MIMO windowing OFDM communication system in high-speed mobile scene and space diversity utilization method thereof

Abstract

The invention relates to an MIMO windowing OFDM communication system in a high-speed mobile scene and a space diversity utilization method thereof, and the method comprises the steps: dividing a system bandwidth into K subcarriers, and transmitting a signal through M transmitting antennas; modulating a frequency domain signal transmitted by a # imgabs0 # transmitting antenna through OFDM (Orthogonal Frequency Division Multiplexing) to obtain a time domain signal, multiplying the time domain signal by a window function and adding a cyclic prefix; coding the transmitting antenna signal according to the space-frequency repetition code, and transmitting the transmitting antenna signal to a receiving end through a dual-selective channel; receiving signals through N receiving antennas at a receiving end; decoding the received signal by adopting an MIMO (Multiple Input Multiple Output) frequency-varying Viterbi decoding scheme; and iteratively executing solution by using a surround viterbi algorithm in the decoding process until the result converges or reaches the maximum iteration times, thereby obtaining a decoding result and realizing space diversity utilization. By adopting the method, a windowing orthogonal frequency division multiplexing scheme can be expanded to a multi-input multi-output system in a high-speed moving scene, and space diversity is utilized.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a MIMO windowed OFDM communication system and a spatial diversity utilization method thereof in a high-speed mobile scenario. Background Art

[0002] Most existing wireless communication technologies consider integer or fractional Doppler shifts and integer delays. However, in practical wireless communication applications, both fractional delays and fractional Doppler shifts are ubiquitous. Considering these factors, Wei et al. [1] modeled OTFS channel estimation as a sparse signal recovery problem, estimating both delay and Doppler shift separately. However, this approach results in high computational complexity.

[0003] Considering the fractional Doppler shift and fractional time delay, references [2] and [3] proposed a windowed OFDM system based on a frequency-varying Viterbi decoding scheme. The time-domain window function can suppress the inter-carrier interference between adjacent subcarriers. Low-complexity Viterbi decoding can effectively reduce the inter-carrier interference. The normalized Doppler shift considered in reference [3] is equal to or less than 1.333, and when the center frequency is 4 GHz, the maximum relative speed between the transmitter and the receiver is 5400 kilometers per hour. However, the windowed OFDM system proposed in references [2] and [3] is for a single-input single-output system. There is a lack of technology that aims to extend the windowed OFDM scheme to a multiple-input multiple-output system and utilize space diversity. In order to utilize space diversity in a quasi-static frequency selective channel, space-frequency block code is usually used. Space-frequency block code is applied to two consecutive OFDM symbols and adjacent subcarriers. However, space-frequency block code cannot be applied to a time-varying frequency selective channel, i.e., a dual-selective channel. This is because, in a time-varying channel, two consecutive OFDM symbols experience different channels. Furthermore, fractional Doppler shift and fractional delay can exacerbate the situation. Therefore, a technique is urgently needed that can extend the windowed OFDM scheme to multiple-input, multiple-output (MIMO) systems and exploit spatial diversity in high-speed mobile wireless communications. Summary of the Invention

[0004] The purpose of the present invention is to address the problems of the prior art and provide a technology that can extend the windowed orthogonal frequency division multiplexing scheme to a multiple-input multiple-output system in a high-speed mobile wireless communication scenario and utilize spatial diversity.

[0005] To achieve the above objectives, a first aspect provides a method for utilizing spatial diversity in a MIMO windowed OFDM communication system in a high-speed mobile scenario, comprising the following steps: The bandwidth of the MIMO windowed OFDM communication system is divided into K subcarriers, and the interval between each subcarrier is , and send signals through M transmitting antennas at the transmitting end; For the first The frequency domain signal transmitted by the transmitting antenna is modulated by OFDM to generate a time domain signal, the time domain signal is multiplied by the window function and a cyclic prefix is ​​added; Performing space-frequency repetition coding on the transmitting antenna signal according to the space-frequency repetition code and transmitting it to the receiving end through the dual-selective channel; At the receiving end, the signal is received through N receiving antennas; The received signal is decoded using a multiple-input multiple-output frequency-variable Viterbi decoding scheme; The decoding is iteratively performed using a wraparound Viterbi algorithm until the result converges or the maximum number of iterations is reached, thereby obtaining a decoding result and realizing the utilization of spatial diversity.

[0006] Preferably, the The frequency domain signal transmitted by the transmitting antenna is modulated by OFDM to generate a time domain signal. The time domain signal is multiplied by a window function and a cyclic prefix is ​​added. Specifically, the following steps are performed: exist On the subcarrier, the Transmitted by the transmitting antenna A signal, represented by:

[0007] After orthogonal frequency division multiplexing OFDM modulation, the time domain signal is expressed as:

[0008] in Indicates the symbol duration, is the spacing of each subcarrier; Multiply the OFDM modulated signal by a window function , and get the windowed signal:

[0009] Adding a cyclic prefix to the windowed signal yields:

[0010] in Indicates the duration of the cyclic prefix.

