Method and apparatus for designing finite-length multi-input multi-output channel shortening pre-filters
View Patent ↗A multi-input, multi-output pre-filter improves operation of a multi-input receiver by shortening the effective memory of the channel with a set of FIR filters. The coefficients of these FIR filters can be fashioned to provide a variety of controls by the designer, for example, the value of the effective memory.
1. A receiver operating in an environment where a transmission channel, H, between a transmitter of information and said receiver has a memory corresponding to n transmitted symbols, said receiver being responsive to an n o plurality of receiving antennas comprising:
a pre-filter having an n o ×n i plurality of FIR filters, F(j,k), where n i is a number of transmitting antennas whose signals said receiver is processing, j is an index running from 1 to n o and k is an index running from 1 to n i , each filter F(j,k) being responsive to a signal that is derived from receiving antenna j, and applying its output signal to a pre-filter output point k;
decision logic responsive to said pre-filter output points; and
a sampling circuit interposed between said n o plurality of antennas and said pre-filter that samples received signal at rate
T
s
=
T
l
,
where l is an integer that is greater than 1, and T is symbol rate of a transmitter whose signals said receiver receives,
where said plurality of FIR filters is expressed by matrix W, and W is computed by W opt *={tilde over (B)} opt *R xy R yy −1 , W opt *={overscore (B)} opt *R xx H*(HR xx H*+R nn ) −1 , or W opt *={overscore (B)} opt *(R xx −1 +H*R mm −1 H) −1 H*R nn −1 , where R xx is an autocorrelation matrix of a block of signals transmitted by a plurality of transmitting antennas to said n 0 antennas via a channel having a transfer characteristic H, W opt is the optimum channel-shortening pre-filter, R nn is an autocorrelation matrix of noise received by said plurality of n o antennas during said block of signals transmitted by said transmitting antennas, R xy =R xx H*, R yy =HR xx *+R nn , are correlation matrices and {tilde over (B)} opt *, is a sub-matrix of matrix B opt *, where B opt =argmin B trace(R ee ) subject to a selected constraint, R ee being the error autocorrelation function.
2. The receiver of claim 1 wherein said plurality of FIR filters are subjected to designer constraints relative to any one or a number of members of the following set: transmission channel memory, size of said block, effective memory of the combination consisting of said transmission channel and said pre-filter; n i , n o , autocorrelation matrix R xx , autocorrelation matrix R nn , value of factor l in said sampling circuit, and decision delay.
3. The receiver of claim 1 , where said matrix W is expressible by W≡[W 0 W 1 . . . W N f −1 ] 1 , where matrix W q , q being an index between 0 and N f−1 , is a matrix that specifies q th tap coefficients of said FIR filters.
4. The receiver of claim 1 where said constraint restricts B so that B*Φ=I n i , where Φ*≡[0 n i ×n i m I n i 0 n i ×n i (N b −m) ] and m is a selected constant.
5. The receiver of claim 4 where B={overscore (R)} −1 Φ(Φ*{overscore (R)}is a sub-matrix of a matrix R ⊥ =R xx −R xy R yy −1 R yx .
6. The receiver of claim 1 where said constraint restrict B so that B*B=I n i .
7. The receiver of claim 6 where B=U[e n i N b . . . e n i (N b +1)−1 ,], each element e p is a vector having a 0 element in all rows other than row p, at which row the element is 1, and U is a matrix that satisfies the equation {overscore (R)}=UΣU*, Σ being a diagonal matrix.