OFDM的原理

1.

In modern society more high dependence and the requirements of communication, communication system and the design and development of high efficiency has become the constant pursuit of communication engineering. The efficiency of the communication system, in the final analysis is the spectrum utilization and power efficiency. Especially in wireless communication scenarios, the requirements of these two indicators more often, especially in spectrumefficiency. Because of the space available spectrum resources are limited, and wireless applications are more and more, making use of wireless spectrum of strict management by governments and unified planning. Thus, a wide variety of communication technology has high spectrum efficiency continues to be developed, OFDM

(Orthogonal Frequency Division Multiplexing) is knownspectral efficiency of a communication system is the highest, the digital modulation, digital signal processing, multi carrier transmission technology combine together, make it in the system spectrum utilization rate, power utilization, systemcomplexities has very strong competitive power, is support for future mobile communication especially is one of the main technology of mobile multimedia communications.

OFDM is a multi carrier transmission technology, the N sub carrier channel is divided into N sub channel, N sub channel parallel transmission.OFDM system has many remarkable advantages. First, OFDM has very high spectrum utilization. The common FDM system to signal from each sub channel, need to set the protection interval in the adjacent channel (band), so that the receiver can use the band-pass filter to isolate signals corresponding to sub channels, which not only protect the sub band waste.OFDM system spectrum resources between channels, and between adjacent channels The mainlobe signal spectrum is overlapping (see Figure 1.5), but the spectrum of each sub channel signal is orthogonal to each other in the frequency domain, each subcarrier is orthogonal in time domain, separating each sub channel signals of the OFDM system (demodulation) by the orthogonality to complete. In addition, sub channel OFDM can also be used M-ary modulation (such as high spectrum efficiency, QAM) to further improve the spectrum efficiency of OFDM system. Second, relatively simple to achieve.

When the channel using QAM or MPSK modulation, modulation demodulation process can be completed by IFFT. The process can be completed by FFT, without oscillation source group without band-pass filter group signal separation. Third, anti multipath interference and anti fading ability. Because of the general OFDM system with cyclic prefix (Cyclic Prefix, CP), so that it can completely eliminate the multipath propagation caused by code interference under certain conditions, completely eliminate the damage of multipath on the inter carrier orthogonality of subcarriers, so OFDM system has good ability of anti multipath interference.OFDM the whole channel into many narrow channel, although the channel is available It can be a very flat fading channel, but the fading on each subchannel is approximately flat (see Figure 1.6), which makes the equalization of subchannels in OFDM system very simple, and usually requires only one tap equalizer

Of course, with the single carrier system, OFDM also has some difficult problems to be solved. These problems are mainly: first, synchronization problem. Theoretical analysis and practice show that the OFDM system of synchronous system requires higher accuracy, synchronization error not only caused the output SNR drop, will destroy the orthogonality of the sub the inter carrier, causing inter carrier interference, which greatly affect the performance of the system, and even make the system does not work. Second, the peak to average power ratio of OFDM signal (Peak-to-Average Power, Ratio, PAPR) are often large, making it The linear range of amplifier requirements, but also reduces the efficiency of the amplifier in the future application of.OFDM in communication system, especially mobile applications in multimedia communication in the future will depend on the degree to solve the above problems.

OFDM technology has been or is gaining some applications, for example, ETSI (European) in broadcast applications in Europe

Telecommunication Standard Institute, the European Telecommunications Standards Institute, has developed the number of OFDM technologies Digital Audio Broadcasting (DVB) standard, digital video broadcasting (Digital Video

Broadcasting，DVB）The standards are being developed; in broadband wireless access applications, IEEE 802.11a and IEEE 802.16 are based on the advice of ETSI OFDM technology, HiperLAN II is a OFDM technology based on the standard; used in digital cellular mobile communication, OFDM technology is one of the hot research at present;

in the wired broadband access technology for example, xDSL (high speed digital subscriber line) technology, a special form of OFDM (Discrete Multito - DMT NE) to get widely used in these applications and so on;.OFDM has shown strong vitality, with solving some key problems which restrict the application of OFDM, I believe OFDM will play an increasingly important role in future communication applications.

