Full-diversity space-frequency codes for mimo-ofdm systems
This paper addresses the problem of space-frequency code design for broadband multi- antenna OFDM systems. We show that space-time codes achieving full diversity in quasi-static flat fading environment can be used to construct space-frequency codes that achieve the maximum diversity available in frequency selective MIMO fading channels. Thus, the abundant classes of existing space-time block and trel- lis codes can be used for full diversity transmission in MIMO-OFDM systems. In order to take advantages of both the MIMO systems and the OFDM, space-jrquency (SF) coded MIMO-OFDM systems were introduced in (l), and later works (2), (3) also de- scribed such systems. The performance criteria for SF coded MIMO-OFDM systems were derived in (4) and (6). In (4), the authors showed that, in general, existing ST codes cannot ex- ploit the diversity available in frequency selective MIMO chan- nels, and it was suggested that a completely new code design procedure will have to be developed for MIMO-OFDM sys- tems. Later in 151, they proposed a class of SF codes achieving full diversity with the assumption that all of the path delays are located exactly at the sampling instances. We consider a SF coded MIMO-OFDM system with Mt transmit antennas, M, receive antennas and N subcarriers. Suppose that the frequency-selective fading channels have L independent delay paths and the same power delay profile. The MIMO channel is assumed to be spatially uncorrelated and constant over each OFDM block period. The channel impulse response from transmit antenna i to receive antenna j can be modeled as hg,j(~) = ai,j(l)S(~ - T,), where 71 is the delay and ai,j(l) is the complex amplitude of the 1-th path between transmit antenna i and receive antenna j. The ai,j(l)'s are modeled as zero-mean complex Gaussian random variables with variances Elaj,j(l)12 = S;, and E,=, 6, = 1. Thus, we consider arbitrary power delay profiles. Each SF codeword is an N x Mt matrix C = {ci(n)}o~n~N-l,) ~iCM,, where ~(n) denotes the channel symbol transmitted over the n-th subcarrier by transmit an- tenna i. The OFDM transmitter applies an N-point IFFT to each column of the matrix C. After appending the cyclic prefix, the OFDM symbol corresponding to the i-th (i = 1,2, . . . , Mt) column of C is transmitted by transmit antenna i. At the receiver, after applying FFT, the received signal at the n-th subcarrier at receive antenna j is given by L-I