Bitrate maximizing per group equalization for DMT-based systems

In a previous paper, we proposed a bitrate maximizing design criterion for time-domain equalizers (TEQ) in DMT transceivers to shorten the channel impulse response, as needed in, e.g., ADSL receivers. The proposed criterion truly maximizes the bitrate, as it is based on an exact formulation of the subchannel SNR as a function of the TEQ taps. In this paper, we show how the BM-TEQ design can be used in a bitrate maximizing per group equalizer (BM-PGEQ): the active tones are divided into groups and each group is provided with a bitrate maximizing equalizer. This BM-PGEQ design allows for a trade-off between memory requirement and performance, keeping computational complexity during data transmission roughly at the same level. It encompasses the BM-TEQ design and the so-called per tone equalization scheme (PTEQ) as extreme cases. We also present an adaptation algorithm to design the BM-TEQ and BM-PGEQ. Through simulation, we show that the BM-PGEQ scheme outperforms an earlier presented tone grouping scheme where the whole tone group was assigned the PTEQ of the group center tone. The BM-PGEQ scheme appears as a useful intermediate between BM-TEQ and PTEQ and closely approaches the PTEQ performance for as few as four tone groups in an ADSL scenario, even in harsh environments with narrowband interference and crosstalk.