Adaptive Interference Nulling and Direction of Arrival Estimation in GPS Dual-Polarized Antenna Receiver - Adaptive Signal Processing in Wireless Communications - page 422

If W c is optimally calculated, and providing D > M , then its rank is M . However, with
adaptive processing, the matrix rank is no longer M . In this way, the first D columns of
u are the column subspace, containing the interference information ( M < D ), and the
last 2 N - D columns of u are the noise subspace. That is,

H

a (θ=0 , ( i = D + 1, …, 2 N ) u (14 . 38)

k i

for k = 1, …, M . The DOAs of the interferers can be obtained by searching the peaks of
the CANAL spectrum

1

P () θ = . (14 . 39)

2 N

∑

2

H

a () θ u

i

iD =+ 1

It is noteworthy that the rank of the cancellation weight matrix W c is min ( D , N ). hat
is, only up to D - 1 RHCP interferers can be considered, compared to N - 1 by the MUSIC
algorithm when operating on the data covariance matrix. By increasing D ( D < N ), the
interference information will be further represented by a larger column subspace, pro-
ducing enhanced interference DOA estimation performance. Accordingly, it is desirable
to add N - D beamformers to achieve a total number of N beamformers. For simplicity,
we define the number of beamformers as L . If D < N , then the L beamformers consist of
D beamformers toward the GPS directions and the L - D beamformers toward arbitrary
directions. In this case, equation (14.26) can be expressed as

a = −1

WrT ()θ (14 .4 0)

and equation (14.31) becomes

1
2

WTW
c

= () − . (14 .41)

a

σ

Therefore, equation (14.39) is rewritten as

1

P () θ = . (14 .4 2)

2 N

∑

2

H

a)u ( θ

i

iL =+ 1

The optimal performance will occur when L = N , and a maximum number of N - 1
interference DOAs can be estimated.