[0011] Preferably, the window function is a window function with rapid sidelobe attenuation, satisfying:

[0012] in, is a positive integer, is the spacing of each subcarrier, is the window function The Fourier transform of .

[0013] Preferably, from The transmitting antenna to the The dual-selective channel between the receiving antennas is:

[0014] in, express The number of paths in 、 and Respectively Middle Fading coefficient, delay and Doppler shift of each path; in, and are all non-integer or fractional forms, and:

[0015] in, Indicates the maximum Doppler shift, fading coefficient Modeled as a zero-mean cyclically symmetric complex Gaussian random variable with fractional time delay Modeled as A uniformly distributed random variable, fractional Doppler shift Modeling is performed according to Jack spectrum, namely:

[0016] in, exist uniformly distributed, and in addition, 、 and , Independent of each other.

[0017] Preferably, the input and output relationship of the dual-selective channel is: the information received on the nth receiving antenna is :

[0018] in, Indicates the The transmit power of each transmitting antenna, is the amplitude, is a channel matrix of the dual-selective channel and is a sparse matrix;

[0019]

[0020]

[0021] in:

[0022]

[0023]

[0024] in, The received signal undergoes continuous-time Fourier transform at the receiving end. The signal on the subcarrier; Indicates in The received signal at each receiving antenna; The power spectral density is Low-pass filtered additive white Gaussian noise.

[0025] Preferably, the space-frequency repetition code is:

[0026] in, and .

[0027] Preferably, the wraparound Viterbi decoding algorithm includes: Construct the state vector based on the space-frequency repetition code:

[0028] Construct the channel response vector:

[0029] Define the metric function:

[0030] in, :

[0031] is the state transition indicator function, when , which means the state Can be in Step transfer to state , and when , indicating the status Will not be in the Step transfer to state ; By wrapping Viterbi decoding from the state To status Iteratively calculate the metric function, and when the condition is met When convergence is reached, the iteration is stopped and the decoding result is obtained. Otherwise, the wraparound frequency-variable Viterbi algorithm is continued until the maximum number of iterations V is reached and the iteration is stopped to obtain the decoding result. The constraint length of the algorithm is .

[0032] Preferably, the spatial diversity utilization method of the MIMO windowed OFDM communication system in the high-speed mobile scenario also includes a power allocation optimization step, by calculating the paired error probability of the transmitted signal, minimizing the paired error probability as the optimization goal, and optimizing the power allocation between different transmitting antennas.

[0033] Preferably, the spatial diversity order obtained by the space-frequency repetition code is ,in is a positive integer constant.

[0034] To achieve the purpose of the invention, a second aspect provides a MIMO windowed OFDM communication system in a high-speed mobile scenario, comprising a transmitting module and a receiving module, wherein the transmitting module and the receiving module are connected via antenna communication; The bandwidth of the system is divided into K subcarriers, and the interval between each subcarrier is ; The transmitting end module is configured with M The transmitting antenna comprises an OFDM modulation unit for modulating a frequency domain signal into a time domain signal through orthogonal frequency division multiplexing; A windowing processing unit, configured to multiply a time domain signal by a window function to obtain a windowed signal; a cyclic prefix adding unit, configured to add a cyclic prefix to the windowed signal; a space-frequency repetition coding unit, configured to perform space-frequency repetition coding on a transmission signal according to a space-frequency repetition code; The receiving end module is configured with N receiving antennas and includes: an OFDM demodulation unit for performing OFDM demodulation on the received signal; A multiple-input multiple-output frequency-variable Viterbi decoder for performing surround Viterbi decoding on a received signal; A pair error probability calculation module, used to calculate the pair error probability of the transmitted signal; A power allocation optimization unit, configured to optimize the power allocation between different transmitting antennas based on the pairwise error probability of the transmitted signal; The system adopts a dual-selective channel for communication connection between the transmitter module and the receiver module.

