Introduction

This article is an overview of the technology of space diversity based communications. Technically referred to by various terms (the most common being Multiple-Input-Multiple-Output or MIMO), it refers to a specialized field of wireless communications which uses the physical diversity in the transmission path to improve the performance of a wireless channel. This is opposed to temporal diversity techniques (such as interleaving), frequency diversity techniques (such as wide-band CDMA) and the like.

The basic principle of spatial diversity based wireless systems is not dissimilar to that of FDM and TDM systems. If we can send multiple transmission to paths having diversity, then the noise characteristics in each of the paths can be made to cancel out and this actually reduces the overall noise. In this article we shall see how this is actualized in the case of spatial diversity.

Contents of this document

In this document, we shall cover the basic theory of spatial diversity based communications. We shall then review two practical schemes which are currently used and how they differ with each other. Finally we shall review practical usage of these schemes in current and upcoming communication standards.

This article is specifically to do with spatial diversity, we shall not cover other antenna based techniques such as beam-forming, or adaptive antenna systems.

Basic concepts of spatial diversity based communications

Multipath

Multipath is a standard problem in all cellular communications. It is caused by multiple reflections of the transmitted signals, in buildings, on water bodies, foliage and a variety of other structures. The reflected signal arrives a little later than the direct signal; however, in many cases, it is as strong or stronger than the direct signal, which can undergo massive attenuation as it is transmitted through different kinds of media. The gap between the line-of-sight signal and the reflected signal is called the delay spread and is responsible for many impairments in the communication link, such as inter-symbol interference. For an excellent overview, see [Hashemi] and others.

To combat multipath, diversity combining technology was invented, where the different received signals are combined in a way so as to combat noise. There are various technologies available for this. An excellent introduction is in this classic paper by [Brennan]. Diversity combination techniques were extensively studied and used in the context of RAKE receivers for CDMA systems, especially for the UMTS networks.

At the same time, the idea was conceived that it is possible to deliberately transmit data on multiple paths and use the similar combining techniques to improve the performance of wireless networks. This could be done by having multiple transmitters (Multiple In) and multiple receivers (Multiple Out). Practically speaking, multiple transmitters and receivers on the base-station is realizable, since the cost can be amortized over the entire cell. However, having them on the remote/mobile terminal may not be feasible, due to issues of cost. This brought interest in MISO systems, as well. Alamouti discovered an ingenious technique to emulate a MIMO transmission in a MISO system; his proposal is now a standard for the wimax systems.

A matrix is nothing but a linear operator, which can transform one space into another. When a vector is multiplied by a matrix, the resultant is another vector, which is the transformation of the existing vector in a different space. However, for each matrix, there are certain vectors, which obey the following equation: Av = λv where A is a matrix, v is a vector and λ is a fixed real or complex scalar value. The vector v is called an eigenvector, and the associated scalar is an eigenvalue. We can interpret this equation as follows; for this particular matrix A, the eigenvector is one vector which is not transformed by the matrix operator, other than a linear scaling. If we treat the matrix operator as a deformation, then the eigenvector is one vector which is not deformed under this operation. A matrix may have upto n eigenvalues, where n is the number of rows/columns in the matrix, with one possibly unique eigenvector associated with each value.A normal matrix with non-degenerate i.e. unique eigenvalues will have n orthogonal eigenvectors i.e. the eigenvectors will span a complete n-dimensional space.

It should be noted that scaling or adding a scaled identity vector to a matrix, has no impact on its eigenvectors, but shifts the eigenvalues. Let B = ρI+A. Then Bv = ρIv + Av = (ρ+λ)v. Thus B has the same eigenvector v, with an associated eigenvalue which is a shift of the previous one.

The general idea

The general idea, thus, is to create a system where there are multiple transmission antennae n_t, and multiple receive antennae n_r. The number of transmitters and receivers need not be the same. The antennae are spaced so that the transmission paths are uncorrelated with each other; this can be achieved by using an antenna spacing of l. Since the wavelength of transmission is of the order of a few cm, this is not a major technical issue.

Modes of spatial diversity

Now, there are two techniques that can be used. In one, we can send the same identical data set through all transmit antenna and try and receive them through all the receive antennae; by combining these optimally, we will recover the original data stream. This is the technique behind standard MIMO systems. In the other case, we shall transmit completely separate data sets through the different antennae; the assignment of data to transmit channel will be determined by the perceived path quality - the idea will be to maximize the overall delivery of data. This is known as spatial multiplexing and this also will be discussed in this section.

Space diversity coding

Space diversity coding consists of sending the same information in multiple streams from n_t transmitters and receiving it in n_r antennas and combining it in the most effective manner. Results by [Foschini] and others show astonishing spectral efficiencies, far exceeding the most optimistic results for other techniques, such as maximal ratio combining. One forecast by Foschini, backed up in [Chiani et al] suggests a spectral efficiency of 19.75 bits/sec/Hz is possible, on a channel with an SNR of 20dB.

Spatial multiplexing

Spatial multiplexing consists of sending different information streams over different transmitter receiver pairs. Thus, a single transmission stream is demultiplexed into n_T streams, which is then independently transmitted over n_T antennae. The BLAST and V-BLAST techniques are examples of spatial multiplexing. In V-BLAST, the receivers and transmitters operate co-channel at synbol rate 1/T with synchronised symbol timing. A quasi-stationary viewpoint is taken, which implies that channel time variation is negligible over the symbol periods comprising a burst. Redundancy is introduced using special coding schemes, which can be exploited by the FEC decoder in the receiving station. Actual experiments have shown a spectral efficiency of 20bps-40bps. In one experiment, a spectral efficiency of 26bps has been demonstrated at an SNR of 28dB, with error rate less than 10^-3

In the next section, we shall review the general theory of multiple antenna systems and see what is it that makes this astonishing efficiency possible.