This chapter develops the fundamental capacity limits and associated transmission techniques for different cognitive radio network paradigms. These limits are based on the premise that the cognitive radios of secondary users are intelligent wireless communication devices that exploit side information about their environment to improve spectrum utilization. This side information typically consists of knowledge about the activity, channels, encoding strategies, and/or transmitted data sequences of the primary users with which the secondary users share the spectrum. Based on the nature of the available side information as well as regulatory constraints on spectrum usage, cognitive radio systems seek to underlay, overlay, or interweave the secondary users' signals with the transmissions of primary users. This chapter develops the fundamental capacity limits for all three cognitive radio paradigms. These capacity limits provide guidelines for the spectral efficiency possible in cognitive radio networks, as well as practical design ideas to optimize performance of such networks.
While the general definition of cognitive radio was provided in Chapter 1, we now interpret that definition in a mathematically precise manner that can be used in the development of cognitive radio capacity limits. Specifically, in the mathematical terminology of information theory, it is the availability and utilization of network side information that defines a cognitive radio, which we formalize as follows.
A cognitive radio is a wireless communication device that intelligently utilizes any available side information about the (a) activity, (b) channel conditions, (c) encoding strategies, or (d) transmitted data sequences of primary users with which it shares the spectrum.
As discussed in Chapter 2, cognitive radio (CR) aims at maximizing the throughput of secondary users coexisting with primary users under a noninterference or a limitedinterference assumption. Both assumptions require the secondary user to collect cognition about the radio environment, or spectrum sensing. Here the concept of spectrum space is extended to multiple dimensions, such as time, space, frequency, and code, and sensing may include not only detecting and classifying the regions of the spectrum space that can be used by secondary users, but also determining what type of signals are occupying the spectrum, including modulation, waveform, bandwidth, carrier frequency, etc. . All these operations assume that the primary user is not aware of the presence of a secondary user.
Spectrum sensing classifies spectrum spaces as follows:
white space, one which is completely empty, except for noise;
gray space, one which is partially occupied by interfering signals;
black space, one which is fully occupied by communication signals, interfering signals, and noise.
With reference to the CR paradigms categorized in Chapter 2, white spaces are relevant to interweaving, which allows secondary users to operate in spectrum regions that are unused, gray spaces to underlaying, which tries to keep the interference on the primary user at a tolerable level, and black spaces to overlaying, where the primary user transmission is overheard, and signals are processed in a way that makes the quality of this transmission unimpaired by the secondary user.
In this chapter we examine spectrum sensing for application to the first two paradigms.
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