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XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SPWe assume that the signal is transmitted in blocks of length The vector ˜S(n) can be related to the transmitted symbols[] T combining these copies, the MU can profit from the channel˜S(n) = ˜s(n) T ˜s(n − 1) T ... ˜s(n − L + 1) T . (8b) diversity to counteract the fading. It is worth noting thatN b , so that the channel variation during one block of data isinsignificant. However, the channel changes from one blockto another, characterizing a block fading channel.s(n) in matrix form as shown by (13), where 0 is a columnvector formed by K zeros and the K × D matrix H t is thespace-time response of the channel during the transmission ofAt a given block t, the received signal y(n) at the MU block t, defined asantenna can be expressed as⎡⎤h 1 (0) h 1 (1) · · · h 1 (D − 1)K∑h 2 (0) h 2 (1) · · · h 2 (D − 1)y(n) = h k (n) ∗ x k (n) (2) H t = ⎢⎣.. . ... ⎥⎦ . (9)k=1h K (0) h K (1) · · · h K (D − 1)where h k (n) is the temporal response of the space-timechannel, relative to the antenna k, which is assumed to have Defining the vector of transmitted symbols s(n) and thelength D and n is the temporal index within the considered block diagonal matrix H t as in (13), we can write the receivedblock. We have not represented the index block t for the sake signal at the MU for block t asof legibility. This index will be explicitly used in the sequel,when needed.y t (n) = W H H t s t (n) . (10)Rewriting the signal y(n) asIt is worth recalling that for each block t the channelpresents a different fading condition, i.e., it can be in a deepK∑D−1∑fade or in a reconstruction condition. This condition affects they(n) = h k (i)x k (n − i) (3)signal received power and, at last, the SNR of each receivedk=1 i=0block at the MU.and recalling that x k (n − i) = L−1 ∑wk ∗ The average power received by the MU during block t is(l)s(n − i − l), wel=0given byobtain thatL−1∑ K∑D−1∑P t = 1 { }E y t (n)yt ∗ (n)y(n) = wk(l)∗ N bh k (i)s(n − i − l) . (4)l=0 k=1 i=0= 1 { }(11)W H H t E s t (n)s H t (n) H H t W .N bDefining ˜s k (n−l) D−1 ∑h k (i)s(n − i − l) and the followingAssuming { that the transmitted } symbols s(n) are i.i.d., wecolumn vectors (see Fig. 1)i=0obtain E s t (n)s H t (n) = σsI 2 and (11) becomes[Hw(l) = w 1 (l) w 2 (l) ... w K (l)][Tl)](5a)P t = σ2 sW H R t W ,N b(12)˜s(n − l) = ˜s 1 (n − l) ˜s 2 (n − l) ... ˜s K (n − (5b) where R t = H t H H t is the space-time covariance matrix,we can rewrite (4) aswhich has a block hermitian structure.L−1∑y(n) = w(l) H˜s(n III. CONSTANT POWER APPROACH− l) , (6)We assume that the MU has only one antenna and it isl=0already equipped with a temporal equalizer. The main idea iswhich can be written in vector notation asto take advantage of the channel space diversity by exploitingy(n) = W H ˜S(n) (7)the spatial decorrelation to emit uncorrelated copies of thedesired signal (by means of the multiple antenna at the BS)wheredelayed by one or more symbol periods. By doing so, the[] H temporal equalizer at the MU can combine this uncorrelatedW = w(0) H w(1) H ... w(L − 1) H (8a) copies to form an estimation of the transmitted signal. By⎡⎤˜s(n)˜s(n − 1)⎢⎥ = ⎢⎣ . ⎦ ⎣˜s(n − L + 1)} {{ }˜S(n)⎡⎤⎡⎤s(n)H t 0 0 · · · 0 0 0s(n − 1)0 H t 0 · · · 0 0 0s(n − 2)... ... ⎥⎦s(n − 3)⎢0 0 0 0 0 · · · H t⎣⎥. ⎦} {{ }s(n − D − L + 1)H t} {{ }s(n)(13)