w = [w0, w1, ..., w L-1 ] Τ This indicates that the mean is 0 and the variance is . Complex Gaussian white noise. Where h has the following form:

[0068]

[0069] y = [y0, y1, ..., y L-1 ] Τ This refers to the received signal received by the receiving antenna.

[0070] Step 5:

[0071] By applying least-squares channel estimation (unbiased), the estimated channel state information is obtained.

[0072] Compared with existing training sequence construction methods, the novel optimal cross-correlation Z-complementary sequence set (pair) construction method proposed in this invention simultaneously includes the lengths of the two existing optimal cross-correlation Z-complementary sequence sets (pairs) without having the same construction. The construction of the training sequence proposed in this invention can simultaneously obtain optimal cross-correlation Z-complementary sequence sets (pairs) in both binary and quaternary formats, which makes the design of the training matrix more flexible and improves the applicability of channel estimation.

[0073] The training sequence construction method proposed in this invention features a novel sequence length format compared to existing methods. This not only enriches the existing training sequence construction methods but also provides more training sequence options for training matrix design. For example, compared to existing methods, the proposed method can generate more training sequences of the same length. Specifically, the optimal cross-correlation Z-complementary sequence pair of length 40 can only be obtained using existing methods with a GCP of length 20, but the proposed method can also obtain it using two GCPs of lengths 2 and 10 respectively. This significantly increases the number of training matrices, thus providing more training matrices for channel estimation to choose from.

[0074] The cross-correlation Z-complementary sequence set (pairs) obtained in this invention is optimal, meaning the width Z of the zero-correlation region reaches its theoretical maximum value. When used to design the optimized training matrix for spatial modulation systems under frequency-selective channels, it can eliminate more interference, thereby ensuring the performance of channel estimation. Compared to Golay complementary sequence pairs, the cross-correlation Z-complementary sequence set considers both the autocorrelation and cross-correlation characteristics of the sequences; therefore, this type of method is worth promoting.

[0075] The above description is merely a basic scheme for a specific implementation of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. All variations falling within the equivalent meaning and scope of the claims will be included within the scope of the claims.

Claims

1. An optimal channel estimation method for spatial modulation systems based on frequency-selective channels, characterized in that: The method includes the following steps: Step 1: Construct a new optimal training sequence and ; The specific construction method is as follows: Step 1-1: set up It is long as complementary Golay sequence pairs, It is long as The Golay complementary sequence pairs are constructed as follows: The parameters that can be obtained are The optimal cross-correlated Z-complementary sequence pair is denoted as ; Steps 1-2: set up It is long as Golay complementary sequence pairs, It is long as The complementary Golay sequence pairs are constructed as follows: The parameters that can be obtained are The optimal set of cross-correlated Z-complementary sequences, denoted as ; in, Represents a sequence and sequence Horizontal cascading; Represents a sequence The conjugate; Represents a sequence Inverse; and They represent lengths of and Two sequences, " represents the Kronecker product, then , length is ; have or form; Step 2: Obtain a new training matrix through the constructed training sequence. and ; Step 3: Assume the number of transmit antennas in the single-carrier general MIMO transmission structure based on the training sequence is... The number of receiving antennas is The system is in a state of latency expansion. Under frequency-selective channel, then the first The channel impulse response from each transmit antenna to the receiver is ;No. The training sequences transmitted on each transmitting antenna are ,in The length of the training sequence; The multipath signals on each transmitting antenna are represented in matrix form. ; Step 4: Multipath signals on each transmitting antenna It was launched, and the system transmission model is as follows: ,in This indicates that the mean is 0 and the variance is . Complex Gaussian white noise, The received signal received by the receiving antenna; Step 5: Apply least-squares unbiased channel estimation to obtain the estimated channel state information. ; Step 6: If the training matrix and The length of the zero-correlation region of the selected training sequence At that time, and It can achieve minimum MSE when used for channel estimation in spatial modulation systems. At this point, the optimal channel estimation has been achieved.

2. The optimal channel estimation method for a spatial modulation system based on a frequency-selective channel according to claim 1, characterized in that: The new training matrix in step 2 is constructed through the following steps: Step 2-1: Design based on Training matrix As shown below: in and The subsequence of CZCP obtained in step 2-1, " indicates a length of A vector in which all elements are 0. "Indicates the number of transmitting antennas, ; Step 2-2: Design based on Training matrix As shown below: in , , and The subsequence of CZCS obtained in step 2-2, " indicates a length of A vector in which all elements are 0. "Indicates the number of transmitting antennas, .

3. The optimal channel estimation method for a spatial modulation system based on a frequency-selective channel according to claim 1, characterized in that: In step 3, the first Training sequences transmitted on each transmitting antenna Having equal energy ,and .

4. The optimal channel estimation method for a spatial modulation system based on a frequency-selective channel according to claim 1, characterized in that: multipath signal in step 3 It has the following form: 。 5. The optimal channel estimation method for a spatial modulation system based on a frequency-selective channel according to claim 1, characterized in that: In step 4 It has the following form: 。 6. The optimal channel estimation method for a spatial modulation system based on a frequency-selective channel according to claim 1, characterized in that: The first Training sequences transmitted on each transmitting antenna For the newly obtained training matrix and The training sequence in.

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