A Case for Frequency Domain Window Based Nyquist Filter Design

In the digital domain, a Square-Root Raised Cosine Filter (SRRC) has historically been used in most of the wireless standards for shaping the spectrum at the Tx and matched filtering the signal at the Rx (the combination forms a Raised Cosine (RC) filter). However, the performance of an SRRC filter in terms of peak ISI and peak sidelobe attenuation is fairly average, to say the least. A transformed lowpass filter designed according to Parks-McClellan algorithm is an alternative pulse shaping technique which is generally believed to be optimal due to the lowpass filter coefficients being the optimal solution based on Remez exchange algorithm and Chebyshev approximation theory such that the maximum error between the desired and the actual frequency response is minimized. In this paper, we show that another technique proposed in [3] based on an optimized frequency domain window convolved with a rectangular spectrum matches fairly well against the lowpass filter based method at all instances in terms of peak ISI and sidelobe attenuation.