Performance analysis of super-resolution beamforming in smart antennas

Auto-regressive (AR) extrapolation has been used in recent years to achieve super-resolution capability in spectral estimation and in antenna beam forming. The performance of an auto-regressive, super-resolution beam forming technique is analyzed and compared with other high-resolution methods. The AR coefficients, which represent an IIR filter, are determined adaptively using the least mean squares (LMS) algorithm. A linear algebra-based analysis is developed to show that the gain in signal-to-noise ratio is determined by the order of the extrapolation filter. It is also shown that if the filter coefficients are chosen such that there are poles on the unit circle corresponding to each source present, then the interference between the sources can be eliminated. However, if a pole is not placed on the unit circle for any given source, then it may interfere with the other sources. This yields no improvement in signal-to-interference-plus-noise ratio. This observation is of great importance in systems such as space division multiple access (SDMA), where separating the signals from sources that utilize the same frequency resources is critical.