[0035] Compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a space-frequency repetition code to perform space-frequency repetition encoding on the transmitting antenna signal, and transmits it to the receiving end through a dual-selective channel. At the receiving end, a multi-input multi-output frequency-variable Viterbi decoding scheme is used to decode the received signal. The decoding result is obtained by iterative solution of the surround Viterbi algorithm, thereby extending the windowed orthogonal frequency division multiplexing scheme to the multi-input multi-output system in the high-speed mobile scenario and utilizing spatial diversity. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flowchart of a method for utilizing spatial diversity in a MIMO windowed OFDM communication system in a high-speed mobile scenario according to one embodiment is provided; Figure 2 The simulated value and approximate value of the covariance function amplitude in one embodiment are relationship diagram; Figure 3 The bit error rate (BER) performance simulation and theoretical derivation of the pair error probability at different maximum Doppler frequency shifts in one embodiment are shown. Comparison chart under value; Figure 4 For different numbers of transmitting antennas in one embodiment Comparison of the bit error rate (BER) performance simulation and theoretically derived pairwise error probability; Figure 5 In one embodiment, the number of receiving antennas is different. Comparison of the bit error rate (BER) performance simulation and theoretically derived pairwise error probability; Figure 6 FIG1 is a comparison diagram of bit error rate (BER) performance simulations of different power allocation schemes in one embodiment; Figure 7 FIG. 4 is a comparison diagram of bit error rate (BER) performance simulations of different power allocation schemes in one embodiment. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0038] Example 1 This embodiment 1 provides a method for utilizing spatial diversity in a MIMO windowed OFDM communication system in a high-speed mobility scenario, including the following steps: S1: Divide the bandwidth of the MIMO windowed OFDM communication system into K subcarriers, with the interval between each subcarrier being , and send signals through M transmitting antennas at the transmitting end; S2: The frequency domain signal transmitted by the transmitting antenna is modulated by OFDM to generate a time domain signal, the time domain signal is multiplied by the window function and a cyclic prefix is ​​added; S3: Perform space-frequency repetition encoding on the transmitting antenna signal according to the space-frequency repetition code and transmit it to the receiving end through the dual-selective channel; S4: Receive signals through N receiving antennas at the receiving end; S5: Decode the received signal using a multiple-input multiple-output frequency-variable Viterbi decoding scheme; S6: During the decoding process, a wraparound Viterbi algorithm is used to iteratively perform calculations until the result converges or the maximum number of iterations is reached, thereby obtaining a decoding result and utilizing spatial diversity.

[0039] The specific description of the method for utilizing spatial diversity in a MIMO windowed OFDM communication system in a high-speed mobility scenario in this embodiment 1 mainly includes five parts (1.1) to (1.5), which are as follows: (1.1) The MIMO windowed OFDM system and its channel model in this embodiment: A MIMO windowed OFDM system in step S1 is applied to high-speed mobile wireless communication scenarios, and its transmitter is equipped with Root transmitting antenna, the receiving end is equipped with The system bandwidth is divided into subcarriers. The interval between each subcarrier is .

[0040] exist On the subcarrier, the Transmitting antennas ( ) A signal, represented by: (1) The emitted in step S1 After the signal is modulated by orthogonal frequency division multiplexing in step S2, the time domain signal is expressed as: (2) in Indicates the duration of each symbol in the signal.

[0041] The OFDM modulated signal is multiplied by a window function ,have: (3) Adding a cyclic prefix to the windowed signal yields: (4) in Indicates the duration of the cyclic prefix. After that, the OFDM modulated signal is The signal is sent out through a transmitting antenna.

[0042] In the MIMO windowed OFDM system of this embodiment, a dual-selective channel model as in step S3 is considered. transmitting antennas, , to receiving antennas, The channel between (5) in express The number of paths in 、 and Respectively Middle The fading coefficient, delay and Doppler shift of each path. More generally, in equation (5), and are all non-integer (i.e. fractional form), among which (6) in Indicates the maximum Doppler shift. In this embodiment, the fading coefficient in equation (5) is Modeled as a zero-mean cyclically symmetric complex Gaussian random variable. Modeled as A random variable uniformly distributed on . Fractional Doppler shift Modeling is done according to the Jack spectrum, i.e., (7) in exist In addition, 、 and , , are independent of each other.

[0043] In the At the receiving antenna, , the received signal is (8) in The power spectral density is The low-pass filtered additive white Gaussian noise of Indicates the The transmit power of each transmitting antenna, Represents the amplitude of the transmitted power. After continuous-time Fourier transform, The signal on the subcarrier is (9) Define the window function The Fourier transform of (10) Substituting equations (2), (3), (8), and (10) into (9), we obtain (11) in: (12) (13) Due to the use of cyclic prefix, ,have .

[0044] From equation (11), we can see that at any sampling time, the signal received by sampling a specific subcarrier is will be interfered by all other subcarrier signals, which constitutes inter-carrier interference. In order to mitigate inter-carrier interference, a window function with fast decaying side lobes in the frequency domain is used. Due to the fast decay of the side lobes, for a certain integer have: (14) Therefore, because ,have: (15) Substituting (15) into (11), we get (16) in, ; (17) (18) in, Indicates the information sent on the mth transmitting antenna (19) In (16), the channel matrix is a Matrix, its Row and The elements of the column are: (20) Note that according to (15), the channel matrix is sparse.

