In this paper, the forward link erlang capacity and outage probability for hierarchical cellular system based on 2 layer macrocell/microcell are derived analytically by considering the impact of imperfect power control and soft hand-off. The analysis on the outage probability is carried out using two methods: lognormal approximation and Chernoff upper bound. We assume that voice and multi-rate data service users are distributed uniformly in each cell and the same spectrum is applied in both layers. In addition, we take into account the base station transmission power ratio between tiers and the relative position of microcell having island distribution in macrocell. The forward link interference is evaluated by using Monte-Carlo simulation introduced in [2]. In this paper, we compare the forward link erlang capacity of 1x system to 3x system and show that 3x system can increase the user capacity by 3.4 times in case of macrocell and microcell, respectively, compared to 1x system.

We explain three random sampling techniques that are simple but widely applicable for various problems involving huge data sets. The first technique is an immediate application of large deviation bounds. The second and the third ones are sequential sampling or adaptive sampling techniques. We fix one simple problem and explain these techniques by demonstrating algorithms for this problem and discussing their correctness and efficiency.

In this paper we analize the performance of Trellis Coded Modulation (TCM) schemes with coherent detection operating in a frequency flat, mobile Rayleigh fading environment, and with different knowledge levels on both the amplitude and phase fading processes (the latter is not assumed as usual to be ideally tracked), or Channel State Information (CSI). For example, whereas ideal CSI means that both the amplitude and phase fading characteristics are perfectly known by the receiver, other situations that are treated consider perfect knowledge of the amplitude (or phase) with complete disregard of the phase (or amplitude), as well as non concern on any of them. Since these are extreme cases, intermediate situations can be also defined to get extended bounds based on Chernoff which allow the phase errors, in either form of constant phase shifts or randomly distributed phase jitter, to be included in the upper bounds attainable by transfer function methods, and are applicable to multiphase/level signaling schemes. We found that when both fading characteristics are considered, the availability of CSI enhances significatively the performance. Furthermore, for non constant envelope schemes with non ideal CSI and for constant envelope schemes with phase errors, an asymmetry property of the pairwise error probability is identified. Theoretical and simulation results are shown in support of the analysis.

Queueing problems are investigated for very wide classes of input traffic and service time models to obtain good loss probability and waiting time probability approximation. The proposed approximation is based on the fundamental recursion formula and the Chernoff bound technique, both of which requires no particular assumption for the stochastic nature of input traffic and service time, such as renewal or markovian properties. The only essential assumption is stationarity. We see that the accuracy of the obtained approximation is confirmed by comparison with computer simulation. There are a number of advantages of the proposed method of approximation when we apply it to network capacity design or path accommodation design problems. First, the proposed method has the advantage of applying to multi-media traffic. In the ATM network, a variety of bursty or non-bursty cell traffic exist and are superposed, so some unified analysis methodology is required without depending each traffic's characteristics. Since our method assumes only the stationarity of input and service process, it is applicable to arbitrary types of cell streams. Further, this approach can be used for the unexpected future traffic models. The second advantage in application is that the proposed probability approximation requires only small amount of computational complexity. Because of the use of the Chernoff bound technique, the convolution of every traffic's probability density fnuction is replaced by the product of probability generating functions. Hence, the proposed method provides a fast algorithm for, say, the call admission control problem. Third, it has the advantage of accuracy. In this paper, we applied the approxmation to the cases of homogeneous CBR traffic, non-homogeneous CBR traffic, M/D/1, AR(1)/D/1, M/M/1 and D/M/1. In all cases, the approximating values have enough accuracy for the exact values or computer simulation results from low traffic load to high load. Moreover, in all cases of the numerical comparison, our approximations are upper bounds of the real values. This is very important for the sake of conservative network design.