MATLAB实现的OFDM多载波通信详解

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MIMO-OFDM无线通信技术是现代无线通信系统中的一个重要组成部分，特别是在宽带数据传输中，它利用多载波调制方法来提高频谱效率和抗多径衰落性能。本资源是一本介绍OFDM（正交频分复用）原理及其在MATLAB环境下的应用的经典教材。OFDM的核心概念在于将高速率的数据流分割成多个低速率子载波，每个子载波独立传输，通过正交性实现并行传输，从而克服单载波系统在高数据率下容易出现的频率选择性衰落问题。第4章深入探讨了单载波与多载波传输的区别。首先，单载波通信系统如图4.1所示，其工作流程包括：带限信道h(t)假设带宽为W，发送端通过脉冲形状滤波器gT(t)将符号包进行预编码，每个符号具有时间间隔T，对应数据速率R=1/T。接收端经过接收滤波器、均衡器和解调器处理。其中，接收滤波器gR(t)、均衡器h1(t)的作用是对信号进行修正，以抵消信道的影响。理想情况下，均衡器可以完美补偿信道效应，如表达式（4.2）所示，接收信号y(t)由子载波信号amg(t-mT)加上噪声z(t)组成。然而，单载波系统的局限性在于当数据速率增加时，带宽需求也相应增大，这可能导致频谱效率低下。OFDM通过将一个宽带宽分成多个窄带子载波，每个子载波采用不同的频率进行独立传输，使得多个子载波可以在不相互干扰的情况下同时工作。这样，即使存在多径衰落，各个子载波上的信号仍保持正交，提高了整个系统的抗干扰能力和频谱利用率。在MATLAB环境中，该教材提供了实际的仿真程序，帮助读者理解OFDM系统的理论概念如何转化为实际操作。例如，设计和实现滤波器、子载波分配、以及如何对信号进行调制和解调等步骤，这对于理解OFDM系统的复杂性及优化设计至关重要。此外，通过这些程序，读者还能掌握如何分析和调试OFDM系统的性能，如误码率、信道容量和系统性能指标。这本MIMO-OFDM Wireless Communications with MATLAB资源不仅介绍了OFDM的基本原理，还提供了实践操作的平台，适合学习者深入理解OFDM在无线通信领域的应用，尤其是在解决高速、宽带无线通信中遇到的技术挑战。

of the typical OFDM transmitter and receiver, including the IFFT and FFT operations. Each

detail of blocks in this diagram will be discussed in the following subsections.

4.2.2 OFDM Guard Interval

4.2.2.1 Effect of Multipath Channel on OFDM Symbols

Consider the lth OFDM signal, x

ðtÞ¼

N1

k¼0

½ke

j2pf

ðtlT

sym

, lT

sym

< t  lT

sym

þnT

.For

the channel with an impulse response of h

ðtÞ, the received signal is given as

ðtÞ¼x

ðtÞ

ðtÞþz

ðtÞ¼

ðtÞx

ðttÞdt þz

ðtÞ; lT

sym

< t  lT

sym

þnT

ð4:18Þ

where z

ðtÞ is the additive white Gaussian noise (AWGN) process. Taking the samples

of Equation (4.18) at nT

¼ nT

sym

=N, Equation (4.18) can be represented in a discrete time

as follows:

½n¼x

½n

½nþz

½n¼

m¼0

½mx

½nmþz

½nð4:19Þ

where x

½n¼x

ðnT

Þ, y

½n¼y

ðnT

Þ, h

½n¼h

ðnT

Þ, and z

½n¼z

ðnT

Þ.

