Performance Analysis Of Time-varying Channels And Precoding In Massive MIMO Systems

By equipping a large number of antenna arrays to obtain rich spatial diversity gain,the massive multiple-input multiple-output(MIMO)technology can efficiently improve the spectral and energy efficiencies of 5G systems,and enhance the system's robustness and reliability.However,the computational complexity of the signal processing process,especially matrix multiplication and inversion,is significantly increased with a large number of antennas in massive MIMO systems.Considering that the massive MIMO systems are mainly equipped with low-cost hardware components,the huge computational complexity will greatly increase the hardware cost.On the other hand,the advantage of array gain for massive MIMO systems deeply relies on accurate channel state information(CSI),while the CSI inaccuracy will incur more severe interference among users.Unfortunately,the channel aging due to time-varying channels and pilot contamination caused by limited pilot resources will undermine the accuracy of CSI estimate.In this paper,we propose algorithms to combat the influence of channel aging and pilot contamination in massive MIMO systems,while achieving the target of reducing the corresponding computational complexity of signal processing and improve the spectral efficiency(SE)performance.Key contributions of this paper addressing above nontrivial aspects are as follows:(1)Considering the high computational complexity cost of signal processing,i.e.,channel estimation,fast Fourier transform(FFT)and calculation of regularized zero-forcing(RZF)matrices in massive MIMO-orthogonal frequency division multiplexing(OFDM)systems,we smartly propose the algorithm of inverse extrapolation by processing channel prediction and inverse extrapolation separately for RZF matrices;The proposed algorithm can effectively extend the OFDM downlink length for reliable communication;Besides,under the inverse extrapolation schemes,we also investigate the influence of system factors such as pilot allocation,signal-noise ratio(SNR)and Doppler frequency shift on the performance of massive MIMO systems.Results show that the inverse extrapolation algorithm can significantly reduce the computational complexity,extend the OFDM downlink length and reduce the frequency of transmitting pilot under reliable communication.(2)Considering that the channel aging problem degrades the CSI estimation accuracy of time-varying massive MIMO-time shifted pilot(TSP)systems,while further degrades the system SE performance,we propose a channel estimation algorithm based on the TSP structure;We derive the probability density function(PDF)expression of the uplink signal to interference plus noise ratio(SINR)with Gamma approximation,and a closed-form expression of the achievable rate is derived for the influence of time-varying channel on system performance;By jointly adopt the previous and upcoming channel observation vectors,we design a channel estimation algorithm to combat the influence of channel aging.Numerical results have shown that the computational complexity can be reduced by 61.84%,and extend the number of downlink length by 5 OFDM symbols.In this case,the frequency for uplink pilot transission is redueced without significant performance loss.(3)Considering that the time-varying channels result in the Doppler spread,reduces CSI estimation accuracy,while degrades the performance of massive MIMO-RZF systems,we design algorithms to adopt high array gains of massive antennas to combat the influence of time variation for channels/precoders;By adopting a high spatial resolution of massive MIMO systems to detect the angle of arriving(AO A)for the upcoming signal,an array steering model for reducing the influence of Doppler spread is designed;Based on the random matrix theory(RMT),we also investigate the relationship between RZF time variation and the number of antennas as well as the temporal variation of channels;Finally,based on the advantage of a large number of antennas in reducing the temporal variation of RZF precoder,we design a Kalman filter to realize the tracking of RZF matrices.Numerical results have proven the accuracy of analytical results,analyze the temporal characteristics of channels and RZF precoders under massive arrays and investigate the computational complexity and achievable rate performance of the proposed Kalman-based RZF tracking algorithm.(4)Considering that pilot contamination problem caused by the limitation of pilot resources in massive MIMO systems degrades the CSI estimation accuracy,increases interference among users and reduces the SE performance,we design an efficient precoder to reduce the influence of pilot contamination problem;Specifically,a closed-form expression of the downlink achievable rate is obtained based on the RMT singular value decomposition(SVD)theory;Besides,by adopting optimization theory,we propose an RZF design scheme to achieve the optimal achievable rate performance;Finally,under the proposed RZF design schemes,we analyze the influence of the number of users,signal-noise ratio(SNR)and pilot reuse factor on system performance.Numerical results have proven the accuracy of analytical results,analyze the influence of pilot contamination and prove the advantage of proposed RZF design schemes in combating pilot contamination,improving the SE performance of massive MIMO systems.In summary,to optimize the performance of massive MIMO systems,we have proposed algorithms to reduce the computational complexity,combat the influence of channel aging and pilot contamination problems.By adopting RMT,probability theory and optimization theory,and taking computational complexity as well as achievable rate as performance indicators,we analyze the performance of proposed algorithms with analytical and numerical results.Conclusions have provided theoretical guidance for the optimal design of massive MIMO systems.