Olusegun O. Odejide

Unified analysis of energy detection of unknown signals over generalized fading channels

Reliable spectrum sensing is the very task upon which the entire operation of cognitive radio rests. Blind sensing of spectral-holes using a radiometer (energy detectors) is one of the solutions that have been proposed for enabling opportunistic spectrum access. This article revisits the problem of energy detection of an unknown deterministic signal over a myriad of fading environments. Specifically, a new approach (based on the canonical series representations of the generalized Marcum Q-function of real order in conjunction with the derivatives of the moment generating function of signal-to-noise ratio) is proposed to analyze the performance of maximal-ratio combining (MRC) and square-law combining (SLC) energy detectors with independent but non-identically distributed (i.n.d) fading statistics, including Rice and mixed-fading channels. Our analytical framework is also capable of treating the Nakagami-m channels with non-integer fading severity indices as well as halfodd integer values for the time-bandwidth product u. Many of these cases were either intractable with the classical probability density function/contour integral approaches, or that heretofore had resisted simple/computationally efficient solutions. Selected numerical results are also provided for the receiver operating characteristic (ROC) of MRC and SLC diversity energy detectors over Rice and Nakagami-m channels.

Further results on area under the ROC curve of energy detectors over generalized fading channels

A simple measurement to analyze the signal detectors performance is desirable. Although, receiver operating characteristic (ROC) curve has long been used for characterizing system performance, area under the ROC curve (AUC) measurement provides meaningful insights of the system performance. Signal detectors performance can be characterized simply by average AUC, since average AUC varies from 0.5 to 1. In the worst case scenario, the detectors performance can be no less than 0.5 and the best can be 1. In this paper simple expression of average AUC is developed based on the kth order derivative of the moment generating function (MGF) over the generalized fading channels for no-diversity and several diversity cases. Simplified expressions are derived for maximum ratio combing (MRC), square-law combing (SLC) diversity schemes and a simple CDF based single integral expression is developed for selection combining (SC) technique. Examples are given considering the Nakagami-m and Rice channels. Our approaches are simple and analytical results are even shown using the half integer bandwidth-time product (u) and the half integer Nakagami-m fading index. Different factors affecting energy sensing has been analyzed, which can be readily used for other applications such as cognitive radio.

Further results on the energy detection of unknown deterministic signals over generalized fading channel

In this article, we consider the performance of energy detection in composite multipath/shadowing fading environment. We also investigate the mitigation of the effect of these fading components on detection performance with the use of diversity techniques. Single channel, maximum ratio combining (MRC), square law combining (SLC), and square-law selection (SLS) diversities are analyzed using the rapidly convergent canonical series representation of Marcum Q-function with derivatives of moment generating function (MGF) of signal-to-noise ratio (SNR) of composite channel. On the other hand, the selection diversity combining (SDC) is analyzed using single integral of cumulative distribution function (CDF) of SNR. In all cases, we model the composite channel fading using the G-distribution which has been shown to be more accurate in representing the Suzuki and Nakagami-Lognormal distributions than K and KG and in closed formed compared to single integral expression for Rice-Lognormal distribution. Using this framework, we found out that the performance of energy detection does not degrade significantly at low and moderate shadowing conditions and that diversity detection greatly mitigates the effect of shadowing on detection performance with MRC giving the best performance, followed by SLC and then SDC or SLS depending on the average channel SNR, number of samples and level of shadowing. To the best of our knowledge, such a simple framework and resulting novel observations have never been reported before.

A performance study of energy detection for dual-hop transmission with fixed gain relays: area under ROC curve (AUC) approach

In this paper, energy detectors performance is investigated for the blind (fixed gain) amplify & forward (AF) dual-hop relay networks using the area under the receiver operating characteristic curve (AUC) metric. Different from the well-known receiver operating characteristics (ROC) metric, AUC is a single statistical parameter which can be used to describe and compare performance of different types of energy detectors. In this article, we derive closed-form AUC expressions for the fixed-gain AF relay networks over the Rayleigh fading channels. The analysis is then extended to the maximum ratio combing (MRC) and square-law combing (SLC) diversity detectors for a dual-hop but multi-relay systems. Our analytical framework and the closed-form AUC expression is based on the kth order derivatives of the moment generating function (MGF) of the combiner output signal-to-noise ratio (SNR).

