A New Statistical WRELAX Algorithm Under Nakagami Multipath Channel Based on Delay Power Spectrum Characteristic

Multipath delay estimation plays an important role in wireless channel estimation, equalization, and synchronization. Weighted Fourier transform and relaxation (WRELAX) algorithm is frequently used for its high resolution and good convergence property. However, the WRELAX algorithm is prone to false estimated delays and irregular multipath sorting under Nakagami-based multipath channel, which is a more practical model than the traditional Rice or Rayleigh-based multipath model, because of the oscillatory cost function property between the received and the known transmitted signals. Given relatively stable characteristics and delay power spectrum distribution characteristics of the wireless channel, together with the principle that the statistical probability of the true estimated delays is larger than that of the false ones through statistical detection, this study proposes a delay power spectrum characteristic-based statistical WRELAX time delay estimation algorithm. The improved algorithm excludes false estimated paths and sorts the delays in size order simultaneously by establishing a two-dimensional relation graph composed of the superposition value of estimated attenuation coefficient and their response-estimated delays. Simulation under three typical Nakagami-based slow fading multipath channels shows that the proposed algorithm has good accuracy and robustness, and the cost of complexity increased by only a few times.