CN114070354A - Adaptive segmented matrix inverse tracking MIMO detection method based on GS iteration method - Google Patents

Adaptive segmented matrix inverse tracking MIMO detection method based on GS iteration method Download PDF

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CN114070354A
CN114070354A CN202111507345.2A CN202111507345A CN114070354A CN 114070354 A CN114070354 A CN 114070354A CN 202111507345 A CN202111507345 A CN 202111507345A CN 114070354 A CN114070354 A CN 114070354A
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张华�
王畅
王俊波
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention discloses a self-adaptive segmented matrix inverse tracking MIMO detection method based on a GS iteration method. Massive MIMO, one of the key technologies of 5G, has the advantages of high information transmission rate, high reliability, and high spectrum utilization rate compared to the conventional single antenna system. In a large-scale MIMO system, signal detection is a key technology for determining system reliability, and is one of difficulties, and the conventional MIMO detection algorithm generally has the disadvantages of high computational complexity and low convergence rate. The invention provides a self-adaptive segmented matrix inverse tracking detection method aiming at the channel change rate on the basis of a GS iterative algorithm and in consideration of the time-varying characteristic of a channel. The invention tracks the MMSE filter matrix by utilizing the correlation characteristic of the channel in the time domain, adaptively updates the tracking step length according to the time domain change rate of the channel, and only carries out GS iterative operation once at each tracking updating moment, thereby not only improving the convergence speed of the algorithm, but also reducing the calculation complexity.

