# Wireless data rates, part 1: Bandwidth, noise, and interference

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*This series is excerpted from "3G Evolution, HSPA and LTE for Mobile Broadband, 2e." Order this book today and receive an additional 20% discount. Go to
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Part 2 discusses higher-order modulation, channel coding, and multi-carrier transmission.*

One main target for the evolution of 3G mobile communication is to provide the possibility for significantly higher end-user data rates compared to what is achievable with, for example, the first releases of the 3G standards. This includes the possibility for higher peak data rates but, as pointed out in the previous chapter, even more so the possibility for significantly higher data rates over the entire cell area, also including, for example, users at the cell edge. The initial part of this chapter will briefly discuss some of the more fundamental constraints that exist in terms of what data rates can actually be achieved in different scenarios. This will provide a background to subsequent discussions in the later part of the chapter, as well as in the following chapters, concerning different means to increase the achievable data rates in different mobile-communication scenarios.

**3.1 High data rates: Fundamental constraints**

In [70], Shannon provided the basic theoretical tools needed to determine the maximum rate, also known as the *channel capacity*, by which information can be transferred over a given communication channel. Although relatively complicated in the general case, for the special case of communication over a channel, e.g. a radio link, only impaired by additive white Gaussian noise, the channel capacity *C *is given by the relatively simple expression [50]

where *BW *is the bandwidth available for the communication, *S *denotes the received signal power, and *N *denotes the power of the white noise impairing the received signal.

Already from (3.1) it should be clear that the two fundamental factors limiting the achievable data rate are the available received signal power, or more generally the available signal-power-to-noise-power ratio *S*/*N*, and the available bandwidth. To further clarify how and when these factors limit the achievable data rate, assume communication with a certain information rate *R*. The received signal power can then be expressed as *S = E _{b}* ⋅

*R*where

*E*is the received energy per information bit. Furthermore, the noise power can be expressed as

_{b }*N = N*

_{0}⋅

*BW*where

*N*

_{0}is the constant noise power spectral density measured in W/Hz.

Clearly, the information rate can never exceed the channel capacity. Together with the above expressions for the received signal power and noise power, this leads to the inequality

or, by defining the radio-link *bandwidth utilization* γ *R*/*BW*,

This inequality can be reformulated to provide a lower bound on the required received energy per information bit, normalized to the noise power density, for a given bandwidth utilization γ

The rightmost expression, i.e. the minimum required *E _{b}*/

*N*

_{0}at the receiver as a function of the bandwidth utilization is illustrated in Figure 3-1. As can be seen, for bandwidth utilizations significantly less than one, that is for information rates substantially smaller than the utilized bandwidth, the minimum required

*E*/

_{b}*N*

_{0}is relatively constant, regardless of γ. For a given noise power density, any increase of the information data rate then implies a similar relative increase in the minimum required signal power

*S = E*·

_{b }*R*at the receiver. On the other hand, for bandwidth utilizations larger than one the minimum required

*E*/

_{b}*N*

_{0}increases rapidly with γ. Thus, in case of data rates in the same order as or larger than the communication bandwidth, any further increase of the information data rate, without a corresponding increase in the available bandwidth, implies a larger, eventually much larger, relative increase in the minimum required received signal power.

*Figure 3-1. Minimum required E*

_{b}/N_{0}at the receiver as a function of bandwidth utilization.