Wavelet based Multi-carrier Communications with Bit Loading under Time-domain Equalization

Abstract

This research explores wavelet packet modulation (WPM) as a potential alternative to orthogonal frequency division multiplexing (OFDM). Unlike OFDM, equalization for WPM cannot depend on the use of cyclic prefix (CP) due to overlapped WPM symbols in the time domain. This research considers time-domain minimum-mean square error (MMSE) equalization. The imperfection of MMSE equalization induces subcarrier signal attenuation and noise amplification. These limitations are taken into account in the development of a bit loading algorithm for WPM. The investigation on the bit error rate (BER) performances is carried out assuming known channel state information (CSI) as well as unknown CSI. For known CSI, mathematical expressions for computing BERs are derived and validated using simulation. The validated mathematical expressions for BERs are used to explore the benefits of bit loading and to show that WPM performs better than OFDM. For unknown CSI, simulation studies show that WPM using MMSE equalization can provide acceptable BER performances with training sequence lengths of moderate overhead. Moreover, WPM with MMSE equalization is shown to outperform OFDM with one-tap equalization. Furthermore, bit loading is performed using the channel impulse response (CIR) estimated based on the solution of an overdetermined system of linear equations. Numerical results demonstrate that the proposed bit loading algorithm with the estimated CIR reduces the BER as compared with equalization alone. In addition, numerical results also show that WPM with bit loading and unknown CIR performs better than OFDM with bit loading and known CIR.