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Journal of Communications and Information Networks, Vol.3, No.2, Jun. 2018

DOI: 10.1007/s41650-018-0014-5 Research paper

Non-Linear and Non-Iterative Based Transceiver

Design for SU-MIMO Systems

Raja Muthalagu

Abstract—This paper considers the design of a

low-complexity and high-performance precoder for

multiple-input multiple-output (MIMO) systems. The

precoder is designed by combining both nonlinear and

non-iterative processing strategies. The proposed nonlin-

ear precoding techniques employ a nonlinear constellation

precoding technique based on maximum distance sepa-

rable codes at the transmitter. We propose to reduce the

computational complexity in iterative-based precoding

algorithms by using less complex non-iterative singular

value decomposition-based joint precoder and decoder

pair design. The maximum likelihood detection for the lin-

ear MIMO channel is considered. The simulation results

showed that the proposed nonlinear and non-iterative

precoding schemes outperform the conventional linear

MIMO precoder design, even when a reduced-complexity

suboptimal strategy is adopted, considering the bit error

rate performance.

Keywords—multiple-input multiple-output, singular

value decomposition, maximum distance separable codes,

subcarrier grouping, diversity channel selection

I. INTRODUCTION

n the last few decades, multiple-input multiple-output

(MIMO) systems have emerged as an important technol-

ogy amongst the methodologies known to guarantee a high

data rate in wireless communication systems. The perfor-

mance improvement of the MIMO systems in terms of either

the link reliability or data throughput depends on the assump-

tion of the availability of channel state information (CSI) at

the transmitter (CSIT) and/or that of the state information at

the receiver (CSIR). Obtaining the correct CSIT or CSIR in

Manuscript received Aug. 14, 2017; accepted Nov. 06, 2017. The asso-

ciate editor coordinating the review of this paper and approving it for publi-

cation was R. S. Kshetrimayum.

R. Muthalagu. Department of EEE, Birla Institute of Technology and

Science (BITS), Pilani, Dubai Campus, Dubai International Academic City,

Dubai 345055, UAE (e-mail: [email protected]).

real time is impossible because of the dynamic nature of the

channel and the channel estimation errors. However, it is im-

portant to outline a system that is sufﬁcient to achieve imper-

fect CSIT and/or CSIR. MIMO systems can be sub-divided

into three fundamental classiﬁcations: spatial diversity, spa-

tial multiplexing

[1-3]

, and beamforming

[4-6]

In single-user MIMO (SU-MIMO) systems, spatial di-

versity can be obtained through the utilization of space-

time codes

[7,8]

. The transmit beamforming with receive

combining

[9,10]

was one of the simplest methodologies to en-

able spatial multiplexing in SU-MIMO systems to accom-

plish full diversity. Appropriate transmit precoding designs

or joint precoder-decoder designs were proposed under a va-

riety of system objectives and different CSI assumptions

[11]

We previously proposed another beamforming method utiliz-

ing singular value decomposition (SVD) for closed-loop SU-

MIMO systems with a convolution encoder and modulation

techniques, for example, M-quadrature amplitude modulation

(M-QAM) and M-phase shift keying (M-PSK) over Rayleigh

fading

[4-6]

As design criteria, different performance measures were

considered, for example, weighted minimum mean square er-

ror (MMSE)

[12]

, total mean square error (TMSE)

[13]

, least bit

error rate (BER)

[14]

. From the point of view of signal pro-

cessing, TMSE is a critical metric for transceiver design and

has been embraced in SU-MIMO systems to minimize the in-

formation estimation error from the received signal. A joint

transceiver design utilizing an MSE paradigm was also dis-

cussed for the SU-MIMO framework

[12]

The above paragraph provides a general introduction and

addresses a few optimization criteria such as an extreme data

rate, least BER, and MMSE. The design of an optimum lin-

ear transceiver for an SU-MIMO channel, possibly with de-

lay spread, utilizing a weighted MMSE paradigm subject to

a transmit power constraint was reported

[12]

. These studies

assumed that the perfect CSI was available on the transmit-

ter side. However, in practical communication systems, the

propagation environment may be more challenging, and the

receiver and transmitter cannot have perfect knowledge of the

CSI. An imperfect CSI may emerge from an assortment of

sources, for example, outdated channel estimates, erroneous

Non-Linear and Non-Iterative Based Transceiver Design for SU-MIMO Systems 85

channel estimation, and quantization of the channel estimate

in the feedback channel

[15]

An important problem to investigate with the aim of obtain-

ing a robust communications system is to determine whether

it would be possible to design MIMO systems with an im-

perfect CSI. Optimal precoding strategies in SU-MIMO sys-

tems were proposed under the assumption that imperfect CSI

is available at the transmitter, and perfect CSI is available at

the transmitter

[16]

. A robust joint precoder and decoder de-

sign to reduce the TMSE with imperfect CSI at both the trans-

mitter and receiver of SU-MIMO systems was proposed in

Refs. [17,18].

