Firstly, OFDM is briefly introduced.
OFDM is the abbreviation of orthogonal frequency division multiplexing. OFDM is a new signal modulation transmission technology based on multi-carriers. Specifically, it decomposes signal data into several independent sub-signal streams, and each sub-signal stream will be transmitted at a relatively low flow rate. It is a typical feature of OFDM to transmit multiple sub-signal streams in parallel at a relatively low flow rate. Compared with the traditional single carrier system, multi-carrier mode can greatly expand the channel capacity. The theoretical research of multi-carrier modulation transmission technology began in the 1960s. Communication technology experts have proved that the performance of information transmission system can be greatly optimized despite the signal interference in multi-carrier transmission. In the early 1970s, OFDM was patented for the first time. In 197 1, Weinstein and Ebert realized multicarrier modulation by discrete Fourier transform, which was published in IEEE magazine. In the following ten years, although people have deeply studied how to use multicarrier modulation technology in the field of mobile communication, multicarrier transmission technology has not been widely used because digital signal processing technology and efficient signal modulation technology have not kept up. This situation did not change until the 1990s. Since then, OFDM technology has been paid attention to and widely used.
Compared with the traditional single carrier system, OFDM technology effectively expands the channel capacity, but it is difficult to correlate the signals in multipath propagation in advance, and the sub-channel signals will inevitably interfere with each other. How to eliminate all kinds of interference is called noise degradation.
Secondly, discrete multitone (DMT) technology prepares for noise signal degradation.
OFDM first uses subchannels with different frequencies to transmit a single large-capacity information stream, instead of transmitting different subchannels separately. In that case, the transmitter uses parallel transmission, which can be compared with single-carrier large-capacity serial transmission in a single channel. If it is simply realized by multiple sets of transmitters and receivers, the cost will be very high. Later, people realized that 9-point QAM modulation technology was applied to multi-carrier modulation system, and the receiver used sub-channel correlation detection and inter-carrier correlation detection.
Discrete Fourier Transform (DFT) technology is to group input signals, so that each group of data contains n complex symbols, and each group of complex symbols occupies a subchannel. The receiver first samples the input signal, and then performs discrete Fourier transform on each group of data to recover the original signal. This mode of OFDM is called DMT, that is, discrete multitone. The main advantage of DMT technology is that it is based on FFT algorithm. Theoretically, the FFT with n symbols only consumes nlogn multiplication operations, and the amount of operation required for directly adopting DFT is n2.
In recent 20 years, OFDM technology, especially DMT technology, has been widely used in various communication technologies. Now, DMT has been used as the standard technology of ADSL.
Thirdly, noise degradation of multi-carrier channel.
OFDM technology, combined with appropriate coding technology and weaving technology, can effectively resist the interference of wireless channels. In the high speed transmission technology of wireless communication, the frequency response curve is generally not flat. The main idea of OFDM is to decompose a given channel into orthogonal subchannels in frequency domain, each subchannel is modulated by a subcarrier, and each subcarrier is transmitted in parallel. Even if the total channel is uneven, the relative flatness of each sub-channel can be guaranteed. Due to the narrowband transmission of subchannels, the signal bandwidth is obviously smaller than the channel bandwidth, which greatly eliminates the interference between subchannels.
The high-speed and large-capacity data stream is decomposed into multi-sub-path low-speed and small-capacity data streams, and the data of each sub-signal stream is modulated and superimposed independently to form a transmission signal. Due to the decrease of channel rate and capacity and the increase of symbol period, multipath interference will be less inherited to the next symbol, thus reducing the percentage of multipath delay in signal symbols and weakening the influence of multipath interference on signal transmission system. Experiments show that the original information signal can be completely recovered according to the encoding interleaving process and the corresponding decoding deinterleaving process specified in the 802. 1 1a standard. The following figure shows the observation results of two probes displayed by the oscilloscope. Comparing the two waveforms, there is no difference in signal sensitivity.
In order to accelerate the fading of the out-of-band part of the OFDM power spectrum, it is necessary to window the OFDM symbols, which can gradually reduce the amplitude of the periodic edge to zero. The raised cosine window function is expressed as the formula (1):
(1)Ts refers to the symbol length before windowing, β refers to the roll-off factor, and (1+β)Ts refers to the symbol length after windowing.
The following formula (2) is often used to describe the equivalence of OFDM output signals.
The OFDM signal described in Equation (2) has a disadvantage: the attenuation speed of out-of-band interference in the power spectrum is too slow. Although increasing the number of subcarriers can speed up the attenuation of out-of-band interference in power spectrum, if windowing technology is not used, the effect is still not ideal.
In the actual communication process, the window opening process is as follows:
(1) padding zeros after n digitally modulated signal symbols to form a sequence of n input sample values.
(2) Perform IFFT operation on the sequence of sample values, respectively implant the last prefix of the output signal before the corresponding OFDM symbol, and then implant the foremost Tpostfix sample of the IFFT output signal after the OFDM symbol.
(3) Multiply OFDM symbols by raised cosine window function brown (t) defined by equation (1) in time domain.
(4) Add the delay Ts of the windowed OFDM symbol with the previous windowed OFDM symbol, and there will be an overlapping area with a bandwidth of βTs between two adjacent OFDM symbols.
Multicarrier modulation (MCM) technology decomposes a nonlinear channel with a certain bandwidth into n approximate subchannels, each of which is approximately linear, and each subchannel transmits data at a low-speed code (1/N symbol rate). The symbol period of low-speed transmission data is long, and when the ratio of delay value to symbol period is less than a certain value, the inter-symbol interference will not be obvious. In essence, MCM is insensitive to channel delay spread, and even without equalizer, better performance can be obtained by using MCM.
According to Shannon formula, when the frequency response of subchannel is approximately linear, the channel capacity almost reaches the maximum. In each subchannel, the transmission power spectral density can be determined according to the channel characteristics, and each channel can be coded independently, and then the signal transmission can be realized by adopting a mapping mode suitable for the subchannel-MQAM mapping mode when the signal-to-noise ratio is high and BPSK or QPSK mapping mode when the signal-to-noise ratio is low. In addition, when the frequency interval Δ f is small enough, C(f) is almost constant, so it is unnecessary for the receiver to use equalization algorithm to compensate, and the inter-symbol crosstalk can be ignored.
refer to
[1] Sunborg J. Universal Personal Telecommunications (UPT), "Concept and Standardization", Ellison Review, 1993, pp. 70-74.
[2] John Proia Keith. Translated by Zhang Zongcheng and Zheng Baoyu. Digital communication (3rd edition) [M]. Electronic Industry Press,1999,2. , pp. 552-560
[3] Jiang Dan. Information theory and coding [M]. China University of Science and Technology Press, 200 1, pp. 125- 130.
[4] Lu Junzhe. OFDM Channel Equalization Technology [D]. xidian university Master's Dissertation, 200 1. 1.
Wang Youzheng. Wireless local area network and personal communication system. State key laboratory of microwave and digital communication. 200 1. 10.
[6] Jim Gail, Wireless Local Area Network: Realizing Interoperability Network, People's Posts and Telecommunications Publishing House &; Macmillan Technology Publishing Company, 200 1.4, p. 107- 126.