2. OFDM 发展简史

OFDM

3. Multicarrier modulation and FFT

OFDM is a multi carrier transmission technology. Let

FK (k = 1,2), OFDM is a multi carrier transmission

technology. Let FK (k = 1,2), The carrier modulated signal can be expressed in the interval of I symbols N ?1 s i (t ) = ∑ X i (k ,t ) exp( j 2πf k t )

（1.2.1） k =0

Among them, X I (k, t) is carried by the signal in the first I symbol interval information, it determines the Si (T) amplitude and phase, generally they are only with the symbol label I related complex constant, they carry the information to be transmitted; for example, if the K is carrier using QPSK modulation, set by pi / 4 way sign, when the I code is "00",

according to the mapping between the symbols and signs can know, X I (k, t) = 22 (1 + J). For simplicity, in just a When the symbol of multi carrier signal, often omit the symbol label I; and when the subcarrier with ordinary (without using waveform formation) QAM or MPSK modulation, X I (k, t) has nothing to do with the T, which will X I (k, t) or X (k), according to the context of such ambiguity not. According to the above agreement, (1.2.1) can be written as

N ?1

s (t ) = ∑ X (k ) exp( j 2πf k t )

（1.2.2） k =0

We hope that the spectrum utilization of this multi carrier transmission method is high, that is to say, the subcarrier interval should be as small as possible, and the system is easy to implement

In order to realize the multi carrier transmission system, the general need N oscillator and the corresponding bandpass filters, the complex structure of the system, does not embody the advantages of multi carrier transmission. However, after careful analysis can be found, the modulation and demodulation of multi carrier transmission system can use the discrete Fourier transform (Discrete Fourier Transform. DFT), due to DFT

A fast algorithm of FFT (Fast Fourier Transform) famous, the multi carrier transmission system implementation is greatly simplified, especially the OFDM system using FFT to achieve, with its simple structure, high spectrum efficiency and attention

2.This paper analyzes the conditions that multicarrier transmission systems can be implemented with DFT In order to determine the frequency interval between subcarriers, we consider how the receiver for signal demodulation of the received signal. We (not to consider the influence of noise and distortion) f s sampling to sampling rate, sampling to demodulate the signal by DFT. Using the N point DFT can calculate the signal frequency spectrum component for k

N ?1

S (k ?f ) = ∑ s (n / f s ) exp(? j 2πnk / N ) （1.2.3）

n =0

Here, S (the K F) is the first k frequency; s (n / f s) (n = 0,1,2, N - 1) is the sampling signal; F = FS / N

It is the resolution of DFT. In order to make DFT correctly calculate the spectrum, the signal must be periodically repeated outside the N point sampling, when the signal is repeated

When the number contains only the harmonic component of the DFT, the condition can be satisfied. The T = n / Fs substitution formula (1.2.2) is obtained

N

?1 s ( n / f s ) = ∑ X ( l ) exp( j 2π f l n / f s )

（1.2.4）

L 0

将式（1.2.4）代入式（1.2.3）得

N ?1 N ?1

S ( k ? f ) = ∑∑ X ( l ) exp( j 2π f l n / f s ) exp( ? j 2π nk /N )

n = 0 l =0 N ?1 N ?1

= ∑ X ( l ) ∑exp( j 2π f l n / f s ) exp( ? j 2π nk / N )

L 0 n =0 N ?1

f

l k

= ∑ X ( l )δ ( ? )

（1.2.5

）

f s l

=0 N 其中

0,

m ≠ n δ(m , n ) =

m = n

1,

观察上式可以发现，当多载波已调信号的频率

f k = kf s （1.2.6）

N

时，There is S (the K F) = CX (k), where C is a constant, that is when each subcarrier frequency demodulation with DFT

K can be demodulated by DFT in the case of integer multiples of the discrimination rate. From the above analysis, it is shown that in order to ensure correct demodulation, X (a) is in the process of demodulation

One symbol interval is constant is necessary, if the QAM or MPSK subcarrier modulation uses a waveform shaping technology, such as the use of cosine waveform, but also specifically by DFT demodulation.

