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1、,Time,Single Carrier System,T=1/B (1s),Frequency,B (1MHz),When _maxT Intersymbol interference (ISI),Bandwidth = B Symbol Duration T=1/B,Equaliser is needed to reduce ISI,Frequency,Time,T (1ms),B,OFDM Systems (N subcarriers),f (1kHz),Available bandwidth is divided into N subband Each symbol occupies
2、a narrow band but longer time period,For each subcarriers Bandwidth f=B/N Symbol duration T=N/B,Baseband model of an OFDM communication system,-,-,-,For the uniform subcarrier spacing,The basic orthogonal function for the kth subcarrier is defined as,The basic functions satisfies the condition of or
3、thogonality,Structure of OFDM systems using FFT,Encoding (BPSK),IFFT,Guard insertion,Lowpass filtering,Carrier modulation,Binary data,Channel,Carrier demodulation,Lowpass filtering A/D converting,Guard deleting,FFT,decoding (BPSK),Binary data,OFDM symbol synchronisation,Channel estimation,X(k),x(n),
4、x(n),s(t),y(k),y(n),y(n),r(t),Example of OFDM signals,data,Real part: cos(2fkt),Imaginary part: sing(2fkt),1,-1,-1,1,1,OFDM,Comparison with FDMA,ch1,ch2,ch3,Frequency guard,Assume the information data sequence be X(k), k=0,1N-1, then the transmitted signal s(t) can be expressed as,and,The received s
5、ignal r(t) is,h(t):Channel response; w(t):AWGN signal,OFDM symbol period,The received on subcarrier k0 is,Assume h(t)=1, w(t)=0 (ideal channel), then Y(k) becomes,Using FFT and IFFT for carrier modulation/demodulation,In practice, such parallel data modulation and coherent demodulation can be simply
6、 done by using inverse fast Fourier transfer (IFFT) and fast Fourier transfer (FFT),The basic orthogonal function is,Signal representations,The transmitted discrete time domain signal x(n) is,After inserting guard interval, the signal becomes x(n) with length N+G,Assume the lowpass filter has rectan
7、gular shape,or,The transmitted time domain signal is,“*” denotes the convolution of two signals,The received signal is,h(t): the equivalent baseband channel impulse response t: time; w(t): white Gaussian noise.,r(t) is sampled to obtain a discrete time domain data sequence y(n). The OFDM symbol sync
8、hronisation is needed Removing the guard intervals, yield the time domain OFDM samples y(n), n=0,1.N-1.,The received signal on subcarrier k is calculated as,OFDM spectrum and ICI,The OFDM subcarrier spectrum can be obtained as follows. Modulating a unit signal on the subcarrier p, where 0pN-1 and N
9、is the total number of subcarriers, the transmitted time domain baseband OFDM signal can be represented as,T=1/f is the OFDM symbol period and f the subcarrier separation rect(0,T) represents the rectangular function of the time period 0,T,The Fourier transform of the standard rectangular function r
10、ect(-T/2,T/2) is the sinc(x) function,Then the time and frequency shifted rectangular function is,Denoting the normalised frequency is k=Tf, where k is a real value, then above equation can be simplified as,For the integer k, the Sk,p represents the received signal on subcarrier k.,The derived OFDM
11、spectrum is a sinc(x) function with phase rotation exp(-jx), which is different from common knowledge of sinc(x) function OFDM spectrum.,Real part of OFDM spectrum,Imaginary part of OFDM spectrum,Comparison of Spectrum and ICI,Amplitude Spectrum of OFDM,3. Carrier to interference ratio (CIR),When th
12、e subcarriers are modulated by the signals ak, (k=0,N-1), then the received signal on the 0th subcarrier can be expressed as,where Sp can be obtained by substituting k=0,The desired carrier signal is determined by the signal modulated on the 0th subcarrier, which can be written as,The ICI signal on
13、0th subcarrier is sum of the ICI signals generated by transmitting data on the rest of subcarriers. This sum can be represented as,Using the zero mean and independent conditions of data sequence ap, that is Eap=0, Eapap=ap2, Eapak=0 for kp, then the average carrier power can be derived as,The averag
14、e ICI signal then can be calculated as,the CIR of the standard OFDM systems can be expressed as,CIR versus for a standard OFDM system,Correlative Coding for OFDM,or,Bandwidth Efficiency is not reduced,CIR for correlative coding,Time Domain Window,Timing of OFDM symbols,Representation of the problems
15、 in timing,When the timing changes, the phase of the received subcarriers change. The relation between the phase i of the subcarrier i and the timing offset is given by,Synchronisation using the cyclic extension,Because the number of independent samples is proportional to the number of subcarriers, the extension correlation techniques is only effective when a larger number of subcarriers are used,192 subcarriers, 20% guard,48 subcarriers, 20% Guard,Exercises problems 12-3, 12-4,