[0045] (1.2) Utilizing spatial diversity based on space-frequency repetition codes: The goal of the spatial diversity utilization method for a MIMO windowed OFDM communication system in a high-speed mobility scenario in this embodiment is to utilize the spatial diversity of the communication system, including transmit diversity and receive diversity, based on the input-output relationship of the communication system, namely, Equation (16). Utilizing receive diversity is relatively simple and can be directly implemented through surround Viterbi decoding. The focus is on how to utilize transmit diversity.

[0046] For MIMO OFDM systems operating in quasi-static frequency-selective channels, space-frequency block codes (SFBCs) are typically used. SFBCs are applied to two consecutive OFDM symbols and adjacent subcarriers. However, SFBCs cannot be used in the dual-selective channels considered in this invention because dual-selective channels are time-varying. Two consecutive OFDM symbols experience different channels. Furthermore, fractional frequency and time delays exacerbate the situation.

[0047] This embodiment proposes a space-frequency repetition code to utilize transmit diversity. The space-frequency repetition code, combined with the "(1.3) Multiple-Input Multiple-Output Frequency-Varying Viterbi Decoding Scheme" described later, can effectively utilize transmit diversity and receive diversity.

[0048] The space-frequency repetition code proposed in this embodiment refers to (twenty one) in, and In the following “(4) Derivation and Calculation of Pairwise Error Probability”, it will be demonstrated that the space-frequency repetition coding scheme effectively achieves transmit diversity under acceptable system complexity.

[0049] (1.3) Multiple-input multiple-output frequency-variable Viterbi decoding scheme: The signal actually sent in the frequency-variable Viterbi decoding solution for the space-frequency repetition coded MIMO windowed OFDM system of this embodiment is: (twenty two) and are independently selected from the constellation with the same probability. Equation (18) is a replica or copy of Equation (22), and different copies are used on different transmit antennas to obtain diversity gain. Under this condition, the maximum likelihood decoding scheme (i.e., frequency-variant Viterbi decoding) can achieve the optimal solution. Using the maximum likelihood decoding scheme, signal decoding is equivalent to solving the following optimization problem: (twenty three) in, It represents the most likely information to be sent obtained by maximum likelihood decoding.

[0050] because Independent of each other, problem (23) can be reformulated as: (twenty four) In addition, for , The elements in are independent of each other. Therefore, problem (24) can be rewritten as: (25) According to (16), we know (26) in: (27) (28) In (26), due to is a Gaussian random variable, problem (25) can be simplified to: (29) Problem (29) can be solved by maximum likelihood sequence decoding (i.e., frequency-variant Viterbi algorithm): Define the metric function: (30) in, Refers to branch metrics; (31) is the state transition indicator function. Specifically: (32) Means status Can be in Step transfer to state ,like (33) It indicates the status Will not be in the Step transfer to state .

[0051] The remaining question is the initial state Unknown. To solve this problem, the wraparound Viterbi algorithm is used, which is designed for tail-biting convolutional codes. The wraparound Viterbi decoding starts from the state To status Iterate until convergence. In the multi-input multi-output frequency-variable Viterbi decoding algorithm proposed in this embodiment, the convergence condition is checked: (34) If (34) is satisfied, the algorithm is determined to have converged. Otherwise, the wraparound Viterbi decoding will continue until the algorithm reaches the maximum number of iterations (denoted as ).

[0052] Complexity analysis: According to (27), the constraint length of the Viterbi algorithm is Therefore, the computational complexity of the frequency-variant Viterbi decoding based on surround is ,in refer to The cardinality of all possible values.

[0053] The computational complexity is It can be seen that the constraint length of the Viterbi algorithm is It has a significant impact on system complexity. To make the system complexity bearable, it should be reduced as much as possible. The index of Given the maximum Doppler shift and window function of the wireless channel, is a constant. This is related to the space-frequency repetition code design in this embodiment.

[0054] In space-frequency repetition code encoding, if the space-frequency repetition code is (35) for and , which will be proved in the following "(1.4) Pairwise Error Probability Derivation Calculation" to achieve optimal performance, however, using this space-frequency repetition code, The index becomes This significantly increases the system complexity. If the space-frequency repetition code is: (36) In the following "(1.4) Derivation and Calculation of Pairwise Error Probability", it will be demonstrated that almost no transmit diversity is obtained by using Equation (36), while the space-frequency repetition code proposed in the above "(1.2) Utilizing Spatial Diversity Based on Space-Frequency Repetition Code" effectively utilizes transmit diversity with acceptable system complexity.

