LU et aL: LDPC-BASED SPACE-TIME CODED OFDM SYSTEMS OVER CORRELATED FADING CHANNELS R An Fred 排3 Fig 1. System description of a multiple-antenna STC-OFDM system over correlated fading channels. Each STC code word spans A subcarriers and P time ots in the syst a particular subcarrier and at a par time slot, STC symbols are transmitted from N transmitter antennas and received by M receive directed least-square estimator and a data detector is introduced At the receiver, the signals are received from M receiver in[18]. For the system considered here, the receiver in [18]per- antennas. After matched filtering and sampling, the discrete forms well at low to medium Doppler frequencies, but exhibits Fourier transform(DFT)is applied to the received discrete-time an irreducible high error floor in fast fading channels. a receiver signal to obtain employing the expectation-maximization(EM) algorithm has recently been proposed for STC systems [19][201, which ex- 3,=H[m,k],k+2,, hibits a good performance, but, on the other hand, its complexity is relatively high for the LDPC-based STC-OFDM systems Here, we develop a novel turbo receiver structure employing where H[p, k]E CAXN is the matrix of complex channel fre- a maximum a posteriori expectation-maximization(MAP-EM) quency responses at the hth subcarrier and at the pth time slot, demodulator and a soft LDPC decoder, which can significantly which is explained below, alp, h]EC andy, k] re- reduce the error floor in fast fading channels with a modest com- spectively the transmitted signals and the received signals at the putational complexity. (A similar iterative receiver structure is hth subcarrier and at the pth time slot, and alp, ]E is the developed for static MIMO channels in [21]) ambient noise, which is circularly symmetric complex Gaussian The rest of this paper is organized as follows. In Section Il, with unit variance multiple-antenna STC-OFDM system over correlated fre- Consider the channel response between the th transmitter an- quency- and time-selective fading channels is described. In tenna and the ith receiver antenna. Following [22], the time-do- Section IlL, the outage capacity of this system is analyzed In main channel impulse response can be modeled as a tapped Section IV, the PEP analysis is given. Based on the analysis delay line. With only the nonzero taps considered, it can be ex in Sections Ill and IV, in Section V, an LDPC-based STC pressed as osed for the OFDM system under consideration. In Section VI, a novel turbo receiver is developed. In Section VIl computer simulation results are given. Section VIll contains the conclusion h;(x;t=∑00(-( where 8( is the Dirac delta function, Lf denotes the number SYSTEM MODEL of nonzero taps, and c (; t)is the complex amplitude of the We consider an STC-OFDM system with K subcarriers, delay is n/(K△r)when N transmitter antennas, and M receiver antennas, signaling integer and Ay is the tone spacing of the OFDM system. In through frequency- and time-selective fading channels, as mobile channels, for the particular(2,3)th antenna pair, the illustrated in Fig. 1. Each STC code word spans P adjacent time-variant tap coeficients ai, i(; t ), V, vt, can be modeled OFDM words, and each OFDM word consists of (NK) STC as wide-sense stationary random processes with uncorrelated symbols, transmitted simultaneously during one time slot. Each scattering (wSSUS)and with band-limited doppler power STC symbol is transmitted at a particular OFDM subcarrier spectrum [22]. For the signal model in(1), we only need and a particular transmitter antenna to consider the time responses of ai, i (l; t) within the time It is assumed that the fading process remains static during interval t E [0, PT] where T is the total time duration of one each OFDM word (one time slot)but varies from one OFDM OFDM word plus its cyclic extension and PT is the total time word to another, and the fading processes associated with involved in transmitting P adjacent OFDM words different transmitter-receiver antenna pairs are uncorrelated. [23], for the particular lth tap of the (i,j)th antenna pair, (However, as will be shown below, in a typical OFDM system, the dimension of the band- and time-limited random process for a particular transmitter-receiver antenna pair, the fading ai, i ( l; t),te [ 0, Pt (defined as the number of significant processes are correlated in both frequency and time. eigenvalues in the