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

OFDM is a multi carrier transmission

3. Multicarrier modulation and FFT

OFDM is a multi carrier transmission technology. Let

FK (k = 1,2), technology. Let FK (k = 1,2), The carrier modulated signal can be expressed in the interval of I symbols N ?1 （1.2.1） si (t) = ∑ X i (k,t) exp( j2πfk t)

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 \

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

（1.2.2） s(t) = ∑ X (k) exp( j2πfk t)

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(? j2πnk / 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 / fs )

L0 （1.2.4）

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 N ?

?1 1

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

L0 n=0 ?1 fl k = ∑ X ( l)δ ( ? ) N

（1.2.5）

（1.2.6） l =0 其中

0,

fs N

m ≠ n m = n

δ(m, n) =

1,

观察上式可以发现，当多载波已调信号的频率

kf s fk = 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(kfs / N )n / fs ]

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

4.Composition 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