On LMMSE bias in CDMA SIMO/MIMO receivers

We revisit CDMA downlink receivers (RX) based on linear minimum mean-square error (LMMSE) chip-equalizer front-end followed by a Walsh code correlator for single-input-single (multi)- output (SISO or SIMO) channels with the purpose of highlighting the non-trivial question of bias in the output of the equalizer. In a linear time-invariant channel, this bias is constant at chip-equalizer output, but evolves over time at code correlator output impacting Signal-to-Interference-plus-noise ratio (SINR) and thus achievable rates in such receivers. In principle, this bias must be taken into account in further RX/decoding stages even if its impact is small. It is shown that a new class of maximum-likelihood (ML) RX leading to potential performance gains is obtained when properly accounting for symbol-level bias across a set of user codes. These results are extended to the multi-input-multi-output (MIMO) case of UMTS high-speed downlink packet access (HSDPA).