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)