In order to understand an ISI effect of the multipath channel, we consider the illustrative

examples for the discrete-time channel in Figure 4.11, where two impulse responses with

different lengths are shown along with their frequency responses. Figure 4.12 illustrates an ISI

effect of the multipath channel over two consecutive OFDM symbols. Let T

sub

denote the

duration of the effective OFDM symbol without guard interval. Since W ¼ 1=T

and thus,

Df ¼ W=N ¼ 1=ðNT

Þand T

sub

¼ NT

¼ 1=Df . By extending the symbol duration by N times

(i.e., T

sub

¼ NT

), the effect of the multipath fading channel is greatly reduced on the OFDM

symbol. However, its effect still remains as a harmful factor that may break the orthogonality

Data source

FEC

coding

Bit

interleaver

Mapper

(QAM/PSK)

Serial to

parallel

(P/S)

IFFT Windowing

Parallel

to serial

(P/S)

DAC

Data sink

FEC

decoding

Bit

deinterleaver

Demapper

(QAM demodulator/PSK

demodulator)

FFT

Remove

Parallel

to serial

(P/S)

ADC

Serial to

parallel

(P/S)

Channel

equalizer

Timing/frequency

synchronization and

channel estimation

Wireless

channel

Add

OFDM signalQAM/PSK modulated symbolBit stream

Pilot symbol

and virtual carrier

AWGN

Figure 4.10 Block diagram of transmitter and receiver in an OFDM system.

126 MIMO-OFDM Wireless Communications with MATLAB



among the subcarriers in the OFDM scheme. As shown in Figure 4.12(b), the ﬁrst received

symbol (plotted in a solid line) is mixed up with the second received symbol (plotted in a dotted

line), which incurs the ISI. It is obvious that all subcarriers are no longer orthogonal over the

duration of each OFDM symbol. To war rant a performance of OFDM, there must be some

means of dealing with the ISI effect over the multipath channel. As discussed in the sequel, a

guard interval between two consecutive OFDM symbols will be essential.

4.2.2.2 Cyclic Preﬁx (CP)

The OFDM guard interval can be inserted in two different ways. One is the zero padding (ZP)

that pads the guard interval with zeros. The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP (cyclic preﬁx) or CS (cyclic sufﬁx). CP is to extend the

OFDM symbol by copying the last samples of the OFDM symbol into its front. Let T

denote

the length of CP in terms of samples. Then, the extended OFDM symbols now have the duration

of T

sym

¼ T

sub

þT

. Figure 4.13(a) shows two consecutive OFDM symbols, each of which has

the CP of length T

, while illustrating the OFDM symbol of length T

sym

¼ T

sub

þT

Meanwhile, Figure 4.13(b) illustrates them jointly in the time and frequency domains.

Figure 4.13(c) shows the ISI effects of a multipath channel on some subcarriers of the OFDM

symbol. It can be seen from this ﬁgure that if the length of the guard interval (CP) is set longer

than or equal to the maximum delay of a multipath channel, the ISI effect of an OFDM

symbol (pl otted in a dotted line) on the next symbol is conﬁned within the guard interval so that

it may not affect the FFTof the next OFDM symbol, taken for the duration of T

sub

. This implies

that the guard interval longer than the maximum delay of the multipath channel allows for

maintaining the orthogonality amo ng the subca rriers. As the continuity of each delayed

subcarrier has been warranted by the CP, its orthogonality with all other subcarriers is

maintained over T

sub

, such that

sub

j2pf

ðtt

j2pf

ðtt

dt ¼ 0; k 6¼ i

for the ﬁrst OFDM signal that arrives with a delay of t

, and

sub

j2pf

ðtt

j2pf

ðtt

T

dt ¼ 0; k 6¼ i

for the second OFDM signal that arrives with a delay of t

þT

Figure 4.14 shows that if the length of the guard interval (CP) is set shorter than the maximum

delay of a multipath channel, the tail part of an OFDM symbol (denoted by a quarter circle)

affects the head part of the next symbol, resulting in the ISI. In practice, symbol timing offset

(STO) may occur, which keeps the head of an OFDM symbol from coinciding with the FFT

window start point. In this context, Figure 4.15 shows that even if the length of CP is set longer

than the maximum delay of the multipath channel, ISI and/or ICI may occur depending on the

timing of the FFT window start point. More speciﬁcally, if the FFT window start point is earlier

than the lagged end of the previous symbol, ISI occurs; if it is later than the beginning of a

symbol, not only ISI (caused by the next symbol), but ICI also occurs [78].

128 MIMO-OFDM Wireless Communications with MATLAB

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