Introduction
About
Problem
Related papers
Codes & Demo
SDR-RBR
LDR
DeepHOTML
Others
Contact

MIMO Problem Statement

alt text 

We consider a standard, but widely encountered MIMO system model:

{bf y}_C = {bf H}_C {bf s}_C + {bf n}_C,

where

  • {bf y}_C in mathbb{C}^M received signal vector;

  • {bf s}_C in mathcal{S}^N transmitted signal vector;

  • M receive dimension;

  • N number of transmitted symbols;

  • {bf n}_C in mathbb{C}^M noise;

  • mathcal{S} symbol constellation set (e.g. QPSK, 16-QAM).

The signal model covers a wide variety of detection problems in multi-user communication and multi-antennas communication. For instance, in a multi-antenna point-to-point wireless link with spatial multiplexing (or V-BLAST) being the transmit scheme, {bf H}_C physically represents a multi-antenna channel where M and N are the number of transmit and receive antennas, respectively. Moreover, in a multiuser CDMA system, we have each column of {bf H}_C being a signature sequence of a particular user (i.e. the spreading code sequence) and N is the number of users. The standard signal model above can also be applied to space-time coding, space-frequency coding, combinations of multiuser and MIMO systems, etc.

The maximum-likelihood (ML) detection problem can be stated as

{bf hat{s}} = arg min_{{bf s}_C in mathcal{S}^N} | {bf y}_C - {bf H}_C{bf s}_C |^2.

ML detection is optimal in yielding the minimum error probability of detecting {bf s}_C. However, the ML detection problem is hard to solve when N and/or the constellation size |mathcal{S}| is large. In order to approximate the ML problem within manageable complexity, the ML problem has been handled by approaches such as sphere decoders, semidefinite relaxation detectors, lattice-reduction-aided detectors, etc.