A simple and efficient approximation to the modified Bessel functions and its applications to Rician fading

Ramy Salahat, Ehab Salahat, A. Hakam, Tasneem Assaf
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引用次数: 15

Abstract

In recent days, relay assisted cellular networks are gaining more importance in research and development because of the recent adoption of new communication standards with relaying and cooperation communication. This has introduced a multichannel diversity along with the multiuser diversity and the channel aware dynamic resource allocation models. The issue of the optimal location of relays has risen especially when dedicated relays are used as the standard proposes instead of the cooperative model of the users. In this paper, we study the optimal location of a single relay. Furthermore, we study the effect of changing the number of users on the optimal location of the relay. The effect of adding multiple relays to the system is examined. The optimal locations are examined when the relay channels are the only channels to be used by the system and when the direct channel (DT) is also available. The problem formulation assumes, Rayleigh block faded channels, half duplex regenerative (repetition coding) decode-and-forward (DF) relaying strategy, long-term average total transmitted power constraint and orthogonal multiplexing of the users messages within the channel blocks. New simple and accurate approximations to the modified Bessel functions of the first kind, zeroth order I0 (z) and first order I1 (z) are presented. The new proposed approximations are given as a simple finite sum of scaled exponential functions. Comparisons are made between the exact functions, classic approximations, and the new approximation in terms of simplicity and accuracy. The new approximation proves to be sufficiently accurate to bridge the gap between the classic large and small argument approximations and has potential applications in allowing one to analytically evaluate integrals containing Modified Bessel Functions, yielding simple closed-form solutions. A generalized closed-form expression for the average bit error rate over Nakagami-n (Rice) fading, and Rayleigh fading as a special case, are derived as sample applications, and the results are compared with Monte Carlo Simulation, where a very good matching is achieved.
修正贝塞尔函数的一种简单而有效的逼近及其在fourier衰落中的应用
近年来,由于采用了中继和合作通信的新通信标准,中继辅助蜂窝网络在研究和开发中变得越来越重要。这就引入了多信道分集、多用户分集和信道感知动态资源分配模型。特别是当使用专用中继作为标准建议而不是用户的合作模式时,中继的最优位置问题就日益突出。本文研究了单继电器的最优位置问题。此外,我们还研究了用户数量变化对中继最佳位置的影响。研究了在系统中加入多个继电器的效果。当中继通道是系统唯一使用的通道并且直接通道(DT)也可用时,检查最佳位置。问题公式假设,瑞利块衰落信道,半双工再生(重复编码)解码转发(DF)中继策略,长期平均总发射功率约束和信道块内用户消息的正交复用。给出了一类修正贝塞尔函数、零阶I0 (z)函数和一阶I1 (z)函数的新的简单而精确的近似。新提出的逼近是一个简单的有限和的比例指数函数。在简单性和准确性方面,对精确函数、经典近似和新近似进行了比较。新的近似被证明是足够精确的,可以弥补经典的大参数近似和小参数近似之间的差距,并且在允许对包含修改贝塞尔函数的积分进行解析计算方面具有潜在的应用,可以得到简单的闭形式解。本文推导了一种广义的中agami-n (Rice)衰落和特殊情况下的瑞利衰落的平均误码率的封闭表达式作为样本应用,并将结果与蒙特卡罗模拟进行了比较,得到了很好的匹配结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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