Robust Reduced-Rank Adaptive LCMV Beamforming Algorithms Based on Joint Iterative Optimization of Parameters - Advances in Heuristic Signal Processing and Applications - page 30

Fig. 2.4 SINR performance of LCMV algorithms against rank ( D ) with M = 32, SNR = 15 dB,

N = 250 snapshots

σ d

the signal-to-noise ratio (SNR) is defined as SNR =

σ 2 . The beamformers are ini-

and S D ( 0 ) =[ I D 0 D × (M − D) ] tialized as w ( 0 ) =[ 10 ... 0 ] , where 0 D × M − D is a

D × (M − D) matrix with zeros in all experiments.
In order to assess the performance of the RJIO and other existing algorithms in
the presence of uncertainties, we consider that the array steering vector is corrupted
by local coherent scattering

4

e jΦ k a sc (θ k ), a p (θ k ) = a (θ k ) + (2.36)

k = 1

where Φ k is uniformly distributed between zero and 2 π and θ k is uniformly dis-
tributed with a standard deviation of 2 degrees with the assumed direction as the
mean. The mismatch changes for every realization and is fixed over the snapshots
of each simulation trial. In the first two experiments, we consider a scenario with
7 interferers at

15 ◦ ,0 ◦ ,45 ◦ ,60 ◦ with powers following a log-
normal distribution with associated standard deviation 3 dB around the SoI's power
level. The SoI impinges on the array at 30 ◦ . The parameters of the algorithms are
optimized.
We first evaluate the SINR performance of the analyzed algorithms against
the rank D using optimized parameters ( μ s , μ w , and forgetting factors λ ) for all
schemes and N =

60 ◦ , 45 ◦ ,30 ◦ − − −

250 snapshots. The results in Fig. 2.4 indicate that the best rank
for the RJIO scheme is D =

4 (which will be used in the second scenario) and it is
very close to the optimal full-rank LCMV beamformer that has knowledge about the