57)
(6.58) y(k) s(k) # h1y(k) s(k T) # h2y(k T ) ny(k)
x(k) s(k) # h1x(k) s(k T) # h2x(k T) nx(k)
RECEIVER DIGITAL SIGNAL PROCESSING 307
STE BER Performance in Flat Rayleigh Fading Channel (fd = 190 Hz),
SNR = 25 dB, M = 2 Antennas, K = 5 Taps (T & T/2 Spaced)
MMSE Cost Function, Rank Investigation
1.E 04
1.E 03
1.E 02
1.E 01
1 2 3 4 5 6 7 8 9 10
Covariance Matrix Rank
BER
STE - Flat (T/2-Spaced)
STE - Flat (T-Spaced)
STE - Flat (T-Spaced)
STE - Flat (T/2-Spaced)
Symbol Spaced STE
Fractionally
Spaced STE
FIGURE 6.12 M 2 antennas and K 5 taps STE performance for various estimation window size lengths.
With this channel environment, we can write the covariance block matrix as follows:
(6.59)
As one can see this block covariance matrix can be separated into four submatrices. The first corresponds
to the first arriving ray, the second submatrix corresponds to the second arriving ray, and the
third and fourth correspond to a mixture of both. They have been written in the absence of noise. The
cross-covariance block matrix can be written as
F Rd (0)hx2(k T )hy2(k T )
RdQ
T
2 Rhx2Qk
3T
2 Rhy2(k T )
Rd(T )hx2(k 2T )hy2(k T )
RdQT
2 Rhx2(k T )hy2Qk
3T
2 R
Rd (0)hx2Qk
3T
2 Rhy2Qk
3T
2 R
RdQ
T
2 Rhx2(k 2T )hy2Qk
3T
2 R
Rd (T )hx2(k T )hy2(k 2T )
RdQT
2 Rhx2Qk
3T
2 Rhy2(k 2T )
Rd (0)hx2(k 2T )hy2(k 2T ) V
Rxy F Rd (0)hx1(k)hy1(k)
RdQ
T
2 Rhx1Qk
T
2 Rhy1(k)
Rd (T )hx1(k T )hy1(k)
RdQ
T
2 Rhx1(k)hy1Qk
T
2 R
Rd (0)hx1Qk
T
2 Rhy1Qk
T
2 R
RdQ
T
2 Rhx1(k T )hy1Qk
T
2 R
Rd (T)hx1(k)hy1(k T )
RdQT
2 Rhx1Qk
T
2 Rhy1(k T )
Rd(0)hx1(k T )hy1(k T ) V
F Rd (T )h1(k)h2(k T )
RdQ
T
2 Rh2(k T )h1Qk
T
2 R
Rd (0)h2(k T )h1(k T )
Rd Q
T
2 Rh2(k T)h1Qk
T
2 R
Rd (T )h2Qk
3T
2 Rh1Qk
T
2 R
RdQ
T
2 Rh2Qk
3T
2 Rh1(k T)
Rd (0)h2(k T )h1(k T )
RdQ
T
2 Rh2Qk
3T
2 Rh1(k T )
Rd (T )h2(k 2T)h1(k T ) V
F Rd (T )h1(k)h2(k T)
RdQ
3T
2 Rh1(k)h2Qk
3T
2 R
Rd (2T)h1(k)h2(k 2T )
RdQ3T
2 Rh1(k)h2Qk
3T
2 R
Rd (T)h1Qk
T
2 Rh2Qk
3T
2 R
RdQ
3T
2 Rh1Qk
T
2 Rh2(k 2T )
Rd (2T )h1(k)h2(k 2T )
RdQ
3T
2 Rh1Qk
T
2 Rh2(k 2T )
Rd (T )h1(k T )h2(k 2T) V
F Rd (0) Zh2(k) Z2
RdQ
T
2 Rh2(k T )h2 Qk
3T
2 R
Rd (T )h2(k T )h2(k 2T )
RdQT
2 Rh2(k T )h2Qk
3T
2 R
Rd (0) Ph2Qk
3T
2 RP2
RdQ
T
2 Rh2Qk
3T
2 Rh2(k 2T )
Rd (T)h2(k T )h2(k 2T )
RdQT
2 Rh2Qk
3T
2 Rh2(k 2T )
Rd (0) Zh2(k 2T ) Z2 V
Rxx F Rd (0) Zh1(k) Z2 RdQT
2 Rh1(k)h1 Qk
T
2 R Rd (T)h1(k)h1(k T)
Rd Q
T
2 Rh1(k)h1 Qk
T
2 R Rd (0) Ph1 Qk
T
2 RP2
Rd QT
2 Rh1 Qk
T
2 Rh1(k T )
Rd (T )h1(k)h1(k T ) Rd Q
T
2 Rh1 Qk
T
2 Rh1(k T ) Rd (0)Zh1(k T )Z2 V
308 CHAPTER SIX
(6.
Pages:
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513