MATLAB教程：MIMO无线通道详解

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"《Practical Guide to the MIMO Radio Channel with MATLAB》是一本实用指南，专为MIMO（Multiple-Input Multiple-Output）无线电信道的理论学习者和Matlab用户设计。本书深入浅出地介绍了MIMO技术的基础概念，包括多天线通信系统如何通过同时传输多个数据流来提高无线通信系统的容量和可靠性。书中涵盖了MIMO系统的原理、信道模型、性能分析以及如何利用MATLAB进行实际的建模和仿真。作为一本入门级教材，它适合对MIMO技术感兴趣但缺乏深入理解的读者，特别是那些希望通过实例操作熟悉Matlab在无线通信领域应用的人。作者Tim Brown、Elisabeth De Carvalho和Persefoni Kyritsi来自英国萨里大学和丹麦奥胡斯大学，他们以其丰富的学术背景和实践经验，确保了本书内容的权威性和实用性。书中内容包括但不限于：MIMO系统的基本构成，如空间分集、空间复用和多用户MIMO；各种信道编码技术在MIMO中的应用；以及如何通过Matlab设计和实现MIMO通信系统的信号处理流程，如均衡器、检测器和解调器。此外，还涵盖了如何分析MIMO系统的性能指标，如信噪比增益、阵列增益和误码率，以及如何通过仿真验证理论预测。读者将从这本书中学到如何解决实际问题，比如优化传输策略、评估系统性能和调试MIMO通信链路。同时，书中提供的MATLAB代码示例有助于读者迅速掌握并实践MIMO技术。整体而言，这是一本既理论翔实又操作性强的参考书籍，对于想要深入了解MIMO技术并在实际工程环境中运用的工程师和研究人员来说，是不可或缺的资源。"

List of Symbols xix

Eigenvector

u Eigenvector element

V Unitary and orthogonal eigenvector matrix

V Quantity of voltage

v Eigenvector or vector describing voltages at an N-port network

v Eigenvector element

Velocity of a mobile terminal

w Digital codeword

w Complex phase weight

w Vector of complex phase weights



Parameter matrix to describe the channel used in the Weichselberger model

X Quantity of reactance in Ohms or an input data packet variable

X Input codeword

x Vector of input data streams

x Input data stream or distance in metres

Function to return the positive or zero value of x, or zero otherwise

Hermitian transpose of vector or matrix x

Y Output data packet variable

Y Output codeword

y Vector of output data streams

y Output data stream or distance in metres

Z Impedance matrix

Z Quantity of complex impedance in Ohms

Z Candidate codeword

z Candidate data stream

z Distance in metres

ζ Angle or phase

Introduction

Tim Brown and Persefoni Kyritsi

People in the modern day are on the move, either just within a home or ofﬁce building or

traveling from place to place. In previous years, having to go to a ﬁxed location in order to

make a telephone call was an inconvenience. Nowadays this inconvenience is minimised

because the facility of a mobile phone allows someone to carry out this mundane task

almost whenever or whenever they please.

As mobile communications have grown exponentially in recent years and, in parallel,

the World Wide Web and its applications have spread widely, the possibility to have access

to Internet, entertainment and multimedia communications wirelessly has accelerated a

similar trend: people want to avoid further inconveniences of having to go to a ﬁxed

location and establish the necessary communication link to get access to the Internet.

Moreover, it is desirable to avoid having to install the corresponding cables into a building

or home and to avoid incurring the related costs.

Speech communication for mobile telephones was at the time a tremendous task to

achieve wirelessly, and internet and multimedia applications which by nature demand a

signiﬁcantly higher volume of data to be transmitted both ways through the communication

link pose today an equally, if not more, challenging problem.

Multiple input multiple output (MIMO) systems have emerged as an enabling technol-

ogy to achieve the design goals of contemporary communication systems and has given

rise to a proliferation of research activity worldwide. The technology itself has hit the

public domain and it is possible for someone today to buy a state of the art wireless access

point and modem with MIMO written on the box. If the wireless communications industry

will be producing more and more products with this technology then there is a need for

engineers to have a comprehensive guide to learning the concept. Therefore, MIMO has

Practical Guide to the MIMO Radio Channel with MATLAB

Examples, First Edition.

Tim Brown, Elisabeth De Carvalho and Persefoni Kyritsi.

2 Practical Guide to the MIMO Radio Channel with MATLAB

Examples

become a widespread research topic and is a major component on the teaching agenda in

many universities delivering courses on modern-day mobile communication systems.

As an aid to the telecommunications engineer of the future, this book aims to approach

the subject in a way that is both intuitive and technical. The goal is to show how MIMO

systems have emerged from conventional systems, and what special technical features

enable MIMO systems to transmit data through a radio environment more rapidly. To the

extent possible, visual means will be used to develop understanding and intuition.

This chapter will explain where MIMO came from, what it is for and how it is used.

The purpose is to help the reader establish on an abstract level the right frame of mind to

read the remainder of the book. The ﬁnal section of this chapter will explain the structure

of the book and how it will take the reader through the different stages of learning about

the subject. The same structure characterises the rest of the book: every chapter contains

a summary at the end, which will provide bullet points of the fundamental facts that the

reader should grasp in order to progress through the book effectively.

