This introductory chapter gives a coverage of the evolution and basics of mobile and personal communications. Details of the digital communications systems issues will not be pursued in the following chapters, except where necessary for a particular topic. The roles of the propagation and antenna engineering are seen respectively as limiting and mitigating factors in a mobile link. The multipath propagation and the path loss limit communications capacity, and the classical gain and diversity gain from signal processing undertaken by the antennas serve to mitigate the capacity limitations. Some of the subsequent chapters discuss the mechanisms of multipath propagation and the antenna signal-processing action and antenna configurations. It is these processes that govern the performance of mobile links.

The simplest case of multipath propagation comprises one reflected path in addition to a direct path. This section discusses the fields resulting from a reflection from a smooth planar surface, which has direct relevance to propagation along streets and across rural areas.

The waves incident on a mobile receiving antenna sometimes arrive via a line-of-sight from the transmitter, but in a general case they emanate mostly from scatterers. The scatterers can be viewed as electromagnetic sources. The scenario comprises these sources and their geometric relation to the receiving antenna. Scenario and propagation channel models are developed. The deterministic two-path model is used extensively as a model since it offers a simple tutorial and can produce representations of most of the behaviour from real-world channels. The deterministic model is developed into stochastic forms, and finally into averaged forms. During the development, the distortion of a signal in the channel is addressed and the antenna interfacing principles are also discussed.The waves incident on a mobile receiving antenna sometimes arrive via a line-of-sight from the transmitter, but in a general case they emanate mostly from scatterers. The scatterers can be viewed as electromagnetic sources. The scenario comprises these sources and their geometric relation to the receiving antenna.

In generating signals similar to those encountered in mobile communications, it is practical to compute signal samples from the scenario model by moving the receiving antenna amongst discrete sources. In simulations, calculations of any metric over a finite sample size will provide only an estimate of the ensemble average value. In this section, basic considerations for computer simulations of the short-term fading channel are discussed. Two aspects of simulation are: the generation of discrete channel samples, that may be mutually independent and have the correct ensemble averaged statistics; and the generation of time (i.e. space-) series which are samples of continuous channel behaviour, and these may comprise closely spaced, correlated samples, which should also have the correct ensemble-averaged statistics.

In the previous chapters receiver diversity related to antenna arrays has been discussed to some extent, but the additional flexibility derived from having more than one antenna element leads to many more uses. The interdependence between the antennas and the propagation environment is even more clear in this new connection. The signal correlation between elements is very important for the potential applications, and this correlation depends on the angular spread as seen from each array antenna. In general there will be M transmitting antennas in a transmit array and N receiving antennas in a receive array. Although there will be reciprocity between any two antennas, it will be necessary to distinguish between the transmit and receive situation, since the knowledge of the channel parameters may be different in the two situations. Also in the most general case the angular spread of the same environment will be different seen from the two sides. Another important distinction will be between one-port and multi-port arrays. In the first case the different elements may have different complex weights, but combined into one port, whereas in the second case each element may be connected to a network with several ports.

This appendix reviews some basic statistics which are commonly used in mobile communications and signal processing, and is associated with Chapter 2. The results are well known and are drawn from several sources such as the classical text by Papoulis (1965) and more recent texts such as Kay (1993). The probability of the real random variable z being less than or equal to a value Z, is written P(z<Z) = J pz(x)dx, (B.l) J - oo where Pχ is the cumulative density function (cdf), also called the cumulative prob ability function (cpf), and pz{z) is the probability density function (pdf); k random variables are statistically independent if their joint pdf, pz(x), factors into the product of the individual random variable pdfs: Pziχ) = Pzι (xi)Pz2(χ2) ....Pzkiχk) (B-2) where z and x are the set of zι and x,-, respectively.

In the context of Huygens' principle and physical optics, it makes sense to consider a volume over which the phase of contributing waves is fairly constant, centred around the line-of-sight where the phase is stationary. Consider the situation in Figure D.l where the distance between the two antennas is d and the total distance to a scattering point is R₁ + R₂.