it leads to a most compact spectrum. A snapshot of the OFDM spectrum with N = 8 is given in Figure 1.1. Figure 1.1 shows that the spectrum of one subcarrier signal overlaps that of the others. It is expected that as N increases to a large value, the overall spectrum tends to be confined by a rectangle with range of N/TN = B. At the receiver, without taking into account the effects of the channel and noise, that is, the received signal y(t) is equal to the transmitted signal x(t), the output signal on the k-th subcarrier Yk is given by (1.3) 1.2 OFDM Principle Figure 1.1 Spectrum of OFDM signals with N = 8, depicted by the dashed line. Because of the orthogonality in Eq. (1.2), Eq. (1.3) can be simplified as Yk = Xk. (1.4) From the above, it is clear that the subcarrier orthogonality ensures interference-free par- allel data transmission. Subcarrier orthogonality can be also interpreted in the frequency domain. In the fre- quency domain, all subcarriers should be orthogonal SO as to separate out the corresponding input signal without interference. According to the Nyquist criterion, no ISI occurs when the condition that the coherence bandwidth is no less than 1/TN. This implies that the min- imum frequency separation required for subcarriers to remain maintain orthogonality over the symbol interval [0, is 1/TN. Obviously, the minimum frequency interval should be set to be 1/TN to save the frequency resource in OFDM. 1.2.2 Discrete Implementation According to the Nyquist criterion, to recover a signal of bandwidth B without causing any distortion, the sampling frequency must be no less than B. Consider the sampling time interval to be At = 1/B. The time-domain discrete transmitted signal can be obtained from Eq. (1.1) as (1.5) where n = 0, 1, ... , N - 1. Obviously, the output of Eq. (1.5) is the inverse discrete Fourier transform (IDFT) of {X, X, ,XN-1}. 1 ICI Cancellation Techniques Based on Data Repetition for OFDM Systems Denote Yn Il y(nAt) as the sampled time-domain received signal. Similarly, without taking 