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Some Fundamental Limits on Cognitive Radio

Cognitive radio refers to wireless architectures in which a communication system does not operate in a fixed assigned band, but rather searches and finds an appropriate band in which to operate. In this paper we explore, from first principles, the fundamental requirements for such system that tries to avoid interference to potential primary users of a band. We first show that in order to deliver real gains, cognitive radios must be able to detect undecodable signals. This is done by showing how to evaluate the tradeoff between secondary user power, available space for secondary operation, and interference protection for the primary receivers. We prove that in general, the performance of the optimal detector for detecting a weak unknown signal from a known zero-mean constellation is like that of the energy detector (radiometer). However we show that the presence of a known pilot signal can help greatly. We further motivate the need for pilot signals by showing that the radiometer is rendered useless by just moderate noise uncertainty. Finally, we show that quantization combined with noise uncertainty can make the detection of signals by any detector absolutely impossible below a certain SNR threshold. 1 Description of problem and some fundamental geographic tradeoffs The enormous success of the ISM bands has strengthened criticism of the FCC’s traditional process which allocates bands to a single use, issues exclusive licenses to a single entity within a geographical area, and prohibits other devices from transmitting significant power within these bands. As a result, the FCC is considering revising its spectrum allocation policies [1], and is moving ahead with the process. Cognitive radios are one proposed idea to take advantage of a more open spectrum policy.[2, 3]. A cognitive radio would be designed to dynamically adapt its transmissions to find and utilize frequencies while minimizing interference. This is inspired by actual measurements showing that most of the allocated spectrum is vastly underutilized [4]. Cognitive radios promise great societal benefits by allowing new applications that can flexibly use what spectrum happens to be available. However, fundamental theoretical questions remain as to the exact requirements for engineering a practical cognitive radio system. For illustrative purposes, consider the world depicted in (1a). Each of the two antennas represents a bustling metropolis. Under current regulations, users in the middle of nowhere are prohibited from using these spectrum bands, even if there are no receivers in the vicinity that might be interfered with. However, cognitive radios may someday be allowed to share the spectrum, on the condition that they not interfere with primary users. These primary users may be providing more socially important services, or they might simply be legacy systems that are unable to change. Figure (1b) depicts the primary transmitter in one metropolis. The dotted circle represents the boundary of decodability for a single-user system. That is, in the absence of all interference, 1