突破传统限制：3D映射空间调制

研究论文

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"Spatial Modulation via 3-D Mapping - 研究论文" 本文是一篇发表在2016年6月IEEE通信信件(Vol.20, No.6)上的研究论文，由Shuaishuai Guo, Haixia Zhang, Shi Jin和Peng Zhang等人撰写。该论文提出了一种基于3维映射的联合空间调制（Jointly Mapped Spatial Modulation, JM-SM）方案，旨在突破传统空间调制（Spatial Modulation, SM）系统中发射天线数量的限制。传统的空间调制技术利用多个天线中的一个来传输信息，而其他天线保持静默，从而将信息编码到空间维度中。然而，这种技术受到发射天线数量的约束，限制了信息传输的效率。作者提出的JM-SM方法通过将传输信息位映射到3维星座点来解决这个问题。他们设计了一个3-D星座方案，该方案通过最小化系统平均比特错误概率（Average Bit Error Probability, ABEP）来建立和分析。此外，论文还讨论了将联合3-D映射扩展到更一般的空间调制策略的可能性。文章首先介绍了空间调制的基本概念，这是一种用于多输入多输出（Multiple-Input Multiple-Output, MIMO）系统的3-D调制技术。SM的优点在于它能够利用空间分集和多流传输，同时保持较低的复杂度和功率消耗。然后，论文详细阐述了JM-SM的工作原理，包括如何将信息位映射到三维空间中的不同位置，以及如何优化星座点分布以提高误码率性能。接着，论文探讨了将这种联合3-D映射应用于具有任意数量发射天线的MIMO系统的方法。通过对不同天线配置的仿真，结果表明，提出的JM-SM方案相比现有的空间调制和MIMO技术，可以提供更好的ABEP性能。这表明JM-SM在提升通信系统的容量和可靠性方面具有显著优势。最后，作者可能讨论了实施和应用JM-SM技术所面临的挑战，如信道估计、检测算法优化以及硬件实现等问题，并提出了未来的研究方向，如进一步提高JM-SM的抗干扰能力、降低实现复杂度以及在实际通信环境中的应用潜力。关键词：空间调制，多输入多输出（MIMO），3-D映射。这篇论文对理解3-D空间调制技术的发展及其在MIMO通信系统中的应用提供了深入见解，对于研究人员和工程师来说，是探索新型调制技术以提高无线通信效率的重要参考资料。

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1096 IEEE COMMUNICATIONS LETTERS, VOL. 20, NO. 6, JUNE 2016

Spatial Modulation via 3-D Mapping

Shuaishuai Guo, Student Member, IEEE, Haixia Zhang, Senior Member, IEEE,

Shi Jin, Member, IEEE, and Peng Zhang

Abstract—This letter proposes a jointly mapped spatial

modulation (JM-SM) scheme to break through the constraint

on the number of transmit antennas in traditional SM systems.

It is realized via jointly mapping the transmit information bits to

3-D constellation points. A 3-D constellation design scheme for

a JM-SM is analyzed and established by minimizing the system

average bit error probability (ABEP). In addition, the extension

of the joint 3-D mapping to generalized spatial modulation is

discussed. The simulation results show that the proposed schemes

can be adapted to multiple-input multiple-output systems with an

arbitrary number of transmit antennas and offer better ABEP

performance than those existing schemes.

Index Terms— Spatial modulation, multiple-input multiple-

output (MIMO), 3-D mapping.

I. INTRODUCTION

PATIAL modulation (SM) [1]–[3] is a new 3-dimension

(3-D) modulation technique developed for multiple-input

multiple-output (MIMO) systems, which exploits both antenna

index and signal modulation for data transmission. Due

to its inherent advantages, e.g., low-complexity and high

energy-efﬁciency [3], it has drawn intensive attention and

been extensively investigated on transceiver design [4]–[7],

error performance analysis [8], [9], extensions like gener-

alized spatial modulation (GSM) [3] and enhanced spatial

modulation (ESM) [10], etc.