1.1 From SISO to MISO/ SIMO to MIMO

1.1.1 Single Input Single Output SISO

SISO stands for Single Input Single Output and has conventionally been the structure

used in communications systems: in general, an ‘input’ is the signal transmitted from

a single antenna, whereas an output is the signal received on a single antenna. Indeed,

conventional wisdom tells us that cellular phones have one single antenna (e.g. visible

antenna extending on one end of the phone, or patch antenna embedded on its back) and

communicate with a single antenna at the base station. In any radio environment there

is going to be more than one user and all the users need to have access to the cellular

services at the same time. The signals to the users are then separated in time (time division

multiple access, TDMA), in frequency (frequency division multiple access, FDMA), or

code (code division multiple access, CDMA). In TDMA systems, all users use the same

set of frequencies to communicate, but not simultaneously. For example, two users can

use the same frequency but they will have allocated time slots as illustrated in Figure 1.1.

In this case, the communication link switches alternately between the two users so that

User 1

User 2

Time

Switching

between

users

Figure 1.1 Illustration of a simple time slot allocation scheme for two users.

Introduction 3

they can take turns to use the spectrum for equal time periods. Therefore each user’s link

will effectively get switched on and off for equal time periods. During the period that each

user is receiving data, the data are conveyed in digital form in packets which are then

re-assembled at the receiver.

In FDMA systems, all users have access to the system at the same time, but they

use different parts of the spectrum to communicate. As long as the users use different

frequencies, their signals do not interfere with each other.

In CDMA systems, all users use the same spectrum at the same time, but their signals

are separated in the code domain, that is, each user’s signal uses a code that is speciﬁc to

this user and orthogonal to other users.

1.1.2 Single Input Multiple Output, SIMO, and Multiple Input Single

Output, MISO

In any of the above cases, the link between the transmit and the receive antenna is impaired

by the features of the radio environment. As the user moves, the signal strength varies over

the small and large scale, and at times, the quality of the link is too low to deliver data

successfully. This leads to unacceptable error rates or radio link failure. In order to combat

this problem, a technique known as ‘diversity’ has been developed. Diversity relies on the

use of multiple copies of the same signal, which the receiver can combine or select from.

The idea behind it is that, even if one copy of the signal is of poor quality, it is unlikely that

all the copies will be so, and therefore this redundancy allows the communication quality

to be maintained.

There are different ﬂavours of diversity techniques, and they can be employed either in

the downlink or in the uplink.

Depending on how the multiple copies are generated, one can distinguish different types

of diversity domains. For example, one can generate multiple copies of the same signal

by transmitting it multiple times, which gives rise to time diversity, or one can generate

multiple copies of the same signal at different parts of the spectrum, which gives rise

to frequency diversity. Moreover, one can exploit the space domain, for example when

the same signal is transmitted from several base station antennas and received at a single

mobile terminal (this is known as large-scale or site diversity), or a receiver has several

spatially separated antennas each of which receives a different copy of the signal (this is

known as small-scale diversity).

Depending on the end of the communication link which employs multiple antennas,

one can distinguish between transmit diversity techniques, where multiple copies of the

signal are transmitted from several antennas and their superposition is received at a single

receive antenna, and receive diversity techniques, where the signal is transmitted from a

single antenna and multiple copies of the signal are received at several antennas. These

combinations gave rise to Multiple Input Single Output techniques (multiple transmit-

ters, a single receiver), and Single Output Multiple Input techniques (single transmitter,

multiple receivers).

4 Practical Guide to the MIMO Radio Channel with MATLAB

Examples

Another way to classify diversity techniques is according to the way the multiple copies

of the signals are exploited. In this respect, one can distinguish, in ascending order of

performance, selection diversity, wherein the ‘best’ copy of the signal is selected; equal

gain combining, wherein the multiple copies of the signal are added; and maximum ratio

combining, wherein the multiple copies of the signal are weighted by appropriately selected

scaling factors such that the quality of the resulting signal is optimised.

As an example, let us consider the scenario in Figure 1.4 and imagine that there is one

transmitting mobile M

and one receiving base station that has two antennas. The signal

transmitted from the mobile station is denoted as x and the signals received at the two base

station antennas are indicated as y

and y

. The relationship between them is

= h

x + n

= h

x + n

(1.1)

where h

are the channel coefﬁcients between the mobile station and the two receive

antennas respectively, and n

are the noise signals at the two receive antennas, which

for simplicity will be assumed to be independent and of the same statistics. The base

station can combine the signals from its two receive antennas to improve the quality of

the signal.

Selection diversity would select the best of the two signals, that is, the one with

the largest channel coefﬁcient, and therefore the output of a selection diversity receiver

would be

sel

= max(|h

|, |h

|)x

+ n

(1.2)

where the index i is the one of the maximum channel coefﬁcient.

Equal gain combining would simply add the two signals, after aligning their phases so

that they add coherently. Therefore the base station apply the phase weights, u

and u

,to

output y

equal

= u

+ u

= (u

+ u

)x + (u

+ u

)

= (|h

|+|h

|)x + (u

+ u

)

(1.3)

If the antenna elements are within close proximity to each other, and one assumes that

the magnitudes of the channel coefﬁcients |h

| and |h

| are the same, only their phase is

different, thus the equation simpliﬁes to y

equal

= 2|h

|x. Therefore the signal received is

twice that of the signal that would be received if there had been only one single antenna

at the receiver. Therefore due to using an array antenna, there is a signal gain, which is

known as an array gain or beamforming gain.

Maximum ratio combining would not simply add the two signals, after aligning their

phases so that they add coherently, but it would scale them suitably so that stronger signals

have more weight. We denote the scaling weights as u

and u

and it can be mathematically

shown that, in the case of equal average noise power, the optimal weights are proportional

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