128)
where
i??™s are the eigenvalues of the matrix, R, and are the associated eigen vectors.
We know the vector space of the covariance matrix, , consists of M linearly independent vectors.
We can go one step further to classify them into vector subspaces: the signal subspace, Vs, and the
noise subspace, VN. The total vector space can be mathematically written as VVSVN. The covariance
matrix can be written as
(5.129)
where the first summation on the right-hand side corresponds to the signal subspace and the second
summation corresponds to the interference plus noise subspace. The MMSE weights can be expressed
as follows where we used the ESD on .
(5.130)
or equivalently as
(5.131)
where the variable Ns is used to denote the dimension of the signal subspace of the covariance matrix. R ^
xx
w^
MMSE caN
s
i1
1
li
# vi # v*i
aM
iNs1
1
li
# vi # v*i
d # r^
xd
w^
MMSE caM
i1
1
li
# vi # v*i
d # r^
xd
R^
xx
R aN
s
i1
li # vi # v*i
aM
iNs1
li # vi # v*i
v
vi
R aM
i1
li # vi # v*i
w^
R^
1
IN # r^
xd
R^
IN
1
NaN
i1
(x r^
xd # d ) # (x r^
xd # d )*
R^
IN
1
NaN
i1
(x h^
# d) # (x h^
# d)*
wMSINR R1
IN # rxd
max
w
w* # Rss # w
w* # RIN # w
PERFORMANCE IMPROVEMENT TECHNIQUES 277
The MSINR array weights can be calculated in a similar manner, except for this case, the ESD was
performed on ?†R
IN matrix, thus giving us
(5.
Pages:
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455