Fundamental limits on detection in low SNR under noise uncertainty

Abstract

Abstract-In this paper we consider the problem of detecting whether a frequency band is being used by a known primary user. We derive fundamental bounds on detection performance in low SNR in the presence of noise uncertainty -the noise is assumed to be white, but we know its distribution only to within a particular set. For clarity of analysis, we focus on primary transmissions that are BPSK-modulated random data without any pilot tones or training sequences. The results should all generalize to more general primary transmissions as long as no deterministic component is present.Specifically, we show that for every 'moment detector' there exists an SNR below which detection becomes impossible in the presence of noise uncertainty. In the neighborhood of that SNR wall, we show how the sample complexity of detection approaches infinity. We also show that if our radio has a finite dynamic range (upper and lower limits to the voltages we can quantize), then at low enough SNR, any detector can be rendered useless even under moderate noise uncertainty.

Sondeo compresivo aplicado a la detección eficiente de espacios en blanco en señales multibanda - validación metodológica

“…Para realizar la función de sondeo de espectro se han propuesto varios métodos, dentro de los que se encuentran, la prueba de tasa de verosimilitud (LRT) [23], la detección de energía [20][21][22][23][24], el filtraje adaptado [21][22][23]32, 35] y la detección por características ciclo-estacionarias [33][34] entre otros. Cada método presenta ventajas y desventajas; por ejemplo, LRT se ha probado que es óptimo [23], sin embargo, no es práctico debido a que requiere conocimiento exacto de la información del canal y de las distribuciones de probabilidad de la fuente de señal y de ruido; la detección por filtraje adaptado, requiere conocimiento perfecto de las características del canal y sincronización; el método basado en características ciclo-estacionarias, necesita conocimiento de las frecuencias cíclicas de los usuarios primarios y presenta una gran complejidad computacional [21]; el método basado en detección de energía no requiere información a priori de la señal o del canal, presentando como ventaja una robustez frente al desvanecimiento, sin embargo, requiere conocimiento de la potencia de ruido, lo que hace que malas estimaciones de la potencia de ruido conduzcan a limitaciones de eficiencia con baja SNR y altas probabilidades de falsa alarma [20-22, 25, 30].…”

Intelligent and efficient development of wireless networks: A review of cognitive radio networks

“…The advantage of the matched filter detection is the short time to achieve a certain probability of a false alarm or probability of a misdetection. The matched filter has a requirement of fewer signal samples, which grows as (1 / SNR) O for a target probability of false alarm at low SNRs [36,37]. Thus, there exists a SNR wall for a matched filtering method [38].…”

Predictive Channel Access in Cognitive Radio Networks Based on Variable Order Markov Models

“…This method is an optimal detection method of a signal in the presence of additive white Gaussian noise [8]. In the case of additive white Gaussian noise the received signals given the respective hypotheses can be presented by the following formula [10].…”

“…It is the most generally used method to sense because of its low complexity and its capability to sense without the knowledge of the transmitted signal [7]. In this case we compare the energy of the signal with a threshold γ which can be represented as [10]:…”

“…The Reader is referred to [7,10,12] for more information on that. The main advantages of this scheme are simplicity in implementation, low computational complexity and scheme being optimal in the case primary user signal is unknown [13].…”