Skip to main content Accessibility help
×
Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-28T10:10:17.415Z Has data issue: false hasContentIssue false

4 - Discrete and continuous maxima in MC signals

Published online by Cambridge University Press:  03 December 2009

Simon Litsyn
Affiliation:
Tel-Aviv University
Get access

Summary

In many situations it is beneficial to deal with a discrete-time “sampled” version of multicarrier signals. This reduction allows passing from the continuous setting to an easier-to-handle discrete one. However, we have to estimate the inaccuracies stemming from the approach. In this chapter, I analyze the ratio between the maximum of the absolute value of a continuous MC signal and the maximum over a set of the signal's samples. We start with considering the ratio when the signal is sampled at the Nyquist frequency, i.e. the number of sampling points equals the number of tones. In this case I show that the maximum of the ratio over all MC signals grows with the number of subcarriers (Theorem 4.2). However, if one computes a weighted sum of the maximum of the signal's samples and the maximum of the signal derivative's samples the ratio already is, at most, a constant (Theorem 4.5). I further show that actually the ratio depends on the maximum of the signal; the larger the maximum is the smaller is the ratio (Theorem 4.6). An even better strategy is to use over sampling. Then the ratio becomes constant tending to 1 when the over sampling rate grows (Theorems 4.8, 4.9, 4.10, and 4.11). Furthermore, I tackle the case when we have to use the maximum estimation, projections on specially chosen measuring axes instead of the absolute values of the signal (Theorem 4.14). Finally, I address the problem of relation between the PAPR and the PMEPR and show that the PMEPR estimates the PAPR quite accurately for large values of the carrier frequency (Theorem 4.19).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2007

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.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved 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
×

Save book to Dropbox

To save 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 saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save 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 saving content to Google Drive.

Available formats
×