Karhunen-Loeve expansion of this randomLU et al.: LDPC-BASED SPACE–TIME CODED OFDM SYSTEMS OVER CORRELATED FADING CHANNELS 75 Fig. 1. System description of a multiple-antenna STC-OFDM system over correlated fading channels. Each STC code word spans K subcarriers and P time slots in the system; at a particular subcarrier and at a particular time slot, STC symbols are transmitted from N transmitter antennas and received by M receiver antennas. directed least-square estimator and a data detector is introduced in [18]. For the system considered here, the receiver in [18] per￾forms well at low to medium Doppler frequencies, but exhibits an irreducible high error floor in fast fading channels. A receiver employing the expectation-maximization (EM) algorithm has recently been proposed for STC systems [19], [20], which ex￾hibits a good performance, but, on the other hand, its complexity is relatively high for the LDPC-based STC-OFDM systems. Here, we develop a novel turbo receiver structure employing a maximum a posteriori expectation-maximization (MAP-EM) demodulator and a soft LDPC decoder, which can significantly reduce the error floor in fast fading channels with a modest com￾putational complexity. (A similar iterative receiver structure is developed for static MIMO channels in [21].) The rest of this paper is organized as follows. In Section II, a multiple-antenna STC-OFDM system over correlated fre￾quency- and time-selective fading channels is described. In Section III, the outage capacity of this system is analyzed. In Section IV, the PEP analysis is given. Based on the analysis in Sections III and IV, in Section V, an LDPC-based STC is proposed for the OFDM system under consideration. In Section VI, a novel turbo receiver is developed. In Section VII, computer simulation results are given. Section VIII contains the conclusion. II. SYSTEM MODEL We consider an STC-OFDM system with subcarriers, transmitter antennas, and receiver antennas, signaling through frequency- and time-selective fading channels, as illustrated in Fig. 1. Each STC code word spans adjacent OFDM words, and each OFDM word consists of ( ) STC symbols, transmitted simultaneously during one time slot. Each STC symbol is transmitted at a particular OFDM subcarrier and a particular transmitter antenna. It is assumed that the fading process remains static during each OFDM word (one time slot) but varies from one OFDM word to another, and the fading processes associated with different transmitter-receiver antenna pairs are uncorrelated. (However, as will be shown below, in a typical OFDM system, for a particular transmitter–receiver antenna pair, the fading processes are correlated in both frequency and time.) At the receiver, the signals are received from receiver antennas. After matched filtering and sampling, the discrete Fourier transform (DFT) is applied to the received discrete-time signal to obtain 0 1 1 (1) where is the matrix of complex channel fre￾quency responses at the th subcarrier and at the th time slot, which is explained below, and are re￾spectively the transmitted signals and the received signals at the th subcarrier and at the th time slot, and is the ambient noise, which is circularly symmetric complex Gaussian with unit variance. Consider the channel response between the th transmitter an￾tenna and the th receiver antenna. Following [22], the time-do￾main channel impulse response can be modeled as a tapped￾delay line. With only the nonzero taps considered, it can be ex￾pressed as (2) where is the Dirac delta function, denotes the number of nonzero taps, and is the complex amplitude of the th nonzero tap, whose delay is , where is an integer and is the tone spacing of the OFDM system. In mobile channels, for the particular ( )th antenna pair, the time-variant tap coefficients can be modeled as wide-sense stationary random processes with uncorrelated scattering (WSSUS) and with band-limited Doppler power spectrum [22]. For the signal model in (1), we only need to consider the time responses of within the time interval 0 , where is the total time duration of one OFDM word plus its cyclic extension and is the total time involved in transmitting adjacent OFDM words. Following [23], for the particular th tap of the ( )th antenna pair, the dimension of the band- and time-limited random process 0 (defined as the number of significant eigenvalues in the Karhunen–Loeve expansion of this random