From the above analysis, when the frequency of each subcarrier is integer multiples of the DFT resolution for demodulation, the DFT can be used to carry multiple loads

Wave modulated signal sampling demodulation. In particular, the frequency interval of the subcarrier is f s / N, by type (1.2.4) is

N ?1 s(n / f

s )=∑ X (k) exp[ j2π(kf s/ N )n / f s]

k =0

N ?1

=∑ X (k) exp[ j2πn / N ] （1.2.7）

k =0

Type is X (k) (k = 0,1,2, N - 1) sequence (the sequence we denoted as X (N)) IDFT

(Inverse Discrete Fourier Transform), namely the subcarrier frequency spacing of F S / N, multi carrier modulated signal time domain sampling sequence can be calculated by IDFT.

The sequence of X carrying information (N) is a multi carrier modulated signal sampling sequence DFT, so we say that the modulation multi carrier modulation system based on FFT is carried out in the frequency domain.

From the above analysis, the modulation of multi carrier modulation system can be completed by IDFT, demodulation can be completed by DFT, by the knowledge of digital signal processing, we can know that IDFT and DFT can be implemented by efficient FFT

https://www.360docs.net/doc/f717873317.html,position of OFDM system

The block diagram of the OFDM system is shown in Figure 1.1

After the input bit sequence is completed and transformed, the corresponding modulation mapping is completed according to the modulation mode adopted, and the modulation is formed

The information sequence X (N) is used to carry out IDFT on X (N), and the time domain sampling sequence of OFDM modulated signal is calculated

CP (cyclic prefix cyclic prefix can enable the OFDM system to completely eliminate multipath propagation caused by intersymbol interference (ISI) and inter carrier interference (ICI) analysis on 1.5 section 1.4 and section), and then D/A transform,

OFDM modulated signal waveform. The receiving end of received signal in A/D remove the CP transform, cyclic prefix, OFDM modulated signal

The sampling sequence is DFT, and the original modulation information sequence X (N) is obtained

输入信号 串并变换 ... 符

号 映射 ... IFF T ...

加入

数/模 射频 CP 转换 调制

并串

信道

输出信号

并串 变换

.. 符号 判决 ... 均 衡

...

FF T

... 去

CP 模/数 射频

串并 转换 解调

图 1.1 OFDM 系统的结构

The introduction of CP [PR 1] cyclic prefix, the OFDM transmission can be completely eliminated due to intersymbol interference caused by multipath propagation under certain conditions (ISI) and inter channel interference (ICI) effect, greatly promote the practical use of OFDM technology in the process. Figure 1.2 is a schematic diagram of the cyclic prefix.

4

图 1.2 CP 示意图

OFDM "symbol" (symbol) is an ambiguous concept. In most of the OFDM

literature, OFDM "symbol" refers to the modulation information sequence X (N), and X (N) of each component (i.e. on each sub carrier modulation information) also used the "symbol" (symbol) said. To avoid this confusion, we will X (N) together with a cyclic prefix called OFDM "frame symbols", referred to as the "symbol",

called X (N) component of the "intra symbol".OFDM in the literature of the inter symbol interference (ISI)

Refers to the inter symbol interference frame, in particular to remove the interference between the cyclic prefix symbol frame, but also refers to the same symbol synchronization symbol synchronization. This frame is consistent with the name of OFDM in literature, and will not cause misunderstanding.