[0055] (1.4) Derivation and calculation of pairwise error probability: In this section, the pairwise error probability (PEP) is derived and calculated, which indicates the spatial diversity order achieved by the system using this method. Furthermore, the PEP provides a theoretical basis for "(1.5) Power Allocation Optimization" below.

[0056] Select two different transmission signal blocks with equal probability and . and Only in There is a different signal on each subcarrier, making (37) Furthermore, in (22), Gray code is used to encode the binary information bits. and The distance between means and Under this condition, the pairwise error probability provides a good approximation of the system bit error rate performance.

[0057] When sending hour, The received signal vector at the receiving antenna is (38) Substituting (16) into (38), we can obtain: (39) in express Circular shift down subcarriers. Similarly, we can get When The received signal vector at the receiving antennas.

[0058] definition: (40) According to formulas (37) and (39), we can know that (41) in Representation matrix No. List.

[0059] According to

[17] , send Time General Mistakenly judged as The pairwise error probability can be expressed as (42) in refers to function.

[0060] In formula (42), is a random variable. To derive the pairwise error probability, we will focus on The probability density function of .

[0061] because Each element of is multiple The weighted sum of expressions should be studied In order to deduce the expression The probability density function of . According to formula (20), Multiple items ( ), where is the fading coefficient of each path. In (5), the term is modeled as a zero-mean cyclically symmetric complex Gaussian random variable. Therefore, the term It is also a cyclically symmetric complex Gaussian random variable with zero mean.

[0062] According to formula (20), and The covariance function between is: (43) In the derivation, the fading coefficient is used , are independent of each other. According to (12), Only with and related, and it is independent of . Therefore, we have: (44) The following derivation is based on the properties of the window function. Substituting (12) into , you can get: (45) In the derivation, the following approximation is adopted: (46) This is because ,therefore In addition, from (16) we can get ,in Much smaller than .

[0063] In (45), there is only one random variable From (7) we can get: (47) The integral in Eq. (47) usually does not have a closed-form expression. Given a window function, it can be obtained by numerical integration: . Note and the summation variable in (44) Therefore, there is (48) in Indicates that from Transmitting antennas ( ) to Receiving antennas ( ), (49) According to the above description, is a zero-mean cyclic symmetric complex Gaussian random vector whose probability density function is determined only by its covariance matrix Determine. In (41), since the wireless channels to different receiving antennas are usually independent of each other, we have: (50) in , , is a matrix, (51) Because the wireless channels from different transmitting antennas are usually independent of each other, we get (52) Use (48), No. Row and The elements of the column are represented as (53) Therefore, we have: (54) In (54), if the covariance matrix is the identity matrix, is a chi-squared distributed random variable. However, in this embodiment, the covariance matrix is not the identity matrix.

[0064] According to (15), matrix , ,have Line and The elements of the column are close to zero. Remove these rows and columns close to zero and get a The positive definite matrix . Therefore, we have: (55) In (55), The dimension is .

[0065] right Perform eigenvalue decomposition: (56) in is a unitary matrix, is a diagonal matrix, (57) in: (58) In (57), yes The eigenvalues ​​of is composed of the corresponding eigenvectors.

[0066] The vector Defined as: (59) (59) is a -dimensional zero-mean cyclically symmetric complex Gaussian random vector. The covariance matrix of can be obtained as follows: (60) It is a degrees of freedom, and (in ) is an exponentially distributed random variable with mean 1.

[0067] Therefore, we have: (61) This means is a weighted chi-squared distributed random variable, where the weights are The eigenvalue of .

[0068] Therefore, the following propositions exist: Proposition 1: The probability density function of is: (62) Proof: See Proof A at the end of Example 1. In obtaining Then, use (63) to calculate the Next, normalize: (63) The corresponding signal-to-noise ratio is: (64) For example, when When using quadrature phase shift keying modulation signal, There are four signals One of have and .

[0069] To calculate , there are the following propositions.

[0070] Proposition 2: There is (65) Proof: See Proof B at the end of Example 1.

[0071] Using Proposition 2, we get: (66) Next, the diversity order of the MIMO windowed OFDM system proposed in Example 1 is studied.

[0072] When the signal-to-noise ratio When , using Taylor series expansion, we get: (67) in: (68) Substituting (67) into (66), we obtain: (69) By definition: (70) in For integers, we have: (71) There are the following propositions: Proposition 3: When Sometimes, there are (72) And when Sometimes, there are (73) Proof: See Proof C at the end of Example 1.

[0073] Using (72) of Proposition 3, we get (74) Using (73) in Proposition 3, we get (75) From (75), we can see that the spatial diversity order of the MIMO windowed OFDM system proposed in this embodiment after using the space-frequency repetition code (21) is , the system computational complexity is , which effectively utilizes transmit diversity and has an affordable computational complexity.

