Home
Hostname: page-component-dc8c957cd-n2smj Total loading time: 0.377 Render date: 2022-01-29T13:08:25.002Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }
Order Statistics in Wireless Communications
Diversity, Adaptation, and Scheduling in MIMO and OFDM Systems
Buy print or eBook[Opens in a new window]

# 3 - Distributions of order statistics

Published online by Cambridge University Press:  07 October 2011

## Summary

Introduction

The previous chapter shows that the performance analysis of wireless communication systems requires the statistics of the signal-to-noise ratio (SNR) at the receiver. In the analysis of many advanced wireless communication techniques in later chapters, we will make use of some order statistical results. This chapter summarizes these results and their derivations for easy reference. Specifically, we first review the basic distribution functions of ordered random variables. After that, we derive some new order statistics results, including the joint distribution functions of partial sums of ordered random variables, for which we also present a novel analytical framework based on the moment generating function (MGF). The chapter is concluded with a discussion on the limiting distributions of extremes. Whenever appropriate, we use the exponential random variable special case as an illustrative example. Note that we focus on those order statistics results that will be employed in later chapters in the performance and complexity analysis of different wireless technologies. For a more thorough treatment of order statistics, the readers are referred to [1, 2].

Basic distribution functions

Order statistics deals with the distributions and statistical properties of the new random variables obtained after ordering the realizations of some random variables. Let γj's, j = 1, 2,…, L denote L independent and identically distributed (i.i.d.) nonnegative random variables with common PDF pγ (·) and CDF Fγ(·). Let γl:L denote the random variable corresponding to the lth largest observation of the L original random variables, such that γ1:L ≥ γ2:L ≥ … ≥ γL:L · γl:L is also called lth order statistics. The ordering process is illustrated in Fig. 3.1.

Type
Chapter
Information
Order Statistics in Wireless Communications
Diversity, Adaptation, and Scheduling in MIMO and OFDM Systems
, pp. 40 - 71
Publisher: Cambridge University Press
Print publication year: 2011

## Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

### Purchase

Buy print or eBook[Opens in a new window]
4
Cited by

# Send book to Kindle

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

# Send book to Dropbox

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

Available formats
×

# Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

Available formats
×