Praise for Fundamentals of WiMAX

406 Chapter 12 • System-Level Performance of WiMAXThe system simulator takes multiple Monte Carlo snapshots of the network to observeergodic samples of the network and to determine how it behaves over long time scales [2]. EachMonte Carlo snapshot samples the behavior of the network over a 5msec frame. During eachsnapshot, the simulator randomly distributes various MSs in each sector and analyzes theexpected instantaneous behavior of the network in terms of data rate, cell throughput, and outageprobability. Information related to the location of each MS and the state of its traffic buffer arepurged at the beginning of the next Monte Carlo snapshot of the network. This way, each MonteCarlo sample is random and completely independent of the previous sample. In each Monte Carlosnapshot, the simulator takes several steps to calculate the cell throughput and user data rates.12.2.1.1 Computation of Time-Domain MIMO ChannelThe instantaneous channel as observed by each MS from all the BSs in the network is calculatedasH' n( ) = PL( d n,k )s n, k g b ( θ n,k )g m ( θ˜ n,k) n H n, k ( τ – τ i ) , (12.4), k τwhere PL( d n,k ) is the median pathloss between the nth MS and the kth BS; H n,k (τ ) is the instantaneousfast-fading component of the MIMO channel; D is the total number of paths—dependson the path-delay profile—τ i is the delay of the ith multipath relative to the first path; d n,k is thedistance between the MS and the BS, s n,k is the instantaneous shadow fading between the MSand the BS, g b and g m are the gain patterns of BS and MS antennas, respectively; andθ˜ n,kare the angle of departure at the BS and angle of arrival at the MS with respect to the boresightdirections of the BS and MS antennas, respectively. The fast-fading MIMO componentH n,k (τ -τ i ) is calculated using the methodology explained in Section 11.1.1, and is a complexmatrix with dimension N r × N t for each path index i, where N r is number of receive antennas,and N t is the number of transmit antennas. The instantaneous shadow-fading components s n,k foreach Monte Carlo snapshot are generated as i.i.d. random variables with a lognormal distribution.Appropriate correlation between the shadow fading observed by a given MS from variousBSs, is also modeled, 2 using a coloring matrix.12.2.1.2 Computation of Frequency-Domain MIMO ChannelThe time-domain MIMO channel is then converted to the frequency-domain MIMO channel,using a Fourier transformation, as given by the following:D∑i = 1θ n,kand2. Since the shadow fading between a BS and an MS is partially dependent on the local neighborhoodof the MS, it is expected that the shadow fading at a given MS from a different BS is correlated toa certain degree.