[0074] If space-frequency repetition code (35) is used, the diversity order is , effectively utilizing transmit diversity, the performance is the highest but the computational complexity of the system is , which is much higher than the formula (21) used in this embodiment 1, and is difficult to accept. If the space-frequency repetition code (36) is used, the diversity order is , no parameters M , transmit diversity is hardly utilized.

[0075] (1.5) Power distribution optimization: Based on the pairwise error probability derivation (1.4), the power allocation between different transmitting antennas is optimized.

[0076] In equation (76), to minimize the pairwise error probability, we should maximize (76) Therefore, the power allocation optimization problem is formulated as follows: (77a) (77b) The logarithmic function is introduced because it is a monotonically increasing function and (78) The logarithmic determinant function is is a concave function, and from (52) we can see that It's about Therefore, the objective function in problem (77) is about Problem (77) is a convex optimization problem that can be solved efficiently using the interior point method to optimize the power allocation between different transmitting antennas.

[0077] Proof A: because , , is an exponentially distributed random variable with mean 1, so: (81) (81) is a mean An exponentially distributed random variable. The probability density function of is: (82) because: (83) so, The probability density function of is: (84) therefore, The characteristic function of is: (85) in express The characteristic function of . The mean is An exponentially distributed random variable, so The characteristic function of is: (86) Substituting (86) into (85), we obtain (87) get After the characteristic function of The probability density function of : (88) In (88), the integrand The extremes of exist only in: (89) for , this only happens if: (90) exist The residue at is: (91) According to the residue theorem, the integral along a closed path in the upper half plane is equal to Multiply by the sum of the interior pole residues. Therefore, we have: (92) Substituting (91) into (92), we get (62).

[0078] Proof B: Will Substituting the function expression into the left side of (65), we can get (93) By exchanging the order of multiple integrals, we can obtain (94) Proof C: Construct a Vandermonde determinant (95) Easy to know: (96) when When Replace the last line with (97) We get another determinant, which is . because , we know the determinant There are two identical lines in . Therefore, we have: (98) The determinant Expanding the last line yields: (99) Substituting equation (96) into equation (100), we can obtain (100) Since usually , so we can get (72).

[0079] when When Replace the last line with (101) We get another determinant, denoted as .have: (102) Therefore, we get: (103) The determinant Expanding the last line, we have: (104) Comparing equations (103) and (104), we obtain equation (73).

[0080] Example 2 This embodiment 2 provides a MIMO windowed OFDM communication system in a high-speed mobility scenario, and applies the spatial diversity utilization method of the MIMO windowed OFDM communication system in a high-speed mobility scenario described in embodiment 1. The system includes a transmitting end module and a receiving end module, and the transmitting end module and the receiving end module are connected via antenna communication. The bandwidth of the system is divided into Ksubcarriers, and the interval between each subcarrier is ; The transmitting end module is configured with M The transmitting antenna comprises an OFDM modulation unit for modulating a frequency domain signal into a time domain signal through orthogonal frequency division multiplexing; A windowing processing unit, configured to multiply a time domain signal by a window function to obtain a windowed signal; a cyclic prefix adding unit, configured to add a cyclic prefix to the windowed signal; a space-frequency repetition coding unit, configured to perform space-frequency repetition coding on a transmission signal according to a space-frequency repetition code; The receiving end module is configured with N receiving antennas and includes: an OFDM demodulation unit for performing OFDM demodulation on the received signal; A multiple-input multiple-output frequency-variable Viterbi decoder for performing surround Viterbi decoding on a received signal; A pair error probability calculation module, used to calculate the pair error probability of the transmitted signal; A power allocation optimization unit, configured to optimize the power allocation between different transmitting antennas based on the pairwise error probability of the transmitted signal; The system adopts a dual-selective channel for communication connection between the transmitter module and the receiver module.

[0081] Example 3 In the simulation, from transmitting antennas, , to receiving antennas, Channel, , is generated based on the TDL-A channel model provided by the 3GPP standard, where the normalized delay The power of each path is given. In this embodiment 3, it is assumed that the delay of each path is (79) in ns refers to the delay spread. In , a random Doppler shift is assigned to each path according to the Jack model (7). In addition, is a cyclically symmetric Gaussian random variable whose power is specified in the TDL-A channel model. Transmitting antennas ( ) to receiving antennas ( ) is assumed to be the channel power between , No. The transmission power of each transmitting antenna is The modulation scheme is quadrature phase shift keying.

[0082] In a MIMO windowed OFDM system, the bandwidth is divided into subcarriers. The interval between each subcarrier is kHz. The duration of the cyclic prefix is s. The system uses a raised cosine roll-off window with a roll-off factor of 1. To evaluate the impact of fractional delay, an upsampling factor of 8 is used. It is assumed that the receiver can obtain a perfect channel state estimate.

