Designing OFDM Radar Waveform for Target Detection Using Multi-objective Optimization - Advances in Heuristic Signal Processing and Applications - page 55

Fig. 3.8 Comparison of performances due to the fixed and adaptive waveforms in Scenario I in
terms of the ( a ) squared Mahalanobis distance, ( b ) weighted trace of Cramér-Rao bound matrix,
and ( c ) squared upper bound on sparse-error, respectively

3.5.3 Redistributions of Signal and Target Energies

To understand the reason behind the performance improvement due to the adap-
tive waveform design, we looked into the energy-distribution of the transmitted sig-
nal and effective target-return across different subchannels both before and after
the waveform design. We used the subset of Pareto-optimal solutions that satis-
fied all the three objective functions at 0 dB to exemplify the results on energy-
redistribution for both the target scenarios in Fig. 3.10 .
We represent the effective transmit-signal energy at different subchannels as

2 , for l

ε S ,l =| a l | = 0 , 1 ,...,L − 1 . (3.42)

On the other hand, the effective target-returns across different subchannels are con-
sidered as