Low Dimensional MIMO Systems with Finite Sized Constellation Inputs

The seminal works in [1] and [2] on multiple antenna elements at the transmitter and the receiver show a huge increase in the throughput of this point-topoint channel referred to also as multiple input multiple output (MIMO) system. These promising results of high spectral efficiency and enhanced reliability shifted the focus of research on multi antenna communications and motivated the introduction of multiple antenna elements in the future communication systems. Researchers persist to strive for finding space time codes (STC) with reduced decoding complexity. These codes take into account both the spatial and temporal dimensions of the MIMO channel. Orthogonal Space-Time Block Codes (OSTBCs) [6] are widely used because they are easy to encode and decode. For the case of two transmit antennas, the OSTBC is known as Alamouti code [7]. OSTBCs are repetition codes that only provide diversity gain. In order to approach the capacity limit they have to be used in concatenation with an outer code. Remarkable coding gains can be obtained if a capacity achieving temporal encoder, such as turbo or Low-Density Parity Check (LDPC) code is used in concatenation with a STC [8]. Recently it has been shown for the ergodic channels that the complex concatenation of the STC and the outer codes can be replaced with temporally coded and spatially multiplexed streams (coded spatial streams) for nearing capacity [9]. Each spatial stream can also be independently coded using temporal encoders as convolutional, turbo or LDPC codes where at the receiver, standard off-the-shelf decoders are used after the demodulator. To combat the frequency selectivity of MIMO wireless channels with low complexity equalization at the receivers, MIMO OFDM is the appropriate alternative. To contest the inherent fading of MIMO OFDM wireless channels, improved code diversity of bit interleaved coded modulation (BICM) for fading channels is rendering it the preferred option. Consequently the future wireless systems shall be based on BICM MIMO OFDM systems. However the requisite antenna spacing combined with the complexity constraints at the receiver are restricting the future MIMO based communication systems to the maximum of 4 spatial streams whereas it is reduced to 2 spatial streams in most scenarios. The existing and forthcoming standards as IEEE 802.11n [3], IEEE 802.16m [4] and Third Generation Partnership Project Long Term Evolution (3GPP LTE) [5] substantiate this argument.