[0083] The pairwise error probability derivation calculation in (1.4) of Example 1 is based on the approximate formula (48). In Figure 2, the simulation value and approximate value of the following formula are given to verify the accuracy of the approximate formula (48): (80) Simulation values ​​and approximate values ​​are Figure 1 In the equation (48), the approximate value of the covariance function (80) is As can be seen from Figure 2, when When the frequencies are 2000 Hz, 5000 Hz and 10000 Hz, the approximate values ​​are consistent with the simulation values.

[0084] In Figure 3, consider the transmitter equipped with A transmitting antenna and a receiver equipped with The simulated bit error rate is compared with the theoretically derived pair error probability. Figure 3 In the paper, they are represented as “simulation” and “theory” respectively. Hz, consider When Hz and 10000 Hz, consider As shown in Figure 3, at low signal-to-noise ratios, the theoretically derived pair error probability is slightly lower than the simulated bit error rate, while at high signal-to-noise ratios, the theoretically derived pair error probability is the same as the simulated bit error rate. This is because the derivation of the pair error probability takes into account the condition of a minimum signal difference of one bit. This holds true at high signal-to-noise ratios. At low signal-to-noise ratios, errors exceeding one bit cause the derived pair error probability to differ from the simulated bit error rate. Because communication systems typically operate under high signal-to-noise ratio and low bit error rate conditions, the theoretically derived pair error probability of the present invention is meaningful.

[0085] To demonstrate the spatial diversity gain, Figure 4 shows the spatial diversity gain for different numbers of transmit antennas. The bit error rate performance of And the maximum Doppler shift is Hz. As can be seen from Figure 4, it is observed that The spatial diversity gain is achieved by increasing from 1 to 4. In addition, when the signal-to-noise ratio is high, the derived pair error probability is almost the same as the simulated bit error rate.

[0086] In Figure 5, the results for different numbers of receiving antennas are shown. The bit error rate performance of And the maximum Doppler shift is Hz. To evaluate the performance under high-order modulation, an 8-phase keying modulation scheme is used. As can be seen from Figure 5, the scheme proposed in this invention can simultaneously achieve transmit diversity and receive diversity gain.

[0087] FIG6 shows the effect of the optimized power allocation scheme of the present invention, in which the transmitter is equipped with transmitting antennas, the maximum Doppler shift is Hz. In the simulation of the case, it is assumed that the channel power is 、 and .for In addition to the above settings, assume 、 and The power allocation scheme proposed in Section 6 is compared with the uniform power allocation scheme (i.e. ), which are represented as “optimal” and “equally divided” in Figure 6. As can be seen from Figure 6, the optimized power allocation scheme proposed in the present invention can achieve a power gain of about 1-2 dB compared to the uniform power allocation scheme.

[0088] In Figure 7, the comparison is made when the transmitter is equipped with transmit antennas and the maximum Doppler shift is Different power distribution schemes at Hz. and In the simulation of the two cases, it is assumed that the channel power is 、 、 and , As can be seen from FIG7 , the optimized power allocation scheme proposed by the present invention is better than the uniform power allocation scheme.

[0089] In summary, the present invention takes into account fractional Doppler shift and fractional delay, and proposes a space-frequency repetition code (SFRC) that utilizes spatial diversity for a multiple-input multiple-output (MIMO) windowed orthogonal frequency division multiplexing (OFDM) system in a dual-selective fading channel. The proposed system also theoretically derives the pairwise error probability, and proposes a power allocation optimization scheme. Simulation results show that under high signal-to-noise ratios, the theoretically derived pairwise error probability is nearly identical to the simulated bit error rate. Furthermore, the results demonstrate that spatial diversity gain can be achieved with an increase in the number of transmitting and / or receiving antennas. Simulation results also indicate that the power allocation scheme proposed by the present invention outperforms the uniform power allocation scheme.

[0090] The above is 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 principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for utilizing spatial diversity in a MIMO windowed OFDM communication system in a high-speed mobile scenario, characterized in that: The following steps are involved: The bandwidth of the MIMO windowed OFDM communication system is divided into K subcarriers, and the interval between each subcarrier is , and send signals through M transmitting antennas at the transmitting end; For the first The frequency domain signal transmitted by the transmitting antenna is modulated by OFDM to generate a time domain signal, the time domain signal is multiplied by the window function and a cyclic prefix is ​​added; Performing space-frequency repetition coding on the transmitting antenna signal according to the space-frequency repetition code and transmitting it to the receiving end through the dual-selective channel; At the receiving end, the signal is received through N receiving antennas; The received signal is decoded using a multiple-input multiple-output frequency-variable Viterbi decoding scheme; During the decoding process, a wraparound Viterbi algorithm is used to iteratively perform calculations until the result converges or the maximum number of iterations is reached, and the decoding result is obtained to realize the utilization of spatial diversity.