5. Time continuous system model of OFDM

There are some different forms of OFDM system. We first establish the corresponding mathematical model [ESBL 1]. on the most popular OFDM system using cyclic prefix

The original OFDM system using digital modulation and demodulation technology, so the OFDM model can be regarded as the ideal model of OFDM system, of course, is generally achieved by digital synthesis technology. Figure 1.3 is a continuous time model of OFDM baseband system.。

图 1.3 OFDM 连续系统基带模型

z transmitter

z

The OFDM system has a N subcarrier, the system bandwidth is W Hz, the symbol length is Ts, and the length of the cyclic prefix CP is Tcp, that is, the transmission time of a OFDM frame symbol is T = Ts + Tcp, considering the influence of the cyclic prefix, the K carrier wave waveform emitted by the transmitter is as follows

1 exp[ j2πW k(t ? T )] t∈[0,T ]

T s N

c p

（1.4.1）

φ

k

(t) =

0, t ?[0,T ]

Note that when the T, [0, Tcp], a diameter of K (T) = K (T + N = /W) with K (T + Ts), which is the cyclic prefix, which makes the signal within a certain period of time. This article looks with periodic I OFDM frames have symbols adjustable waveform

N ?1

s i (t)=∑ X i(k)φk(t ? iT )

（1.4.2

）k =0

When the transmission is an infinite OFDM symbol sequence, the OFDM modulated signal waveform can be expressed as

∞

s(t)=∑ s

i (t)

i= z channel

∞ N ?1

=∑∑ X i(k)φk(t ? iT )

（1.4.3

）

i= k =0

We assume that the channel impulse response g (tau; t) the support of less than the cyclic prefix CP, namely r e [0, Tcp], the signal is received by the receiver for

T cp

~ （1.4.4

）r(t)=(g ? s)(t)=∫ g(τ;t)s(t ?τ)dτ+ n (t)

Here, n~(t) is the additive white noise (complex form) of the channel Gauss.

z receiver

The OFDM receiver consists of a filter bank, where the first k filter is matched with the back part [Tcp, T] of the carrier wave waveform K (T)

?

(T?t), t ∈[0,T s]

ψ

k

(t) = φk （1.4.5

）

0, t ?[0,T

s ]

That is to say, the cyclic prefix CP is deleted. Because the CP contains all the symbols in front of the inter symbol interference (ISI), so the output sampling receiver filter group will not contain ISI. therefore, we in the calculation of the K sampling the output of the matched filter

We can ignore the time label I, the use of formula (1.4.3), (1.4.4), (1.4.5), and we obtain

y

k

=(r ?ψk)(t)t=T=∫?∞∞ r(t)ψk(T ? t)dt

T T

cp N ?1 ?T ~ ?

= ∫T ∫

′(t)dt + ∫

T

n (T?t)φ

k

(t)dt.

g(τ;t)∑ X (k )φ

k′

(t ?τ) dτφk

cp k =0 cp

A channel impulse response invariant in an OFDM symbol interval, the G (tau), so you get

N

?1

T T c

p ?T ~ ?

∑′

y = ∫

0 g(τ)φ(t?τ)dτφ(t)dt + n (T ? t)

φ(t)dt.

X

(k )

k ∫T

cp k

′k ∫T cp k

k

=0

6

Tcp T < < T integral interval and 0 < < 0 < R Tcp contains T and T. In the integral r < type can be written as

T c p T c p ′ exp[ j 2πk (t ? τ ? T cp

)W / N ]

∫

g (τ)φk ′ (t ? τ)d τ = ∫0 g (τ) T s

d τ

′

N ] T

c p

′

exp[ j 2πk (t ? T cp

)W / T cp < t <

T = T s

∫0 g (τ) exp[? j 2πk τW / N ]d τ,

The integral part behind the upper part is the sampling of the channel impulse response in the frequency domain. The sampling frequency is f = k 'W / N, that is, at the K' carrier frequency

W T

h k ′ = G (k ′ N ) = ∫0 cp g (τ) exp(? j 2πk ′τW / N )d τ,

Here is the G (f) g (tau) Fourier transform. Using these mark, the output filter can be reduced to the receiver ′ ? T ~ ? N ?1

T exp( j 2πk (t ? T cp )W / N y k = ∑ X (k ′)∫Tcp T s h k ′φk (t )dt + ∫

Tcp

n (T ? t )φk (t )dt k

=0

N

?1

=

∑ x k ′h k ′

∫T T φk ′ (t )φ?k (t )dt + n k ,

（1.4.6）

k =0 c p

这里 n k = T ~ ?

