Analysis of post-combiner equalizers in cosine-modulated filterbank-based transmultiplexer systems

In this paper, we present an analysis of the post-combiner equalizers used to compensate for channel distortion in cosine-modulated-based transmultiplexer systems. Such equalizers have been widely used in multicarrier modulation (MCM) systems that use cosine modulated filterbanks (CMFB) for signal modulation and demodulation. By making the reasonable assumption that the number of subchannels in the system is large enough such that each subchannel can be approximated by a constant complex gain, we derive close-form equations for optimum post-combiner transfer functions. These transfer functions are found to be finite impulse response (FIR) and closely related to the prototype filter in CMFB analysis and synthesis blocks. Moreover, by making use of the results of our analysis, we propose a new post-combiner structure in which the number of adaptive parameters are about one third of those in the earlier reports. This reduction in the number of adaptive parameters results in a three-fold increase in convergence speed of the least mean square (LMS) algorithm when it is used for adaptation of the post combiners. We also present a convergence analysis of the post-combiner when the LMS algorithm is used for adaptation. We study the correlation matrix whose eigenvalues determine convergence behavior of the LMS algorithm. We show that all eigenvalues of this matrix are equal. This implies that in the case of the post-combiner, the LMS algorithm experiences no slow mode of convergence, as is the case in many other applications. Computer simulations that corroborate our theoretical findings are also presented.