Multi-Frequency Spherical Near-Field Antenna Measurements Using Compressive Sensing

We propose compressive sensing approaches for broadband spherical near-field measurements that reduce measurement demands beyond what is achievable using conventional single-frequency compressive sensing. Our approaches use two different compressive signal models—sparsity-based and low-rank-based—whose viability we establish using a simulated standard gain horn antenna. Under mild assumptions on the device being tested, we prove that sparsity-based broadband compressive sensing provides significant measurement number reductions over single-frequency compressive sensing. We find that our proposed low-rank model also provides an effective means of achieving broadband compressive sensing, using numerical experiments, with performance on par with the best broadband sparsity-based method. Exemplifying these best-case results, even in the presence of measurement noise, the methods we propose can achieve relative errors of −40 dB using about 1/4 of the measurements required for conventional sampling. This is equivalent to about 1/2 sample per unknown, whereas traditional spherical near-field measurements require a minimum of roughly 2 measurements per unknown.