(t )dt 。根据滤波器组的正交性 ∫T cp n (T ? t )φk

φk ′ (t )φ?k (t )dt = ′ / N exp( j 2πk (t ? T cp )W / N dt T T exp( j 2πk (t ? T cp )W ∫T cp ∫T cp

T s T s

= δ(k ? k ′),

这里 δ(k ) 是 Kronecker δ 函数。这样式（1.4.6）可以简化为

y k = h k X (k)+ n k

（1.4.7

）

其中n k是加性高斯白噪声（AWGN）。

6. OFDM 的时间离散系统模型

OFDM 时间离散系统模型与时间连续系统模型相似，如图 1.4 所示。

7

图 1.4 OFDM 系统的离散时间模型

OFDM 信号s(n) 通过时变多径信道，设信道衰落比较缓慢，在一个 OFDM 符号间隔内

信道的冲击响应不变，记为g(n) ，则 OFDM 接收机收到的信号r(n) 为= ?+ ~

r(n) s(n) g(n) N (n)

其中，“?”表示离散序列的（线性）卷积运算。

循环前缀 CP 使得s(n) 成为s1 (n) 的循环扩展，根据数字信号处理的知识当CP 的长度

≥g(n) （的支撑即最大非零定义域）长度时，r(n) 去掉循环前缀后所得r1 (n) 为= ?+ ~

r

(n) s1(n) g(n) N1(n)

1

其中，“?”表示循环卷积运算[WSY 1]。

根据 DFT 的时域卷积定理，r1 (n) 经过 FFT 后的输出Y ( k) 为

= ?+

Y ( k ) DFT {[ IDFT ( X ( k )] g( k ) N

( k)}

1

=X ( k )? DFT [ g ( k )]+ N 1( k)

=X ( k )? G ( k )+ N 1( k)

其中G ( k) 是信道的频域响应，通过简单的均衡就可用消除其影响，提取出所传输的数据

X ( k)。

应该指出，虽然 CP 在一定条件下可以完全消除 ISI 和 ICI，但接收信号去掉 CP 后在作 DFT 前，仍然存在帧内符号间干扰，即 OFDM 帧符号与信道作

了（循环）卷积，经 DFT 解

卷积后，通过均衡消除了帧内符号间干扰并得到信息序列X (N ) 。

8

我们知道，两个N长序列的时域循环卷积是N长序列，经DFT 变换到频域后，对应的是两个N长序列 DFT 的乘积，这就是著名的 DFT 的卷积定理。即 DFT 解卷积解的是循环卷积，由于离散序列经过线性系统后的输出是序列与线性系统的冲击响应的线性卷积，因此不可以直接用DFT 解卷积。循环前缀CP 的作用就是将线性系统对离散序列的卷积作用变成循环卷积（根据数字信号处理的理论可以知道，只有CP 的长度≥信道冲击响应的长度时才是如此），从而可以利用 DFT 解卷积。

当 CP 的长度大于信道的最大时延时，一方面 CP 起到了保护间隔的作用，所以可以完全消除由于信道的多径传播造成的 OFDM 的符号间干扰；另一方面，从以上分析可以知道， DFT 的输出的信号项仅受到（子）信道的固定的衰减，而不存在子信道间的干扰，即 CP 还起到了保持子载波间的正交性的作用，从而消除了载波间干扰（Intercarrier Interference，ICI）。

