Praise for Fundamentals of WiMAX

80 Chapter 3 • The Challenge of Broadband Wireless Channelswhere N is the size of a cluster equivalent to the inverse of the frequency-reuse factor. Obviously,a higher value of Q reduces cochannel interference so that it improves the quality of the communicationlink and capacity. However, the overall spectral efficiency decreases with the size of acluster N; hence, N should be minimized only to keep the received SINR above acceptable levels.Since the background-noise power is negligible compared to the interference power in aninterference-limited environment, the received SIR can be used instead of SINR. If the numberof interfering cells is N t , the SIR for a mobile station can be given bySI=SN I∑Iii=1, (3.25)where S is the received power of the desired signal, and I iis the interference power from the ithcochannel base station. The received SIR depends on the location of each mobile station andshould be kept above an appropriate threshold for reliable communication. The received SIR at thecell boundaries is of great interest, since this corresponds to the worst-interference scenario. Forexample, if the empirical pathloss formula given in Equation (3.10) and universal frequency reuseare considered, the received SIR for the worst case given in Figure 3.6 is expressed asSI=0χ02511−α−α∑ i2 ∑ i(2.633) ∑ ii=1i=3i=6χ + χ + χ +χ, (3.26)where χ i denotes the shadowing from the ith base station. Since the sum of lognormal randomvariables is well approximated by a lognormal random variable [10, 27], the denominator can beapproximated as a lognormal random variable, and then the received SIR follows a lognormal distribution[5]. Therefore, the outage probability that the received SIR falls below a threshold canbe derived from the distribution. If the mean and the standard deviation of the lognormal distributionare µ and σ s in dB, the outage probability is derived in the form of Q function asPo⎛ γ − µ ⎞= Q⎝⎜ σ ⎠⎟s, (3.27)where γ is the threshold SIR level in dB. Usually, the SINR at the cell boundaries is too low toachieve the outage-probability design target if universal frequency reuse is adopted. Therefore, alower frequency-reuse factor is typically adopted in the system design to satisfy the target outageprobability at the sacrifice of spectral efficiency.Figure 3.7 highlights the OCI problem in a cellular system if universal frequency reuse isadopted. The figure shows the regions of a cell in various SIR bins of the systems with universalfrequency reuse and f =1/3frequency reuse. The figure is based on a two-tier cellular structureand the simple empirical pathloss model given in Equation (3.7) with α = 3.5.The SIR in mostparts of the cell is very low if universal frequency reuse is adopted. The OCI problem can be mit-