随机优化辅助的OFDM/SDMA系统：联合信道估计与多用户检测

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"这篇研究论文探讨了在OFDM/SDMA系统中，如何利用随机优化算法辅助进行联合信道估计和多用户检测。研究对比了遗传算法（GA）、重复加权增强搜索（RWBS）、粒子群优化（PSO）和差分进化（DE）等方法在解决连续值CE优化问题和离散值MUD优化问题上的表现。仿真结果显示，这些随机优化技术能实现接近最大似然MUD的Cramer-Rao下界（CRLB）和误码率（BER）性能，但计算复杂度显著低于最优的最大似然方法。" 正文: 这篇研究论文深入研究了在多用户多输入多输出（MIMO）环境下的OFDM/SDMA系统，其中OFDM技术用于频率分隔，SDMA则用于空间分隔，从而提高频谱效率。在这种背景下，联合信道估计（CE）和多用户检测（MUD）是两个关键的技术挑战，它们对系统的整体性能有着显著影响。信道估计是获取信道状态信息的过程，而多用户检测则是从干扰中分离出各个用户的信号。文章提出了一种新的方法，即采用随机优化算法辅助的联合CE和MUD。随机优化算法近年来在信号处理和通信领域中得到了广泛应用，例如遗传算法（GA）、重复加权增强搜索（RWBS）、粒子群优化（PSO）和差分进化（DE）。这些算法能够有效地搜索复杂的优化问题空间，找到近似全局最优解。然而，将这些随机优化算法应用于联合CE和MUD的量化性能和复杂性分析是一个未被充分研究的问题。研究者们填补了这一空白，通过对这些算法的实证评估，展示了它们在解决连续优化问题（CE）和离散优化问题（MUD）上的潜力。结果表明，这些随机优化方法在保持较低计算复杂度的同时，可以达到接近最大似然MUD的性能水平，这意味着它们能够在不显著增加计算负担的情况下提供接近最优的解。此外，论文中的仿真结果提供了关于不同优化算法性能的定量比较。Cramer-Rao下界（CRLB）通常被用作信道估计理论性能的基准，而误码率（BER）则是衡量多用户检测性能的关键指标。通过比较这些性能指标，研究者得出了每种算法在实际应用中的优劣。这项研究为OFDM/SDMA系统中的信道估计和多用户检测提供了新的视角，即利用随机优化算法实现高效且性能优良的解决方案。这种方法不仅提升了系统性能，还降低了计算复杂性，对于未来无线通信系统的优化设计具有重要的参考价值。

Stochastic Optimization Assisted Joint Channel Estimation and Multi-User Detection for

OFDM/SDMA

Jiankang Zhang

†∗

, Sheng Chen

∗

, Xiaomin Mu

†

, Lajos Hanzo

∗

† School of Information Engineering, Zhengzhou University, Zhengzhou, China,

∗ School of ECS, University of Southampton, SO17 1BJ, United Kingdom.

Tel: +44-23-8059 3125, Fax: +44-23-8059 4508, http://www-mobile.ecs.soton.ac.uk

Email: jz09v@ecs.soton.ac.uk, sqc@ecs.soton.ac.uk, iexmmu@zzu.edu.cn, lh@ecs.soton.ac.uk

Abstract— Stochastic optimization assisted joint Channel Estimation

(CE) and Multi-User Detection (MUD) were conceived and compared

in the context of multi-user Multiple-Input Multiple-Output (MIMO)

aided Orthogonal Frequency-Division Multiplexing/Space Division Mul-

tiple Access (OFDM/SDMA) systems. The development of stochastic

optimization algorithms, such as Genetic Algorithms (GA), Repeated

Weighted Boosting Search (RWBS), Particle Swarm Optimization (PSO)

and Differential Evolution (DE) has stimulated wide interests in the

signal processing and communication research community. However,

the quantitative performance versus complexity comparison of GA,

RWBS, PSO and DE techniques applied to joint CE and MUD is a

challenging open issue at the time of writing, which has to consider

both the continuous-valued CE optimization problem and the discrete-

valued MUD optimization problem. In this study we ﬁll this gap in

the open literature. Our simulation results demonstrated that stochastic

optimization assisted joint CE and MUD is capable of approaching

both the Cramer-Rao Lower Bound (CRLB) and the Bit Error Ratio

(BER) performance of the optimal ML-MUD, respectively, despite the

fact that its computational complexity is only a fraction of the optimal

ML complexity.

Index Terms— Orthogonal frequency division multiplexing (OFDM),

space division multiple access (SDMA), channel estimation, multiuser

detection, stochastic optimization algorithm.