7. OFDM 信号的频谱特性

当各子载波用 QAM 或 MPSK 进行调制时，如果基带信号采用矩形波，则每个子信道上

已调信号的频谱为Sa(x) 形状，其主瓣宽度为 2 / T s Hz，其中T s为 OFDM 符号长度（不包括CP）。由于在T s时间内共有OFDM 信号的N个抽样，所以OFDM 信号的时域抽样周期

为T s / N。由于相邻子载波之间的频率间隔为?f = f s / N，其中f s为 OFDM 信号的抽样

频率，即f s = N / T s ，所以

?f = f s/ N =1 /T s （1.7.1）

即这些已调子载波信号频谱Sa(x) 函数的主瓣宽度为 2 / T s，间隔为1/ T s。根据Sa(x) 函数

的性质，知道它们在频域上正交，这就是正交频分复用（OFDM）名称的由来。

我们知道，一般的频分复用传输系统的各子信道之间要有一定的保护频带，以便在接收端可以用带通滤波器分离出各子信道的信号。保护频带降低了

整个系统的频谱利用率。 OFDM 系统的子信道间不但没有保护频带，而且各子信道的信号频谱还相互重叠，如图 1.5 所示，这使得 OFDM 系统的频谱利用率相比普通频分复用系统有很大提高，而各子载波可以采用频谱效率高的QAM 和 MPSK 调制方式，进一步提高了 OFDM 系统的频谱效率。

应该指出，由于循环前缀的影响，OFDM 信号的频谱结构将发生一定的变化，但这仅仅使信号的某些频谱成份得到增强，而不会使 OFDM 信号增加新的频率成份。

我们知道，移动信道一般存在多径传播问题，使信道表现出明显的衰落特性。信道的多径衰落在单载波传输系统中往往会产生严重的码间干扰，使得接收机往往需要比较复杂的均衡滤波器，所以设计单载波高速移动通信系统的均衡器是一项富有挑战性的工作。OFDM

9

图 1.5 OFDM 信号的频谱

OFDM 子信道

responsefrequency

responsefrequency

frequency

frequency 图 1.6 OFDM 的各子信道近似是平坦衰落

系统利用N个子载波，将整个信道划分成N个窄子信道，在每个子信道上信道

的衰落近似平坦衰落，如图1.6 所示，而且每个子信道上的码速率也比较低，这

使得OFDM 系统的均衡滤波器的设计比较容易，一般每个子信道只需要一个单

抽头的（自适应）均衡器即可，这也是 OFDM 吸引人的特点之一。

OFDM 子信道间的间隔对系统的性能有很大影响。子信道间隔越大，由于各种

因素造成的子信道间的干扰越小，但同时系统的频谱效率也越低，由于子信道带

宽的加大，系统抗击频率选择性衰落的能力也下降；反之，为提高系统的频谱效

率而缩小子信道间的间隔，必然使系统的子载波间的干扰加大；系统设计人员需

要在它们之间折衷。信道带宽和 FFT 的点数决定了 OFDM 子信道间的间隔，确

定子信道间隔的一般原则是，满足系统频谱利用率和保证OFDM 系统的良好的抗击频率选择性衰落的前提下，尽可能加大子载波间的间隔。

8. 虚载波

OFDM 的调制解调可以采用DFT 实现，这大大简化了OFDM 的实现复杂性，是OFDM 发展过程中有里程碑意义的进展。但基于DFT 的实现方式也给OFDM 带来一些问题，我们这里进行简单讨论。

我们知道，理想的 OFDM 信号各个子信道上的频谱是 Sa 函数形状的，因此从理论上来说，OFDM 信号是非带限信号（具有无限带宽）。而具有DFT 实现方式的OFDM 其信号处理是在离散域上采用数字信号处理技术完成的，也就是对OFDM 的抽样信号进行的处理，

例如，前面假设的一帧OFDM 符号X(0), X(1),, X( N?1) ，应该被看成一帧OFDM 信号s ( t) 在一个帧周期内的抽样信号作 DFT 变换后的结果。对信号进行时域抽样，其必要条