Novel precoding techniques to enhance the performance of

the downlink in MU-MIMO systems were studied with an im-

proper constellation

[19]

. The precoder that was designed

[19,20]

was more appropriate for a MIMO system with improper sig-

nal constellation. The joint precoder and decoder design un-

der the minimum TMSE measure produced exceptional BER

performance for proper constellation techniques, e.g., M-PSK

and M-QAM

[21,22]

. Then again, when applying the same out-

line to the improper constellation techniques, e.g., M-ASK

and BPSK, the performance is fundamentally corrupt. A min-

imum TMSE design for an SU-MIMO system with improper

modulation techniques was proposed and found to perform

predominantly in terms of BER compared to the traditional

design

[23]

A novel optimal strategy for nonlinear precoding in a

MIMO system was designed

[24]

, and simulation results were

provided to show that the proposed nonlinear precoding ap-

proach clearly outperforms the optimal linear precoding ap-

proaches. To avoid the computational complexity in iterative-

based linear uplink MU-MIMO systems, a non-iterative joint

SVD-based precoder and decoder for uplink MIMO systems

with perfect CSI was proposed

[24]

and the design was com-

pared with conventional iterative-based linear uplink MIMO

systems. Signiﬁcant performance gains of the non-iterative

approach over previous iterative designs in terms of the BER

of the system were thoroughly demonstrated with simulation

results.

A literature review revealed that a transceiver design of

both a nonlinear and non-iterative nature is neither avail-

able for SU-MIMO nor for MU-MIMO systems. Our re-

search aimed to address this shortcoming by examining the

problem of a nonlinear and non-iterative precoder design for

an SU-MIMO system with maximum likelihood (ML) de-

coding as the main objective of this study. Based on the

nonlinear structure of the precoder, three different methods

(Method 1, Method 2, and Method 3) are proposed. The ap-

proach we followed was to design a less complex and most

efﬁcient MIMO transceiver by combining nonlinearity and a

non-iterative structure in the MIMO system. The simulation

results veriﬁed the superiority of all the proposed methods

over conventional methods. In the near future, we plan to use

the proposed methods in large-scale or massive MIMO

[25,26]

to increase the spectral efﬁciency for next generation wireless

systems.

The remainder of the paper is organized as follows. The

system model for the proposed nonlinear and non-iterative

precoder design for MIMO systems is presented in section II.

The proposed NCP methods for MIMO systems are presented

in section III together with a suitable example. The simula-

tion results are presented in section IV. Section V concludes

the paper.

Notation: Throughout this paper, (·)

denotes ma-

trix transpose, (·)

represents matrix conjugate transpose,

diag[H(1), ··· ,H(n)] is an n × n diagonal matrix with diag-

onal elements H(i), i = 1, ·· · ,n, and I

is an n × n identity

matrix.

II. SYSTEM MODEL FOR PROPOSED

NONLINEAR AND NON-ITERATIVE

PRECODER DESIGN FOR MIMO SYSTEMS

A. Literature Review

To enable spatial multiplexing in SU-MIMO systems,

the appropriate transmit precoding design or joint precoder-

decoder designs were proposed under a variety of system ob-

jectives and different CSI assumptions

[27]

. Most of the studies

assumed that the perfect CSI was available at the transmit-

ter side. However, in practical communication systems, the

propagation environment may be more challenging, and the

receiver and transmitter cannot have a perfect knowledge of

the CSI. A robust communications system can be obtained by

designing MIMO systems with imperfect CSI as an important

matter to investigate

[28]

. The optimum joint linear transceiver

is designed for SU-MIMO systems that utilize improper con-

stellation strategies, either under the imperfect or perfect CSI

that was proposed

[17]

. The computation complexity in an it-

erative structure was reduced by proposing and designing an

SVD-based non-iterative transceiver for MIMO systems

[29]

When the base station (BS) obtains the perfect CSI of all

mobile stations, and each of the mobile stations has its own

speciﬁc perfect CSI, the SVD-assisted method can decouple

the multi-user channel into multiple independent SISO sub-

channels. A novel optimal nonlinear transceiver design for

a MIMO system is also proposed to show that the nonlin-

ear precoding-based MIMO system outperforms the equiva-

lent linear system

[24]

In this work, we combined both non-iterative and nonlinear

MIMO systems to produce a less complex and more efﬁcient

SU-MIMO system. Tab. 1 presents a comparison of the var-

ious parameters of the different conventional transceiver and

proposed transceiver schemes.

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