I. INTRODUCTION

In recent years, multiple antennas have been employed both at the

transmitter and/or the receiver for achieving various design goals [1],

such as maximizing the attainable multiplexing gain, maximizing the

number of users supported or maximizing the achievable diversity

gain. As one of the most wide-spread multiple antenna aided sys-

tems, Orthogonal Frequency-Division Multiplexing/Spatial Division

Multiple Access (OFDM/SDMA) [2] exploits the advantages of both

OFDM and SDMA, which increase the attainable spectral efﬁciency

by sharing the same bandwidth and time slots by several users

roaming in different geographical locations, which are differentiated

by their unique, user-speciﬁc ’spatial signature’, i.e. by their Channel

Impulse Responses (CIRs).

More speciﬁcally, the transmitted signals of U simultaneous single-

antenna aided UpLink (UL) Mobile Stations (MSs) are received

by an array of antennas at the Base Station (BS), where Multi-

User Detection (MUD) techniques are invoked for separating the

signals of the different MSs with the aid of their unique, user-speciﬁc

’spatial signature’, i.e. CIRs. Naturally, for near-single-user MUD

the CIRs have to be accurately estimated [1, 3]. Intensive research

efforts have been devoted to developing efﬁcient approaches for

Channel Estimation (CE) in multi-user OFDM/SDMA systems [1,

4–6]. In order to achieve a near-optimal performance, joint CE and

signal detection schemes have recently received signiﬁcant research

attention [7–9]. The optimal solutions of CE and/or MUD, namely

Maximum-likelihood (ML) CE and ML-MUD, are naturally desired.

However, we have to settle for suboptimal solutions due to the

excessive computational complexity of the optimal ML solutions,

Acknowledgments: The ﬁnancial support of the EPSRC under the auspices

of the China-UK Science Bridge as well as of the RC-UK under the India-UK

Advanced Technology centre initiative is gratefully acknowledged.

especially for a high number of users/antennas relying on Quadrature

Amplitude Modulation (QAM).

Fortunately, stochastic optimization algorithms are capable of ﬁnd-

ing the globally optimal solution with a high probability at a fraction

of the optimal ML MUD’s complexity, even for problems associated

with a non-smooth Cost Function (CF) exhibiting multiple local

optima. The most popular algorithms

include Genetic Algorithms

(GA) [12], Repeated Weighted Boosting Search (RWBS) [13], Parti-

cle Swarm Optimization (PSO) [14] and Differential Evolution (DE)

[15]. More speciﬁcally, signiﬁcant advances have been made in the

development of these stochastic optimization algorithms, including

single-user joint channel and data estimation [13, 16], CE and/or

MUD in the multi-user Code Division Multiple Access (CDMA)

UpLink (UL) [17–20], in the SDMA aided OFDM UL [1, 7, 9], in

MUD assisted Space-Time Block Coding (STBC) [21, 22], in CE for

Multiple Input Multiple Output (MIMO) systems [23], in the Multi-

User Transmission (MUT) aided DownLink (DL) [24, 25], in channel

allocation [26, 27] as well as in a diverse range of other applications.

In general, the optimization problems in communications may be

classiﬁed as: continuous and discrete optimization problems. For

example, the CIRs to be estimated are continuous-valued, while the

transmitted signals are discrete. To the best of our knowledge, no

performance versus complexity comparisons of GA, RWBS, PSO and

DE techniques applied to joint CE and MUD have been presented in

the open literature.

Against this background, our new contribution is that we provide a

performance versus complexity comparison of stochastic optimization

algorithms in the context of joint CE and MUD in ODFM/SDMA sys-

tems. More speciﬁcally, continuous stochastic optimization algorithms

will be employed for CE, relying on Continuous GA assisted CE

(CGA-CE), Continuous RWBS assisted CE (CRWBS-CE), Continuous

PSO assisted CE (CPSO-CE) and Continuous DE assisted CE (CDE-

CE). By contrast, the discrete binary version of the corresponding

stochastic optimization algorithms will be employed for MUD, in-

voking Discrete Binary GA assisted MUD (DBGA-MUD), Discrete

Binary RWBS assisted MUD (DBRWBS-MUD), Discrete Binary PSO

assisted MUD (DBPSO-MUD) and Discrete Binary DE assisted ML-

MUD (DBDE-MUD).

The rest of this paper is organized as follows. The system model of

the multi-user OFDM/SDMA UL is described in Section II. Section

III is devoted to the optimization problems of joint CE and MUD

in the OFDM/SDMA systems considered. In Section IV, we will

brieﬂy characterize the proposed stochastic optimization algorithms.

Our simulation results and discussions are presented in Section V,

while our conclusions are offered in Section VI.

II. S

YSTEM MODEL

In the OFDM/SDMA UL systems, U simultaneous users are

equipped with a single transmission antenna, while the BS employs

There are numerous other stochastic optimization algorithms, such as the

Ant Colony [10] and other evolutionary algorithms [11], but given our limited

space, we concentrate on the above four algorithms in this paper.

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