In Chapters 1 and 2, the drivers for the development of the cellular system architecture were discussed and an overview of the key network elements and principles of operation for a GSM cellular solution was provided. The remainder of the book will address the activities necessary to design and deploy profitable wireless networks. Figure 3.1 summarises where these key processes are to be found by chapter.

In this chapter, the principles and processes that are used to plan wireless access networks will be developed. The major focus will be on cellular networks, as these usually represent the most complex planning cases, but an overview of the corresponding processes for 802.11 is also provided. Circuit voice networks will be examined initially; the treatment will then be extended to understand the additional considerations that come into play as first circuit-data and subsequently packet-data-based applications are introduced.

With the planning sequence understood, the way in which information from such processes can be used to explore the potential profitability of networks well in advance of deployment will be addressed. Choices regarding which applications are to be supported in the network and the quality of service offered will be shown to have a major impact on the profitability of network projects.

Circuit voice networks

In most forms of retailing, the introduction of new products follows the ‘S curve’ sequence first recognised by Rogers [1].

In Chapter 3, the generic principles, processes and deployment configurations applicable to cellular network planning were developed. In this chapter and the following four, a detailed design process will be developed to address, step by step, the practical deployment process for four different wireless networks.

This chapter describes the steps in the planning process that are essentially common, regardless of the specific air interface under consideration. The high-level planning of Chapter 3 will have estimated the total number of cell sites and the maximum cell size, and made decisions on the applications to be deployed. The detailed plan will define the actual locations of cell sites, antenna types, mast heights, etc., using topographical data for the specific regions. The plan will also assure guaranteed levels of coverage, capacity and availability for the applications to be supported.

The changing relative implementation cost and impact on battery life of particular technologies at points in time over the last 25 years has given rise to three distinct RAN standards:

• TDMA (as employed in GSM, GPRS, EDGE),

• CDMA (as employed in UMTS releases 99, 4, 5, 6, 7 and CDMA 2000),

• OFDMA (as employed in 802.11, 802.16e (WiMAX) and as planned for 3G LTE).

These technologies are expected to dominate wireless deployments over the next 20 years and it is a comprehensive understanding of major factors, such as coverage, capacity and latency, that will enable system designers to exploit their potential fully.

The effects of roundoff noise in control and signal processing systems, and in numerical computation have been described in detail in the previous chapters.

There is another kind of quantization that takes place in these systems however, which has not yet been discussed, and that is coefficient quantization.

The coefficients of an equation being implemented by computer must be represented according to a given numerical scale. The representation is of course done with a finite number of bits. The same would be true for the coefficients of a digital filter or for the gains of a control system.

If a coefficient can be perfectly represented by the allowed number of bits, there would be no error in the system implementation. If the coefficient required more bits than the allowed word length, then the coefficient would need to be rounded to the nearest number on the allowed number scale. The rounding of the coefficient would result in a change in the implementation and would cause an error in the computed result. This error is distinct from and independent of quantization noise introduced by roundoff in computation. Its effect is bias–like, rather than the PQN nature of roundoff, studied previously.

If a numerical equation is being implemented or simulated by computer, quantization of the coefficients causes the implementation of a slightly different equation.

The purpose of this chapter is to provide an introduction to the basics of statistical analysis, to discuss the ideas of probability density function (PDF), characteristic function (CF), and moments. Our goal is to show how the characteristic function can be used to obtain the PDF and moments of functions of statistically related variables. This subject is useful for the study of quantization noise.

PROBABILITY DENSITY FUNCTION

Figure 3.1(a) shows an ensemble of random time functions, sampled at time instant t = t1 as indicated by the vertical dashed line. Each of the samples is quantized in amplitude. A “histogram” is shown in Fig. 3.1(b). This is a “bar graph” indicating the relative frequency of the samples falling within the given quantum box. Each bar can be constructed to have an area equal to the probability of the signal falling within the corresponding quantum box at time t = t1. The sum of the areas must total to 1. The ensemble should have an arbitrarily large number of member functions. As such, the probability will be equal to the ratio of the number of “hits” in the given quantum box divided by the number of samples. If the quantum box size is made smaller and smaller, in the limit the histogram becomes fx(x), the probability density function (PDF) of x, sketched in Fig. 3.1(c).

The extremely fast rolloff of the characteristic function of Gaussian variables provides nearly perfect fulfillment of the quantization theorems under most circumstances, and allows easy approximation of the errors in Sheppard's corrections by the first terms of their series expression. However, for most other distributions, this is not the case.

As an example, let us study the behavior of the residual error of Sheppard's first correction in the case of a sinusoidal quantizer input of amplitude A.

Plots of the error are shown in Fig. G.1.

It can be observed that neither of the functions is smooth, that is, a high–order Fourier series is necessary for properly representing the residual error in Sheppard's first correction, R1(A, μ) with sufficient accuracy. The maxima and minima of R1(A, μ) obtained for each value of A by changing μ, exhibits oscillatory behavior. For some values of A, for example as A ≈ 1.43q or A ≈ 1.93q (marked by vertical dotted lines in Fig. G.1(b)), the residual error of Sheppard's correction remains quite small for any value of the mean, but the limits of the error jump apart rapidly for values of A even close to these. A conservative upper bound of the error is therefore as high as the peaks in Fig. G.1(b). One could use the envelope of the error function for this purpose.