Per tone equalization for DMT-based transmission over IIR channels

Recently, an alternative receiver structure was presented for discrete multitone (DMT)-based systems. The traditional structure consisting of a (real) time domain equalizer (TEQ) with a (complex) 1-tap frequency domain equalizer (FEQ) per tone is modified into a structure with a (complex) multitap FEQ per tone. The signal-to-noise ratio (SNR) for each individual tone is maximized, hence the term "per tone equalization". Here, we derive an equalization scheme for DMT-based systems in an alternative way. We start from the assumption that the transmission channel to equalize has an infinite impulse response (IIR) or pole-zero model. We conclude that, under certain numerator and denominator conditions, the per tone equalizer is a close approximation of the optimal minimum mean square error (MMSE) equalizer. In case the numerator order condition is not fulfilled, we propose a low-complexity generalization of the per tone equalizer. This generalization is based on a suboptimal MMSE criterion and exploits transmit redundancy introduced by means of pilot and/or unused tones. We evaluate the performance of the new, generalized per tone equalizer in an ADSL context. The principles are applicable to OFDM as well