Robust Reduced-Rank Adaptive LCMV Beamforming Algorithms Based on Joint Iterative Optimization of Parameters - Advances in Heuristic Signal Processing and Applications - page 19

Fig. 2.1 Block diagram of a sensor-array array system with interfering signals

analysis of the computational complexity, and the rank adaptation technique. Sec-
tion 2.6 presents and discusses the simulation results and Sect. 2.7 gives the con-
cluding remarks.

2.2 System Model

Let us consider a sensor-array system equipped with a uniform linear array (ULA)
of M elements, as shown in Fig. 2.1 . Assuming that the sources are in the far field
of the array, the signals of K narrowband sources impinge on the array (K <M)
with unknown directions of arrival (DOA) θ l for l

1 , 2 ,...,K .
The input data from the antenna array can be organized in an M

=

×

1 vector

expressed by

r (i) = A (θ) s (i) + n (i), (2.1)

where

= a (θ 1 ),..., a (θ K )

A (θ)

is the M × K matrix of signal steering vectors. The M × 1 signal steering vector is

defined as

= 1 ,e − 2 πj d λ c cos θ l ,...,e − 2 πj(M − 1 ) d λ c cos θ l T

a (θ l ) (2.2)