贝叶斯压缩感知算法在认知无线电网络中的应用

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"这篇外文文献详细介绍了贝叶斯压缩感知算法在宽频带认知无线电网络中的应用，即Space-time Bayesian Compressed Spectrum Sensing (ST-BCSS)。作者包括Zhenghao Zhang、Husheng Li、Depeng Yang和Changxing Pei，分别来自西安电子科技大学的ISN实验室和田纳西大学的EECS部门。" 在无线通信领域，尤其是认知无线电网络中，宽频带谱感测是一个长期存在的挑战，主要由于宽频带信号的获取实施难度大。压缩谱感测（Compressed Spectrum Sensing, CSS）提供了一种有效的方法来捕获这些宽频带信号。然而，宽频带CSS在处理噪声和低采样率时的性能受到限制。为此，作者提出了一个概率性的空间-时间贝叶斯压缩谱感测（ST-BCSS）框架，旨在对抗宽频带压缩谱感测中的噪声问题。 ST-BCSS的核心是利用时空先验信息建立一个信息丰富的层次概率模型，以恢复被压缩的谱。这种先验信息使得谱感测在噪声环境和低采样率条件下更具鲁棒性。通过概率框架，作者阐述了如何表示、传递和融合多源先验信息，以优化局部压缩谱的重建效果。文献中进行了数值模拟，结果表明ST-BCSS算法能显著提高压缩谱重构的性能，证明了该方法的有效性。此算法对宽频带认知无线电网络的谱效率和可靠性提升具有重要意义，为未来的研究提供了新的思路和技术基础。贝叶斯压缩感知算法（Bayesian Compressed Sensing, BCS）是一种结合了贝叶斯统计和压缩感知理论的方法。在传统压缩感知中，目标是从少量采样数据中恢复原始信号，而贝叶斯方法引入了先验知识，如信号的统计特性，以进一步提高重构质量。通过贝叶斯推理，可以得到信号参数的后验分布，从而更准确地估计信号。这篇文献深入探讨了贝叶斯压缩感知在实际无线通信系统中的应用，特别是在宽频带认知无线电网络中的谱感测问题，为解决噪声和采样率限制提供了新的解决方案。

The received signal of k-th secondary user is represented by

(t)=



m=1

(t) ⊗ s

(t)+n

(t), (2)

where s

(t) and h

(t) represent the primary user’s trans-

mitting signal and the channel impulse response between

the primary user and the k-th secondary user on the m-th

subchannel, respectively. ⊗ denotes the convolution operator.

The noise n

(t) is assumed to be white Gaussian noise with

zero mean and power spectral density (PSD) σ

for the k-th

secondary user. Similar to the notes in [29], we operate an M

point discrete Fourier transform for the received signal y

(t).

We can use an M × 1 vector Y

to represent the received

signal on frequency-domain, which is given by



m=1

 s

+ n

, (3)

where  denotes elementwise multiplication. h

, s

, and

are the discrete Fourier transforms of h

(t) s

(t) and

(t), respectively. We can construct a diagonal matrix H

diag(h

) and rewrite (3) in a matrix form, which is given by



m=1

+ n

. (4)

Then the detection problem for each secondary user is to do

the following binary hypothesis test on M subchannels in

frequency domain, i.e.

0,m

: Y

= n

0,m

: Y

= H

+ n

, (5)

where m =1, 2, ..., M and k =1, 2, ..., K denote the m-th

subchannel and the k-th secondary user, respectively.

In a wideband wireless application, between two adjacent

spectrum sensing periods, it has a low probability that all

subchannels change their occupancy status, since spectrum

sensing is implemented in a relative short period (

e.g.

in 802.22

WRANs’ draft, it is supposed to carry out spectrum sensing

every 24.2 ms [22]). Then the spectrum occupancies between

two adjacent sensing periods are correlated, which offers us

the temporal redundancy information for compressed signal

reconstruction. On the other hand, the spectrum observations

of difference cooperative secondary users also have spatial

correlation which provides us spatial redundancy.

frequency

n-1=[ 0 0 1 0 0 1 1 0 0 ]

Dn =[ 1 0 1 0 0 1 0 0 0 ]

frequency

Fig. 2: An illustration of the spectrum temporal correlation

As illustrated in Figure 2, we deﬁne a general correlation

factor τ, which represents either the temporal or the spatial

correlation level, which is given by

τ  1 −

D

− D

n−1



. (6)

In section V, we will demonstrate that different correlation

levels provide different performance gains.

III. C

OMPRESSED SPECTRUM SENSING AND BAYE S I A N

LEARNING

In this section, we brieﬂy introduce the compressed sensing

and Bayesian learning, thus providing the background for our

proposed ST-BCSS algorithm.

A. Compressed Sensing

Brieﬂy speaking, compressed sensing solves an ill-posed

inverse problem. Given an N × 1 observation vector g and an

N × M (N<M) matrix Φ, M × M matrix Ψ, the task is to

ﬁnd an M × 1 solution vector f to satisfy an equation, which

is given by

g =ΦΨf, (7)

where Φ is the compressed matrix and Ψ is the projection

matrix. The vector f has a sparse representation projected

by Ψ. When matrix Φ,Ψ and vector f satisfy the Restricted

Isometry Property (RIP) [6], it can be solved by following

optimization problem:

f = arg min 

f

s.t. g =ΦΨ

f. (8)

Compressed sensing based Analog-to-Information Conver-

sion (AIC) was proposed in [14] [21]. Eldar proposed a

blind wideband analog reconstruction method [17]. Based on

the autocorrelation reconstruction, [19] [30] [31] presented

a scheme of analog signal acquisition, which endows us

an implementation structure to acquire the wideband signal

within an affordable hardware cost. In this paper, based on

these implementation structures, we represent the analog signal

acquisition in a projection matrix, for simplicity. We construct

an N × M linear random sampling matrix A, to attain N

time domain samples from discrete received signal y

, which

is given by

= Ay

, (9)

where A can be a Gaussian or Bernoulli random matrix and

the noise

remains to be white Gaussian noise. In wideband

spectrum sensing, the vector y

can be represented sparsely

in the Fourier transformation domain, which is given by

= F

−1

, (10)

where F

−1

is the inverse Fourier transform matrix and w

the sparse representation. Substituting (10) into (9) we obtain

= AF

−1

= Θw

, (11)

where Θ = AF

−1

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE DySPAN 2010 proceedings

Authorized licensed use limited to: SOUTH CENTRAL UNIVERSITY FOR NATIONALITIES. Downloaded on July 22,2010 at 09:42:42 UTC from IEEE Xplore. Restrictions apply.

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