A QUADRATURE MEDIAN MATCHED FILTER FOR ROBUST DETECTION AND ESTIMATION

We present a Quadrature Median Matched Filter (QMMF) for robust detection and estimation of constant modulus signals in additive complex white noise. We show the nonlinear QMMF is an unbiased estimator of the desired signal's complex amplitude like the standard linear Matched Filter (MF), while also having a simple computational structure. A theoretical detection performance analysis compares the QMMF with the MF in ideal complex white Gaussian noise, quantified as a function of the number of input samples K. The difference between the QMMF and MF output noise power, or mean square error (MSE), is seen to be about 2 dB. Even though the QMMF has a higher noise power it is highly robust to outliers and non-Gaussian noise due to use of the sample median function vs. the sample mean used in the MF. We provide an example of performance with measured data from a wireless communications application based on a constant modulus, linear frequency modulated (LFM) chirp waveform.