Spectrum sensing in cognitive radios: Design of DFT filter banks achieving maximal time-frequency resolution

Filter banks facilitate an estimation of the power spectral density of broad-band non-stationary signals, an operation required in many cognitive radio systems. The samples at the filter bank output may serve as a basis for an estimation of the input signal energy within any time-frequency (TF) region of interest. In order to achieve a high resolution in both time and frequency, the prototype window underlying a Discrete Fourier Transform (DFT) filter bank needs to exhibit high TF concentration. Moreover, in order to provide uncorrelated samples in case of white input processes, the TF-translated versions of the prototype window that underlie the elementary filtering operations need to constitute an orthogonal set. In this paper we present a technique to design DFT filter banks that possess these two required properties in an optimal manner. The numerical optimization procedure takes advantage of a parametrization of paraunitary filter banks and relies on semidefinite programming. We analyze the residual leakage of our optimized filter banks and draw a comparison against Thomson's multitaper method.