to (1.11) The channel matrix of dimensions N x N in Eq. (1.11) now becomes a circular matrix, which can be decomposed into the multiplication of an IFFT matrix, a diagonal matrix, and an FFT matrix. Benefiting from the cyclic convolution, the subcarrier signal Yk can be directly obtained by Xk and the corresponding frequency response Hk from (1.12) where e = = 0,1,...,N. and (1.13) The overall block diagram of an OFDM transceiver is shown in Figure 1.3. At the trans- mitter, the incoming bit stream is divided into N substreams via a serial-to-parallel (S/P) converter. Then, all bit substreams are independently mapped to the corresponding con- stellation points by amplitude phase modulation, such as phase shift keying (PSK) and quadrature amplitude modulation (QAM), yielding X,X1, ,XN-1 An N-point IFFT oper- ation follows, converting the signal from frequency domain to time domain. After that, a CP 1 ICI Cancellation Techniques Based on Data Repetition for OFDM Systems Bit stream Modulation Add CP Lowpass x(t) Carrier filtering modulation Channel Bit stream Discard Lowpass Carrier Demodulation filtering demodulation Figure 1.3 Block diagram of OFDM systems. of length M is appended to the time-domain signal, which is further passed through a low- pass filter to generate the baseband transmitted signal. Finally, the baseband transmitted signal is converted up to the passband by a carrier frequency fc, and sent over the chan- nel. At the receiver, the received signal is first converted down to the baseband by using a local carrier signal of carrier frequency fc. Then, the receiver follows the reverse baseband processing procedure at the transmitter to finally obtain the estimated bit stream. 1.3 Carrier Frequency Offset Effect Ideally, fc is identical to fc. However, due to hardware imperfection and/or Doppler, this may not hold, resulting in a CFO Afc=fc-fc. = - Denote € as the normalized CFO, which is given by (1.14) To investigate the effect of CFO, we assume a fixed E. From Eq. (1.9), the time-domain received sig