Description

Adaptive segmented matrix inverse tracking MIMO detection method based on GS iteration method
Technical Field
The invention relates to a self-adaptive segmented matrix inverse tracking MIMO (multiple input multiple output) detection method based on a GS (Gauss-Seidel) iteration method, and belongs to the technical field of wireless communication.
Background
Massive MIMO technology has received sufficient attention in recent years as a key technology of 5G. The MIMO detection is a technical difficulty in a large-scale MIMO scene, the MIMO detection algorithm is mainly divided into a linear type and a nonlinear type, and the invention improves the linear detection algorithm.
The technical difficulty in the linear detection method mainly lies in solving the inverse of a filter matrix, the precise calculation complexity of the matrix inverse is extremely high, the hardware realization is very difficult, the iterative algorithm is generally adopted in engineering to calculate the matrix approximate inverse, and the commonly used iterative algorithms include Newton (Newton), Gauss-Seidel, Successive Over-Relaxation (SOR), Richardson, Jacobi and the like. For the above iterative algorithm, as the number of iterations increases, the error between the approximate inverse and the exact inverse of the filter matrix is continuously reduced, but the corresponding computational complexity is increased, and generally, when the number of iterations exceeds 3, the computational complexity of the iterative algorithm exceeds the exact computation. Therefore, the current research mainly focuses on how to improve the convergence rate of the iterative algorithm, such as the research on the coefficient value taking problem and the iterative initial value selection problem in the Richardson algorithm under the non-stationary condition. However, these studies do not consider the correlation characteristic of the channel in time, but perform independent iterative operation at each sampling point, and actually, the channel matrix is a continuous change process in time, especially in an indoor MIMO scenario, the channel is slowly changed in time.
Disclosure of Invention
The technical problem is as follows: the main technical problem to be solved by the invention is to avoid the defects in the background technology, and provide a self-adaptive segmented matrix inverse tracking MIMO detection method based on a GS iteration method.
The technical scheme is as follows: the invention provides an adaptive segmented matrix inverse tracking method based on a GS iterative method according to the time-varying characteristic of a channel, which comprises the following steps:
in the first step, for the filter matrix G of the MMSE detection algorithm, the inverse D of the diagonal matrix is adopted-1And as an iteration initial value, performing 1 iteration by using a GS iteration algorithm to calculate the initial value of the algorithm.
And secondly, tracking the inverse of the matrix according to the time-varying characteristic of the channel, adaptively determining a tracking step length according to the time-domain variation rate of the channel, and performing GS iteration once by using the iteration result of the previous tracking update time as the iteration initial value of the next tracking update time, namely performing adaptive step length segmented matrix inverse tracking.
And thirdly, restoring the transmitted signal according to the iteration result, and verifying whether the algorithm can accelerate iteration convergence by evaluating the hard decision error rate.
Further, the first step specifically includes: defining Gram matrix G ═ HHH, and
Figure BDA0003404842940000021
where H is the channel matrix and y is the received signal. Then in accordance with the MMSE detection algorithm,
Figure BDA0003404842940000022
wherein sigma2Is the noise variance, W is the filter matrix, I is the unit matrix,
Figure BDA0003404842940000023
is the recovered signal. Considering the channel hardening characteristic of Massive-MIMO channel, the filter matrix has diagonal dominance, so the inverse of the diagonal matrix D of W can be used as the iteration initial value according to GS iteration algorithm
W-1(k)＝(D+L)-1(I-LHW-1(k-1))k＝1,2,…
And (4) performing iteration, and performing iteration operation only once to reduce the calculation complexity to obtain an iteration result of the algorithm at the first sampling point.
In the second step, the channel matrix H is a continuous variation process in time, and correspondingly, the MMSE filter matrix W is also continuous in time, which results in that the inverses of the filter matrices corresponding to the adjacent closer sampling points are closer under the condition that the time domain variation rate of the channel is smaller, so that the same matrix inverse can be used in a section of sampling points, and the approximate inverse W of the previous section is usedinv,tAs initial value for next iteration
Figure BDA0003404842940000024
And lambda is the length of each segment, namely the inverse tracking step length of the matrix, and is determined in a self-adaptive mode according to the change rate of the channel. Adaptive compensation and segmented tracking process with filter matrix inverse obtained from above
Figure BDA0003404842940000025
The matrix inverse tracking method combines the adaptive step size and the GS iterative algorithm, makes full use of the relevant characteristics of the channel in time, and can obtain a convergence speed which is higher than that of the traditional algorithm for multiple iterations under the condition of only one iteration.
Third, based on the channel estimation result and the received signal
Figure BDA0003404842940000026
Recovering a transmitted signal
Figure BDA0003404842940000027
The information bits transmitted by the transmitting end are obtained through the receiving end demodulation module, the known information bits are transmitted at the transmitting end, the data demodulated by the receiving end are compared, the error rate of the method can be obtained, and the algorithm performance of the method can be evaluated according to the error rate.
Has the advantages that: the invention provides a self-adaptive segmented matrix inverse tracking detection method aiming at the channel change rate on the basis of a GS iterative algorithm by considering the time-varying characteristic of a channel.
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Fig. 1 is a flowchart of an adaptive segmented matrix inverse tracking MIMO detection method based on a GS iterative method according to an embodiment of the present invention.
Fig. 2 is a schematic structural diagram of an adaptive segmented matrix inverse tracking MIMO detection system based on a GS iterative method according to an embodiment of the present invention.
FIG. 3 is a graph comparing the performance of the method of the present invention with that of a conventional method.
Detailed Description
The invention provides a self-adaptive segmented matrix inverse tracking MIMO (multiple input multiple output) detection method based on a GS (Gauss-Seidel) iterative method, aiming at a scene with low channel time-varying rate in a large-scale MIMO system, the method is improved on the basis of a traditional GS iterative algorithm, a self-adaptive step length segmented matrix inverse tracking detection algorithm is provided, and the convergence speed is improved while the low calculation complexity is kept.
System model
Let the number of transmitting antennas be NtThe number of receiving antennas is NrConsider an Nr×NtIn the MIMO system, as shown in fig. 2, a transmission signal is modulated by a transmitter, transmitted through multiple antennas, and a receiver receives a signal for demodulation, which may be represented as y ═ Hx + z, where H is a channel matrix:
Figure BDA0003404842940000031
element hjiDenotes the channel gain from the ith transmitting antenna to the jth receiving antenna, j is 1,2, …, Nr；i＝1,2,…,Nt。x＝[x1,x2,…,xt]TTo transmit a signal, wherein xiThe signal sent by the ith transmitting antenna; y ═ y1,y2,…,yr]TTo transmit a signal, wherein yjFor the signal received by the jth receive antenna. z is ═ z1,z2,…,zr]TIs a noise vector, zjRepresents the additive white noise of the j-th antenna with a variance of
Figure BDA0003404842940000032
In an actual scene, the influence of fading also needs to be considered, and for the indoor environment where the system is located, a rice fading model is adopted due to the existence of a strong direct path. The Rice channel matrix can represent
Figure BDA0003404842940000033
Wherein, HLOSTo determine a component of the channel matrix, HRayleighFor the random channel matrix component, K is the rice factor.
When an algorithm performance simulation environment is built, in order to be more consistent with the actual channel of the system, the main diagonal is strengthened on the basis, namely, the main diagonal is increased
Figure BDA0003404842940000034
And (4) components. Meanwhile, in order to compare the system performances of different channels conveniently, the channel matrix needs to be normalized
Figure BDA0003404842940000041
Wherein | · | purple sweetFrobeniusRepresenting the Frobenius norm of the matrix.
(II) GS iterative algorithm
Defining Gram matrix G ═ HHH, and
Figure BDA0003404842940000042
where H is the channel matrix and y is the received signal. Then in accordance with the MMSE detection algorithm,
Figure BDA0003404842940000043
wherein sigma2Is the noise variance, W is the filter matrix, I is the unit matrix,
Figure BDA0003404842940000044
is the recovered signal. Considering the channel hardening characteristics of Massive-MIMO channel, W is approximately a Hermition positive definite matrix, so W ═ D + LHWherein D, L, LHDiagonal of W respectivelyMatrix, lower triangular matrix and upper triangular matrix, the GS iterative algorithm of MMSE linear detection can be expressed as:
x(k)＝(D+L)-1(yMF-LHx(k-1))k＝1,2,…
where k is the number of iterations. The iteration result of the above formula is the estimated transmission signal
Figure BDA0003404842940000045
However, the matrix inverse tracking algorithm proposed by the present invention needs to track the inverse of the filter matrix, and therefore needs to deform the GS iterative algorithm
W-1(k)＝(D+L)-1(I-LHW-1(k-1))k＝1,2,…
Wherein I is a unit array. Because W has diagonal dominance characteristic, the inverse of diagonal matrix D of W can be used as an iteration initial value for iteration, and only one iteration operation is performed to reduce the calculation complexity, so that the iteration result of the algorithm at the first sampling point is obtained.
(III) adaptive piecewise matrix inverse tracking
In fact, the channel matrix H is a continuous variation process in time, and accordingly, the MMSE filter matrix W is also continuous in time, which results in that, under the condition that the time domain variation rate of the channel is small, the inverses of the filter matrices corresponding to the adjacent and closer sampling points are relatively close, so that the same matrix inverse in one sampling point section can be used, and the approximate inverse W of the previous section can be usedinv,tAs initial value for next iteration
Figure BDA0003404842940000046
And lambda is the length of each segment, namely the inverse tracking step length of the matrix, and is determined in a self-adaptive mode according to the change rate of the channel. Adaptive compensation and segmented tracking process with filter matrix inverse obtained from above
Figure BDA0003404842940000047
The matrix inverse tracking method combines the adaptive step size and the GS iterative algorithm, makes full use of the relevant characteristics of the channel in time, and can obtain a convergence speed which is higher than that of the traditional algorithm for multiple iterations under the condition of only one iteration. As shown in fig. 3, in the 64QAM modulation and 8 × 8MIMO scenario with the channel rice factor K being 10, when the snr is greater than 20dB, the performance of the method of the present invention is significantly improved compared to the conventional GS iterative algorithm (3 iterations), and is already close to the performance of the MMSE algorithm.
The embodiments of the present invention will be described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (3)