2. The method according to claim 1, characterized in that The said The frequency domain signal transmitted by the transmitting antenna is modulated by OFDM to generate a time domain signal. The time domain signal is multiplied by a window function and a cyclic prefix is ​​added. Specifically, the following steps are performed: exist On the subcarrier, the Transmitted by the transmitting antenna A signal, represented by: After orthogonal frequency division multiplexing OFDM modulation, the time domain signal is expressed as: in Indicates the symbol duration, is the spacing of each subcarrier; Multiply the OFDM modulated signal by a window function , and get the windowed signal: Adding a cyclic prefix to the windowed signal yields: in Indicates the duration of the cyclic prefix.

3. The method according to claim 2, characterized in that The window function is a window function with rapid sidelobe attenuation, which satisfies: in, is a positive integer, is the spacing of each subcarrier, is the window function The Fourier transform of .

4. The method according to claim 1, wherein From The transmitting antenna to the The dual-selective channel between the receiving antennas is: in, express The number of paths in 、 and Respectively Middle Fading coefficient, delay and Doppler shift of each path; in, and are all non-integer or fractional forms, and: in, Indicates the maximum Doppler shift, fading coefficient Modeled as a zero-mean cyclically symmetric complex Gaussian random variable with fractional time delay Modeled as A uniformly distributed random variable, fractional Doppler shift Modeling is performed according to Jack spectrum, namely: in, exist uniformly distributed, and in addition, 、 and , Independent of each other.

5. The method according to claim 4, characterized in that The input-output relationship of the dual-selective channel, that is, the information received by the nth receiving antenna is : in, Indicates the The transmit power of each transmitting antenna, Indicates the amplitude of the transmitted power, is the channel matrix of the dual-selective channel and is a sparse matrix; in: in, The received signal undergoes continuous-time Fourier transform at the receiving end. The signal on the subcarrier; Indicates in The received signal at each receiving antenna; The power spectral density is Low-pass filtered additive white Gaussian noise.

6. The method according to claim 5, characterized in that The space-frequency repetition code is: in, and .

7. The method according to claim 6, characterized in that The multiple-input multiple-output frequency-variable Viterbi decoding scheme includes: Construct the state vector based on the space-frequency repetition code: Construct the channel response vector: Define the metric function: in, : is the state transition indicator function, when , which means the state Can be in Step transfer to state , and when , then it indicates the status Will not be in the Step transfer to state ; During the decoding process, the wrap-around Viterbi algorithm is used to decode the state To status Iteratively calculate the metric function, and when the condition is met When convergence is reached, the iteration is stopped and the decoding result is obtained. Otherwise, the wraparound frequency-variable Viterbi algorithm is continued until the maximum number of iterations V is reached and the iteration is stopped to obtain the decoding result. The constraint length of the algorithm is .

8. The method according to claim 1, characterized in that The method for utilizing spatial diversity in a MIMO windowed OFDM communication system in a high-speed mobile scenario also includes a power allocation optimization step, which optimizes the power allocation between different transmitting antennas by calculating the paired error probability of the transmitted signal and minimizing the paired error probability as the optimization goal.

9. The method according to claim 1, characterized in that The spatial diversity order obtained by the space-frequency repetition code is: ,in is a positive integer constant.

10. A MIMO windowed OFDM communication system for high-speed mobility scenarios, comprising a transmitter module and a receiver module, wherein the transmitter module and the receiver module are connected via antenna communication, and characterized in that: The bandwidth of the system is divided into K subcarriers, and the interval between each subcarrier is ; The transmitting end module is configured with M The transmitting antenna comprises an OFDM modulation unit for modulating a frequency domain signal into a time domain signal through orthogonal frequency division multiplexing; A windowing processing unit, configured to multiply a time domain signal by a window function to obtain a windowed signal; a cyclic prefix adding unit, configured to add a cyclic prefix to the windowed signal; a space-frequency repetition coding unit, configured to perform space-frequency repetition coding on a transmission signal according to a space-frequency repetition code; The receiving end module is configured with N receiving antennas and includes: an OFDM demodulation unit for performing OFDM demodulation on the received signal; A multiple-input multiple-output frequency-variable Viterbi decoder for performing surround Viterbi decoding on a received signal; A pair error probability calculation module, used to calculate the pair error probability of the transmitted signal; A power allocation optimization unit, configured to optimize the power allocation between different transmitting antennas based on the pairwise error probability of the transmitted signal; The system adopts a dual-selective channel for communication connection between the transmitter module and the receiver module.

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