Conventionally, SM is fulﬁlled in two steps. First, the

information bits are split into two parts; second, part of the

split bits are mapped to the activated antennas and the rest

bits are mapped to traditional modulated symbols [1]. In such

separate mapping processes, the number of bits mapped to

antenna indices must be an integer, and thus the number of

transmit antennas should be a power of two [3]. To break

through this constraint on antenna deployment, fractional bit

encoded spatial modulation (FBE-SM) [11] and bit padding

method [12] have been proposed. However, they have caused

new problems. For instance, FBE-SM suffers from error prop-

agation [11], and the bit padding method might cause bits

loss or bits increase during its depadding process when the

data symbol is detected incorrectly.

Manuscript received February 22, 2016; revised April 10, 2016; accepted

April 17, 2016. Date of publication April 20, 2016; date of current version

June 8, 2016. This work was supported in part by the International S&T

Cooperation Program of China under Grant 2014DFA11640; by the National

Natural Science Foundation of China under Grant 61371109, Grant 61271229,

Grant 61531011, and Grant 61471269; and by the Distinguished Young

Scientists Foundation of Shandong Province under Grant JQ201315. The

associate editor coordinating the review of this letter and approving it for

publication was M. Di Renzo.

S. Guo and H. Zhang are with the Shandong Provincial Key Laboratory of

Wireless Communication Technologies, Shandong University, Jinan 250100,

China (e-mail: shuaiguosdu@gmail.com; haixia.zhang@sdu.edu.cn).

S. Jin is with the National Mobile Communications Research Laboratory,

Southeast University, Nanjing 210096, China (e-mail: jinshi@seu.edu.cn).

P. Zhang is with the School of Computer Engineering, Weifang University,

Weifang 261061, China (e-mail: sduzhangp@163.com).

Digital Object Identiﬁer 10.1109/LCOMM.2016.2556685

Fig. 1. System model of JM-SM MIMO transmission systems.

In this letter, a jointly mapped spatial modulation (JM-SM)

is proposed, with which the above mentioned constraint on

SM can be released. In addition, a 3-D constellation design

for JM-SM is analyzed and established. It is demonstrated

that employing exhaustive search method for 3-D constella-

tion design can achieve optimal performance but may cause

prohibitively high computational complexity. Assuming that

M-ary PSK (MPSK) is employed, an efﬁcient 3-D con-

stellation design algorithm with much lower computational

complexity is proposed. Furthermore, the extension of the joint

3-D mapping to GSM is also discussed. Simulation results and

comparisons show that the proposed schemes outperform those

existing transmission schemes in terms of the average bit error

probability (ABEP).

II. S

YSTEM MODEL AND PROBLEM FORMULATION

A. System Model With 3-D Mapping

We consider a MIMO system with N

transmit antennas and

receive antennas, as illustrated in Fig. 1. It is assumed that

the system transmission rate is n bits per channel use (bpcu).

At the transmitter, the information bits are divided into groups,

and each group has n bits. For each channel use, a group

of n bits is directly mapped to a transmit vector, x

∈ C

q = 1, 2, ··· , 2

, which is referred as a 3-D constellation

point [3]. x

is composed of two parts and can be expressed

as x

= e

,inwhiche

is an N

-dimensional vector

whose i-th element is one and the rest are zeros, and s

is a complex constellation point drawn from a given M-ary

signal constellation S

. For clarity, let L

={s

, s

, ··· , s

(0 ≤ m

≤ M) represent the sub-signal-constellation used

for transmission when the i-th transmit antenna is activated.

Then the transmit vector set T ={x

|q = 1, 2, ··· , 2

}

(i.e., 3-D constellation) can be expressed as (1). For simplicity,

the JM-SM MIMO system using such a 3D constellation

as (1) is denoted by JM-SM (N

, N

, S

, n). The 3-D con-

stellation in (1) shows that JM-SM is feasible if and only if



i=1

= 2

. This relaxes the constraint of the conventional

SM that N

M = 2

, where both N

and M should be a

power of two. Besides, as it is shown that in each JM-SM

constellation point, i.e., one column of (1), there is only

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