MIMO-OFDM系统半盲稀疏信道估计算法

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"MIMO-OFDM系统的半盲稀疏信道估计" 在无线通信领域，MIMO（Multiple-Input Multiple-Output）与OFDM（Orthogonal Frequency Division Multiplexing）技术结合，形成了高效的MIMO-OFDM系统，能显著提高频谱效率和传输可靠性。然而，这种系统面临的一个关键挑战是信道估计，特别是在信道具有稀疏特性的场景下。本文介绍了一种针对MIMO-OFDM系统的半盲稀疏信道估计算法。信道的稀疏性是指在多径传播环境中，只有少数路径对信号衰落有显著贡献，这些主要路径被称为最显著 taps（MSTs）。在MIMO-OFDM系统中，准确估计这些MSTs对于正确解调和前向纠错至关重要。传统的信道估计算法通常依赖于训练序列，但这会占用宝贵的传输带宽。论文首先分析了通过稀疏MIMO信道接收信号的二阶统计特性。研究发现，接收信号的协方差矩阵可以由稀疏信道的主要路径来表示。基于这一观察，论文提出了一种盲约束，用于确定与MST位置相对应的有效信道矢量。这个盲约束随后与基于训练的最小二乘准则相结合，形成一种半盲估计算法，专门用于估计稀疏信道的MSTs。为验证该算法的性能，论文进行了信号扰动分析。分析表明，提出的半盲解决方案对信号扰动误差不敏感，这意味着即使在存在信号失真的情况下，也能保持良好的信道估计精度。这是一项重要的改进，因为实际无线环境中的信号往往受到各种噪声和干扰的影响。此外，文章可能还讨论了算法的复杂度、收敛速度以及与其他信道估计算法的比较，以证明其在实际应用中的优势。通常，半盲方法能够在减少训练开销的同时，提供接近全知（即有训练数据）信道估计的性能，这对于资源受限的无线通信系统至关重要。总结起来，这篇论文为MIMO-OFDM系统的信道估计提供了一个新的视角，通过利用信道的稀疏性和接收信号的统计特性，提出了一种有效且鲁棒的半盲估计算法。这种方法有望在未来的无线通信标准中得到应用，以提高系统性能并优化资源利用率。

WA N et al.: SEMIBLIND SPARSE CHANNEL ESTIMATION FOR MIMO-OFDM SYSTEMS 2571

spatiotemporally uncorrelated noise with zero mean and vari-

ance σ

. The aforementioned channel and signal models will be

used in the next section to develop a semiblind sparse channel

estimation algorithm.

B. Linear-Prediction-Based Semiblind MIMO-OFDM

Channel Estimation

We now brieﬂy review our previous work on the linear-

prediction-based semiblind MIMO-OFDM channel estimation

[19]. The key is to employ the second-order statistics-based

MIMO linear prediction method to obtain a blind constraint on

the channel vector, i.e.,



,...,h



where h

=[h

(0),...,h

(L−1),...,h

(L−1)]

By deﬁning

y(n)

=[y

(n),...,y

(n)]

(3)

(n − 1)



(n − 1),...,y

(n − P )



(4)

we have the autocorrelation matrix of y

(n − 1) and the cross-

correlation matrix of y

(n − 1) and y(n) as

n−1



(n − 1)y

(n − 1)



(5)



y(n)y

(n − 1)



. (6)

Then, the MIMO linear predictor can be written as [19], [32]

=[P

(1), P

(2),...,P

(P )] =

−1

n−1

(7)

where P is the length of linear predictor, and P

(n), n =

1,...,P,isanN

× N

matrix that represents the nth tap of

the prediction ﬁlter. In the aforementioned equations, the index

m has been omitted for notational convenience. By using the

properties of the MIMO linear predictor, a blind constraint for

the channel vector h can be derived as [19]

B =(I ⊗ P

(8)

where E

is a known permutation matrix, and P

is a matrix

that is determined by a block Toeplitz matrix that consists of

(n), n =1,...,P, and the null subspace of H(0), which

can be estimated from the covariance matrix of the prediction

error δ

y,P

= R(0) − P

By combining the blind constraint with a training-based

LS criterion, a semiblind channel estimation problem can be

formulated as

min

Δ=Y

pilot

−

h

+ α

h

(9)

where

A is a pilot signal matrix that can be constructed as

shown in [30, Sec. IV], Y

pilot

is the corresponding received

signal vector,

B is an estimate of the blind constraint, and α>0

is a weighting factor. The solution to this optimization problem

is given by

h =(

A + α

†

pilot

(10)

where the value of α can be determined using the scheme

proposed in [19]. In the aforementioned semiblind approach

and in several existing MIMO-OFDM channel estimation meth-

ods, e.g., the techniques proposed in [2], [3], [5], [8], [9],

and [20], the sparse case of the wireless channel has not

been considered. Thus, the semiblind solution obtained is not

efﬁcient when the channel is sparse. In the next section, we will

propose a new semiblind algorithm for the estimation of sparse

channels that contain only a small number of signiﬁcant or non-

zero taps.

III. P

ROPOSED SEMIBLIND SPARSE CHANNEL

ESTIMATION ALGORITHM

A. Second-Order Statistics of the Signal Received Through

Sparse MIMO

It is known that a wireless channel can very often be modeled

as a sparse channel that contains several zero taps in the uniform

delay line [21]–[29]. In this paper, we consider point-to-point

MIMO systems, in which the transmit and receive antennas are

colocated. In this case, the propagation delay is roughly the

same for all transmit–receive antenna pairs [33], [34], which

has been considered in the generations of multipath MIMO

channels in practical channel models, e.g., the spatial channel

model (SCM) [35]. Because the delay in the FIR channel is

uniquely determined by the propagation delay of the multi-

paths, when the channel is sparse, the MSTs of the channel

should happen at the same positions for all transmit–receive

antenna pairs [33]. Therefore, the MIMO channel matrix with

respect to the dth (d =0, 1,...,D− 1) MST can be ex-

pressed as

Z(d)=H(l

) (11)

where l

(d =0, 1,...,D− 1) are integers, with 0=l

< ···<l

D−1

, and H(l

) is, in general, considered Rayleigh

distributed. To distinguish from H(l), Z(d) is referred to as the

effective channel matrix throughout this paper.

The correlation matrix of the received signal vector y(n) can

be, in general, deﬁned as

R(l)



y(n)y

(n − l)



, (l =0, 1,...,P). (12)

Obviously, (12) includes the autocorrelation matrix of y(n) as a

special case when l =0. It has been proved in [30] that, for the

noise-free case, R(l) can be expressed in terms of the effective

sparse channel matrix Z(d), d =0, 1,...,D− 1. Using (2),

(3), and (11) in (12), we obtain

R(l)=Z

x,D

(l)Z

(13)

where

=[Z(0) Z(1) ··· Z(D−1) ] (14)

x,D

(l)

⎧

⎪

⎨

⎪

⎩

⎡

⎢

⎣

x(n)

x(n−l

)

x(n−l

D−1

)

⎤

⎥

⎦

⎡

⎢

⎣

x(n−l)

x(n−l

−l)

x(n−l

D−1

−l)

⎤

⎥

⎦

⎫

⎪

⎬

⎪

⎭

(15)

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