件是信号是带限的，不然抽样后必然会产生频谱混叠，这显然是矛盾的。

工程上解决上述矛盾的方法是对 OFDM 进行带限处理：对 OFDM 基带信号进行滤波，滤除其频谱旁瓣。这样处理后，靠近频带边缘的子载波的一部分能量还比较大的旁瓣被滤除，破坏了子载波的正交性，会造成子载波之间的干扰，造成检测上的麻烦。为了减少带限处理给OFDM 信号带来的上述影响，工程上一般在信号频谱的边缘设置一定数量的虚载波

(Virtual Carrier)，即相应的子载波幅度置零。例如，IEEE 802.11a 标准中，子载波共有 64 个，

其中虚载波共有12 个。采用虚载波后，再对OFDM 信号进行带限处理，就不会对 OFDM 信号产生明显的影响了。

9. OFDM 系统参数的选择

10. OFDM 的子载波调制

OFDM 的子载波调制一般采用QAM 或MPSK 方式。各子载波不必要采用相同的状态数（进制数），甚至不必要采用相同的调制方式。这使得 OFDM 支持的传输速率可以在一个较大的范围内变化，并可以根据子信道的干扰情况，

在不同的子信道上采用不同状态数的调制，甚至采用不同的调制方式。调制信号星座的形成在IDFT 前由相应的调制映射完成。具体地说，就是根据串并变换后的比特序列以及 QAM（或 MPSK）的星座映射关系，计算出

相应的同相分量a i和正交分量b i，得到X (i) = a i + jb i，这就是第i个载波被调制后在一个

OFDM 符号周期内的频谱（所以我们说OFDM 的子载波调制是在频域上进行的），然后将该符号周期内的频域信号变成时域信号，这个过程由IDFT 完成。IDFT 的输出加上循环前缀后，分实部虚部分别作D/A 变换得到要传输的实部和虚部的波形信号，它们可以采用串行

传输的方式传输，或者计算出信息序列X (N ) 后，将信息序列延长成长度为

2N+2，变成共

轭对称的形式，如图1.7 所示，根据数字信号处理的理论，这样的序列作IDFT 后为实信号，可以直接传输。上述两种方案的效率较低，目前更流行的方式是采用正交调制（即一般是将实部和虚部分别调制到同一频率的cos 和sin 载波上）方式并行传输。

下面以子载波采用 16QAM 调制为例，说明 16QAM 调制映射的实现。

一种最简单的 16QAM 信号星座图如下面图 1.8 所示，这种星座图不是最佳的，即这种星座图形式的16QAM 对信号功率的利用没有达到最佳，但是这种星座图实现最容易。关于信号星座图的优化设计见[Chen 1]。

图 1.7 将信息序列扩展成共轭对称形式的方法

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图 1.8 16QAM 星座图图中的横轴表示同相分量的信息比特，纵轴表示正交分量的信息比特，当然也可以作

另外的假设。设第k个子信道上要传输的信息比特为“1101”，从图 1.8 可知，X ( k ) = 1 ?j；

同样若信息比特为“1010”，则X ( k ) = 3 + 3 j，等等。

由于OFDM 的子载波调制是在频域上根据信号星座图计算出来的，而且完成调制的 IDFT 也需要大量的运算，因此 OFDM 系统的发射机必须有强大的计算能力（其实接收机也是如此），这可以由专门的DSP 芯片或FPGA 芯片完成，随着计算机技术的进步，未来也有可能由通用计算机完成。从这种意义上说，OFDM 是通信和计算技术的融合。由于OFDM 的发射机和接收机有强大的一般计算能力，所以在 OFDM 子载波调制中，不必考虑复杂的星座图信号在实现上的复杂性，这样 OFDM 的子载波调制中可以采用任何先进的信号星座图优化技术，以提高信号的功率利用率。

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