1. A self-adaptive segmented matrix inverse tracking MIMO detection method based on a GS iterative method is characterized in that:
in the first step, for the filter matrix W of the MMSE detection algorithm, the inverse D of the diagonal matrix is adopted-1As an iteration initial value, performing 1 iteration by using a GS iteration algorithm, and calculating an initial value of an MMSE detection algorithm;
secondly, tracking the inverse of the matrix according to the time-varying characteristic of the channel, adaptively determining a tracking step length according to the time-domain variation rate of the channel, and performing GS iteration once by using the iteration result of the previous tracking update time as the iteration initial value of the next tracking update time, namely performing adaptive step length segmented matrix inverse tracking;
and thirdly, restoring the transmitted signal according to the iteration result, and verifying whether the algorithm can accelerate iteration convergence by evaluating the hard decision error rate.
2. The adaptive segmented matrix inverse tracking MIMO detection method based on the GS iterative method as claimed in claim 1, wherein: the first step specifically comprises: the channel hardening characteristic of the Massive-MIMO channel and the filter matrix W have diagonal dominance, so the inverse of the diagonal matrix D of W can be used as an iteration initial value according to the GS iteration algorithm
W-1(k)＝(D+L)-1(I-LHW-1(k-1))k＝1,2,…
Performing an iteration, where L is a lower triangular matrix of the filter matrix, W-1(k-1)As a result of the last iteration, W-1(k)I is a unit array for a current iteration result; in order to reduce the calculation complexity, GS iterative operation is performed only once to obtain the iterative result of the MMSE detection algorithm at the first sampling point.
3. The adaptive segmented matrix inverse tracking MIMO detection method based on the GS iterative method as claimed in claim 1, wherein: under the condition of small time domain change rate of the channel, the same matrix inverse is used in a section of sampling points, and the approximate inverse W of the previous section is usedinv,tAs initial value for next iteration
Figure FDA0003404842930000011
Lambda is the length of each segment, namely the inverse tracking step length of the matrix, and is determined in a self-adaptive manner according to the change rate of a channel; adaptive compensation and segmented tracking process with filter matrix inverse obtained from above
Figure FDA0003404842930000012
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CN115173899B (en) * 2022-06-30 2024-07-09 东南大学 Self-adaptive segmented matrix inverse tracking MIMO detection method based on Richardson iteration method

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