LU et a: LDPC-BASED SPACE-TIME CODED OFDM SYSTEMS OVER CORRELATED FADING CHANNELS ∑cPx]=xyl channel estimates. The procedure is listed in Table I. In Table I lo [(k Freg-filter denotes either the least-square estimator (Lse) or the minimum mean-square-error estimator(MMSE)as ∑c-xp|-g(x)+ log P(ac LSE:Freq-filter y, x=(w xXw-l ∑xep|-dx)+logP(x X WHXH MMSE: Freqfilter(3. x=(wHx'xw+ET APEd(k) (26) x wx y (27) where C; is the set of r for which the jth LDPC coded bit is where X represents either the pilot symbols or x( provided "+1" and C is similarly defined. The extrinsic a priori LLRs by the MAP-EM demodulator Comparing these two estimators Aep di(k)I i k are provided by the soft LDPC decoder at the the lse does not need any statistical information of h, but the previous turbo iteration(where P denotes the previous turbo it- MMSE offers better performance in terms of mean-square-error eration; at the first turbo iteration, A2[d(k)]=O). Finally, (MSE). Hence, in the pilot slot, the LSE is used to estimate chan- he extrinsic a posteriori LLRS Aid(k li k are sent to the nels and to measure >h, and in the rest of data slots the MMSE soft LDPC decoder, which in turn iteratively computes the ex- is used. In Table L, Temp-filter denotes the temporal filter trinsic LLRs A2[d (k)]i k and then feeds them back to the which is used to further exploit the time-domain correlation of MAP-EM demodulator and thus completes one turbo iteration. the channel At the end of the last turbo iteration, hard decisions of the infor mation bits are output by the LDPC decoder. For details of the Temp-filterhlp-11 hp-21 soft LDPC decoder, see [111 全∑a- C. Initialization of MAP-EM Demodulator The performance of the MAP-EM demodulator(and hence where hp-j, j= 1, ..,t, is computed from(**)[cf. the overall receiver)is closely related to the quality of the initial Table I]; laj -I denotes the coefficients of an L-length yalue ofXoplfcf. (19)]. At each turbo iteration, x()[p] needs (l s Pa) temporal filter, which can be obtained by solving to be specified to initialize the MAP-EM demodulator. Except the Wiener equation or from the robust design as in [33 and for the first turbo iteration, xop] is simply taken as x(p| [34]. From the above discussions, it is seen that the compu- given by(24)from the previous turbo iteration. We next discuss tation involved in initializing Xo[] mainly consists of the the procedure for computing Xo)lp] at the first turbo iteration. ML detection of xo[p] in(*)and the estimation of h[p] in The initial estimate of X(o] is based on the method pro-(*). In general, for an STC-OFDM system with parameters osed in [33] and[34], which makes use of pilot symbols and (N,M,K, Lf), the total complexity in initializing x Lp] is decision-feedback as well as spatial and temporal filtering for O[(K )+M(NL1 Q(xixo)=-Eml(3. xD)lly-XWll?)+const Eml(v x o)(y-XWh)(XWh-XWh)I)+const -xP(x)(④a-)wxxw+cm Iy-XWh 12-traceXwsnwHx)+const. ∑{[x+21时}+om with a[k=[-1[k], x2[k-J52x W() (k) wF(h) WEnW]o+1 +1) [WE,wHK K+k+1,+ WWk+k++1)W立W1k+k+15++)2×2LU et al.: LDPC-BASED SPACE–TIME CODED OFDM SYSTEMS OVER CORRELATED FADING CHANNELS 83 (26) where is the set of for which the th LDPC coded bit is “ ” and is similarly defined. The extrinsic a priori LLRs are provided by the soft LDPC decoder at the previous turbo iteration (where denotes the previous turbo it￾eration; at the first turbo iteration, 0). Finally, the extrinsic a posteriori LLRs are sent to the soft LDPC decoder, which in turn iteratively computes the ex￾trinsic LLRs and then feeds them back to the MAP-EM demodulator and thus completes one turbo iteration. At the end of the last turbo iteration, hard decisions of the infor￾mation bits are output by the LDPC decoder. For details of the soft LDPC decoder, see [11]. C. Initialization of MAP-EM Demodulator The performance of the MAP-EM demodulator (and hence the overall receiver) is closely related to the quality of the initial value of [cf. (19)]. At each turbo iteration, needs to be specified to initialize the MAP-EM demodulator. Except for the first turbo iteration, is simply taken as given by (24) from the previous turbo iteration. We next discuss the procedure for computing at the first turbo iteration. The initial estimate of is based on the method pro￾posed in [33] and [34], which makes use of pilot symbols and decision-feedback as well as spatial and temporal filtering for channel estimates. The procedure is listed in Table I. In Table I, - denotes either the least-square estimator (LSE) or the minimum mean-square-error estimator (MMSE) as LSE: - MMSE: - (27) where represents either the pilot symbols or provided by the MAP-EM demodulator. Comparing these two estimators, the LSE does not need any statistical information of , but the MMSE offers better performance in terms of mean-square-error (MSE). Hence, in the pilot slot, the LSE is used to estimate chan￾nels and to measure , and in the rest of data slots the MMSE is used. In Table I, - denotes the temporal filter, which is used to further exploit the time-domain correlation of the channel - (28) where 1 is computed from ( ) [cf. Table I]; denotes the coefficients of an -length ( ) temporal filter, which can be obtained by solving the Wiener equation or from the robust design as in [33] and [34]. From the above discussions, it is seen that the compu￾tation involved in initializing mainly consists of the ML detection of in ( ) and the estimation of in ( ). In general, for an STC-OFDM system with parameters ( ), the total complexity in initializing is . with (23)