Robust Reduced-Rank Adaptive LCMV Beamforming Algorithms Based on Joint Iterative Optimization of Parameters - Advances in Heuristic Signal Processing and Applications - page 27

Ta b l e 2 . 1 Computational complexity of LCMV algorithms

Algorithm Additions Multiplications

LCMV-SG [ 4 ] 3 M + 1 3 M + 2

3 M 2 6 M 2

LCMV-RLS [ 6 ] − 2 M + 3 + 2 M + 2

RJIO-SG 3 DM + 4 M + 2 D − 2 5 DM + 2 M + 5 D + 2

3 M 2 3 D 2 7 M 2 7 D 2 RJIO-RLS − M + 3 + − 7 D + 3 + 3 M + + 10 D

2 / 3 M 3 3 M 2 2 / 3 M 3 5 M 2 SMI [ 23 ] + +

Fig. 2.3 Computational complexity in terms of arithmetic operations against M

2.5.3 Complexity of RJIO Algorithms

Here, we evaluate the computational complexity of the RJIO and analyzed LCMV
algorithms. The complexity expressed in terms of additions and multiplications is
depicted in Table 2.1 . We can verify that the RJIO-SG algorithm has a complex-
ity that grows linearly with DM , which is about D times higher than the full-
rank LCMV-SG algorithm and significantly lower than the remaining techniques.
If D M (as we will see later) then the additional complexity can be acceptable

provided the gains in performance justify them. In the case of the RJIO-RLS algo-
rithm, the complexity is quadratic with M 2 and D 2 . This corresponds to a complex-
ity slightly higher than the one observed for the full-rank LCMV-RLS algorithm,
provided D is significantly less than M , and lower than the robust beamforming
algorithms WC-SOC [ 9 ] and WC-ME [ 10 ].
In order to illustrate the main trends in what concerns the complexity of the
proposed and analyzed algorithms, we show in Fig. 2.3 the complexity in terms of
additions and multiplications versus the number of input samples M . The curves