Broadband Array Processing by Shefeng Yan

Author:Shefeng Yan
Language: eng
Format: epub, pdf
ISBN: 9789811368028
Publisher: Springer Singapore

We solve the optimization problem (5.43) to obtain the FIR beamformers corresponding to the two desired mainlobe patterns. The beam pattern as a function of the frequency and direction are calculated on the grids using Eq. (5.9). The superposition of the achieved beam patterns at the 33 subbands for the case and are shown in Fig. 5.12b and c respectively.

It is seen from Fig. 5.12 that, when we choose , the resulting mainlobe pattern is severely distorted and the mainlobe synthesis error is very large. When is chosen, the resulting beam pattern within the mainlobe is approximately constant over the frequency band of interest and the sidelobes are strictly guaranteed to be below −30 dB.

From this example, we can conclude that the performance of this array pattern synthesis method depends on the choosing of desired mainlobe pattern. An arbitrarily chosen desired mainlobe pattern can result in very poor synthesized pattern. Therefore, how to choose an optimal desired beam pattern is the main limitation of this method.

We then apply the peak sidelobes constrained minimax MSRV beamformer design method shown in Eq. (5.47) to design the frequency-invariant FIR beamformer. We choose and . Assume that the center frequency is chosen as the reference frequency, i.e., .

The resulting beam patterns at the 33 subbands are shown in Fig. 5.13. It is seen that the mainlobe pattern is approximately constant and the sidelobes are strictly guaranteed to be below −30 dB.

Fig. 5.13Superposition of 33 beam patterns using peak sidelobes constrained minimax MSRV design method in Eq. (5.47)

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