1.3 Monte-Carlo Basics

The statistical methodology used as a basis for SEAMCAT is the Monte Carlo method. Statistical simulation methods may be contrasted to conventional analytical methods, which are typically applied to ordinary or partial differential equations that describe some underlying physical or mathematical system. In many applications of the Monte Carlo method, the physical process is simulated directly and there is no need to even write down the differential equations that describe the behaviour of the system.

The Monte-Carlo simulation method is based upon the principle of taking samples of random variables from a given distribution. Before the simulation the distributions need to be defined for all relevant parameters of the wireless systems to be modelled (e.g. antenna heights, powers, operating frequencies, positions of the transceivers, etc.). Fixed values can be specified for parmaters which do not vary in the scenario (e.g. systems with specific frequenecies or heights). The technical specifications of the receiver and transmitter are generally extracted from relevant equipment standard (e.g. standards produced by ETSI, 3GPP, IEEE etc.). 

SEAMCAT uses these distributions to generate random events (Event, snapshot and simulation trial have the same meaning in this report) using samples of the above mentioned distributions. For each event, SEAMCAT stores the signal strength of the interfering and the desired signals calculated in dedicated data arrays. As a very final step, the probability of interference can be calculated by comparing the wanted and unwanted signals at the victim link receiver in each event to the relevant interference criterion (e.g. C/I).

The only requirement is that the physical or mathematical parameter can be described by a probability density function (PDF). Once the PDFs of the relevant parameters are known, the Monte Carlo simulation can proceed by randomly sampling them. Many simulation trials are performed with different random samples for each trial and the desired result is taken as an average over the number of observations. In many practical applications one can predict the statistical error in this average result and hence an estimate of the number of Monte Carlo trials that are needed to achieve a given error.

SEAMCAT models one single victim link receiver (VLR) connected to a victim link transmitter (VLT) operating amongst a population of one or more interfering link transmitters (ILT) which are linked to an interfering link receiver (ILR). These interferers may belong to the same system as the victim, a different system or a mixture of both. The locations of the interferers are distributed around the victim either completely randomly or with some relation to the location of victim in a manner that can be specified by the user.

Figure 5 illustrates the terminology of the various elements that are simulated for (a) ‘generic’ systems (i.e. non-cellular) and (b) cellular systems.'

It is common practice to use a uniform random distribution for the locations of the transceivers. The density of interferers is set in line with the environment being modelled, i.e. an urban environment should have a higher density than a rural environment. Only a proportion of the interferers are active at any instance. This proportion may depend for example on the day of the week as well as the time of day. Figure 6 illustrates how the interferers and victim may appear for one simulation trial. Also illustrated is the victim link transmitter providing the victim’s wanted signal (dRSS: desired Received Signal Strength).

Figure 6: A typical victim and interferer scenario for a Monte Carlo simulation trial

For cellular simulations, the generation of events includes additional complexity - several iterations of a power control loop (CDMA) may be needed within each event, and some initial pre-calculations are required, such as the calculation of non-interfered (nominal) capacity. For victim CDMA systems the interference criterion is the excess outage, i.e. the percentage of previously served users disconnected as a result of the interference impact. For victim OFDMA systems the interference criterion is the bitrate loss, i.e. the percentage of bit-rate lost compared to a non interfered victim network.