二维压缩感知优化算法提升大规模MIMO信道估计效率

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大规模多输入多输出(Massive MIMO)通信系统是一种无线通信技术，其中多个天线同时服务于众多用户，旨在提高频谱效率和信号质量。在这样的系统中，信道估计是一个关键步骤，因为它直接影响到数据传输的准确性。传统的信道估计方法可能在大规模天线阵列和密集用户环境中变得复杂和计算密集。本文的研究集中在大规模MIMO信道估计的问题上，特别关注的是如何利用压缩感知(Compressed Sensing, CS)理论来简化这一过程。压缩感知是一种信息理论概念，它指出即使在信号维度远小于传统采样理论所需的情况下，通过稀疏性（即信号中的大部分信息可以被少数非零元素表示）也能实现高效的信息恢复。传统的CS方法通常假设信号是全局稀疏，但在大规模MIMO系统中，由于物理传播环境中的共享本地散射器，用户信道矩阵呈现出一种局部的、分块稀疏结构，这种特性使得问题更加复杂。为了适应这种特殊的结构，研究者提出了一种改进的二维压缩传感方案——修改后的二维子空间追踪算法（Modified Two-Dimensional Subspace Pursuit, M-2DSP）。这个算法利用了信号的可用先验支持信息和分块稀疏性，通过迭代搜索过程来精确地识别和恢复信道矩阵中稀疏的部分。这种方法的优势在于： 1. **适应性强**：M-2DSP算法能够有效地处理大规模MIMO系统中复杂的信道特征，包括隐藏的稀疏性和时间相关性。 2. **计算效率**：通过利用信号的局部特性，算法减少了不必要的计算量，提高了估计的实时性。 3. **理论证明**：论文提供了理论分析，证明了M-2DSP算法的有效性，这为算法的可靠性和性能提供了坚实的数学基础。 4. **实证验证**：通过实验模拟，文章展示了该算法在实际应用中的优越性能，证实了其在大规模MIMO信道估计中的实用性和优势。总结来说，这篇研究论文为大规模MIMO系统的信道估计提供了一个创新且高效的解决方案，通过将压缩感知与MIMO系统的特定结构相结合，实现了更准确、快速的信道估计，这对于提高无线通信系统的整体性能具有重要意义。

Modiﬁed Two-Dimensional Compressed Sensing

Scheme for Massive MIMO Channel Estimation

Yingxiang Wang

∗

, Hairong Wang

†

, Youhua Fu

∗

College of Electronic Science and Engineering

†

College of Telecommunications and Information Engineering

Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

Email: {1014020712, hrwang, fuyh}@njupt.edu.cn

Abstract—The problem of compressed sensing (CS) is consid-

ered in two-dimensional (2D) sparse decomposition measurement

model. Correspondingly, a novel recovery algorithm – modiﬁed

2D subspace pursuit (M-2DSP) algorithm is proposed with the

available prior support and chunk sparse structure. The massive

multi-input multi-out (MIMO) system show a concealed sparse

structure and temporal correlation in the user (UE) channel

matrix in virtue of the shared local scatterers in the physical

propagation environment. Thereby the proposed scheme can

be applied to sparse channel estimation in massive MIMO

systems with temporal correlation. Furthermore its effectiveness

is proved, both theoretical analysis and experiment simulations

testify the usefulness and advantages of the new algorithm in

recovery performance, especially in smaller overhead training

pilot quantity and lower transmit signal noise ratio (SNR).

Index Terms—Compressed Sensing, Two-Dimensional Mea-

surement Model, Massive MIMO, Sparse Structure, Sparse

Channel Estimation.

I. INTRODUCTION

Compressed sensing (CS), a principle might enable dra-

matically reduced measurement time, dramatically reduced

sampling rates, or reduced use of analog-to-digital converter

resources [1], been applied extensively in contemporary com-

munication systems. In the research community, the issue of

recovering sparse signals from a great many of compressed

measurements have been attracting a great deal of attention [2].

Specially, attracted amounts of interests in signal processing

and statistics, where the objectives are to recover the unknown

sparse signals based on the measurements and the measure-

ment matrices. Various methods have been designed to approx-

imately solve the problem. Such as the convex approximation

approach via l

-norm minimization (BP) is presented in [3].

After that in [4], the orthogonal matching pursuit (OMP) of

greedy-based algorithms is mentioned. Then subspace pursuit

(SP) is proposed in [5]. Furthermore, in [6], a conventional

block sparsity structure with the algorithm of block subspace

pursuit (BSP) is provided. These algorithms are able to restore

effectively with fewer measurements compared with the signal

dimensions due to the tools of the restricted isometry property

(RIP) [3] being used. However, only one-dimensional (1D)

static CS recovery is considered in them.

To cover more application scenarios, sparse decomposition

of two-dimensional (2D) signals is considered in [7], where it

demonstrated that CS of 2D model can be transformed to the

previous 1D problem. Multiple measurement vector (MMV)

joint sparsity model using convex relaxation is offered in [8].

2D-SL0 algorithm, an improvement of CS methods emerged

in [7], is used to further applications and the effectiveness of

the algorithm is analyzed in [9]. Nevertheless, in [7]-[9] the

prior support information of the signals are not exploited.

In practice, the signal sparse patterns are constant temporal

correlation. For instance, in spectrum sensing, the index set

of the occupied frequency band usually varies slowly [10].

In virtue of the slowly varying propagation environment be-

tween base stations (BS) and users (UE) [11], consecutive

frames share some multi-paths in sparse channel estimation.

Currently, for the effect of limited local scattering [12], the

massive MIMO channel has been testiﬁed to be sparsity. By

exploiting the channel sparsity, CS techniques are exploited

to cut down the required pilot overhead of channel state

information (CSI). In [13], a distributed CS framework is

supplied to enhance both the channel estimation and feedback

performance in downlink massive MIMO system. Moreover,

in [14] uplink massive MIMO system is considered, where

a CS-based low-rank approximation scheme and a sparse

Bayesian-learning algorithm are appeared to improve the chan-

nel recovery performance respectively. Nevertheless, existing

approaches in [13] and [14] only a one-time slot static scenario

is considered. With the research progress, the new method of

modiﬁed subspace pursuit which is the extension of multiple

measurement vector subspace pursuit (MMVSP) arise in [15],

where shows the great potential of using prior signal support

in enhancing the performance of CS recovery.

In massive MIMO systems with temporal correlated mul-

tipaths, there are available to exploit the channel temporal

correlation for reducing acquisition. Therefore a more com-

plete 2D measurement model is proposed regarding the prior

support of the signal. In Section II, the 2D CS model set

up with a general sparse signal model introduced and a

prior support information illustrated. In Section III, adaptively

exploiting the prior support and sparsity structure, a novel

recovery algorithm – modiﬁed 2D subspace pursuit (M-2DSP)

algorithm is proposed for sparse decomposition of 2D signals.

After that, in Section IV, the presented scheme is applied

to sparse channel estimation in massive MIMO systems with

correlation of time for certifying the usefulness and excellent

capability of the proposed method. Furthermore, numerical

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