Energy detector's performance evaluation in a relay based cognitive radio network: Area under the ROC curve (AUC) approach

In this paper, energy detectors performance is analyzed for the two-hop relay network using the area under the receiver operating characteristic (ROC) curve (AUC) in contrast to the ROC based analysis. AUC provides summary measures for the performance of a system. It provides meaningful performance analysis as it varies only from 0.5 to 1. In the worst case scenario, the practical detectors performance can be no less than 0.5 and the best can be 1. A simple generalized AUC framework is developed based on the canonical series representations of the generalized Marcum Q-function of real order in conjunction with the kth order derivative of the moment generating function (MGF) of signal to noise ratio (SNR) of the channel. The framework is then applied to analyze the energy-detection performance for single and multiple two-hop relay networks. For multiple two-hop relay networks, the receiver combining techniques are analyzed in particular maximum ratio combining (MRC) and square-law combining (SLC) as the representative of various combining techniques. Different factors such as the sampling number, number of relays and fading severity influencing the energy sensing have been analyzed. Proposed approach is simple in terms of computation and performance analysis and the results can be used readily for selecting proper cognitive radio operating parameters. Also the solution is capable of handling the half odd-integer bandwidth-time product (u) and the half odd-integer Nakagami-m fading severity index (m).

Adaptive Multiresolution Modulation for multimedia traffic

Future wireless communication systems and networks will be required to support a multitude of services with different reliability requirements. However, achieving such flexible systems are challenging in Mobile Ad-hoc Networks (MANET) due to limited battery resources at mobile nodes. However, by employing adaptive signaling techniques with Unequal Error Protection (UEP), we strive to improve the energy efficiency and increase the data rate (spectral efficiency) over a fading channel. In this article, we demonstrate the efficacy of the exponential approximation for the Adaptive Multiresolution Modulation (AMM) scheme in terms of PER using the asymmetric Phase-Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM).

Sparseness Measures of Signals for Compressive Sampling

Recent theoretical developments in compressive sampling (or compressed sensing) show that if a signal has a sparse representation in some basis, then it is possible to capture the signal information via a small number of projections. Furthermore, the signal can be accurately reconstructed using low complexity algorithms. Although the information encoding process may be agnostic to signal type - random projections can capture the information with high probability - accurate reconstruction of the signal often depends on proper selection of a reconstruction basis. In this paper, we evaluate techniques for measuring sparseness, including some not traditionally used in signal processing, and apply them to compressive sampling with the goal of selecting the best basis for signal reconstruction.

Application of Analytic Wavelet Transform for Signal Detection in Nyquist Folding Analog-to-Information Receiver

One of the challenges in Cognitive Radio (CR) is efficiently monitoring a wideband radio frequency (RF) spectrum in order to identify unoccupied bands. Compressive Sensing (CS) has recently been proposed to address this problem. Typical CS techniques, however, involve random projections followed by a computationally intensive signal reconstruction process. Since spectral monitoring does require full signal reconstruction - only identification of occupied regions to avoid - we propose a novel spectrum monitoring approach based on the Nyquist Folding Receiver (NYFR) in conjunction with the Analytic Wavelet Transform. The NYFR performs analog compression via a non-uniform sampling process that induces a chirp-like modulation on each received signal. This induced modulation can be measured using time-frequency analysis techniques to determine the original RF band of origin without full signal reconstruction. This paper investigates the feasibility of using the Analytic Wavelet Transform to perform NYFR information recovery in support of CR wideband spectrum sensing.

Cross-layer throughput optimization using adaptive PHY/MAC layer techniques: A unified approach

This article develops a unified mathematical framework for maximization of the user throughput over generalized wireless channels using the symbol rate, packet length and constellation size of two distinct classes of digital modulation schemes (M-PSK and M-QAM) as optimization variables. First, we show that the throughput optimization problem for truncated selective-repeat automatic repeat request (SR-ARQ) is identical to that of no retransmission case ( NRMAX = 0 ) or the conventional SR-ARQ ( NRMAX = ∞ ) protocol that guarantees the end-to-end delivery of packet. Subsequently, we derive optimization equations for each of the above degrees of freedom in closed-form. A simple algorithm for triplet-parameter optimization is also presented. Numerical results reveal that it is sufficient to adapt symbol rate alone in the low average signal-to-noise (SNR) regime while joint optimization of both the packet length and the constellation size parameters is required in the high average SNR regime, to achieve maximum throughput in a myriad of wireless fading environments.

Adaptive multiresolution modulation for multimedia traffic in dynamic wireless environment

Modern day wireless systems requires the ability to support multitude of services with different reliability requirements. Challenges of achieving reliable multimedia services include limited battery resources at mobile nodes, coupled with hostile propagation environments. We believe that adaptive signaling techniques can be designed to take advantage of differences in the quality of service (QoS) requirements among different types of multimedia traffic besides improving spectral efficiency. Furthermore, we also demonstrate that it is essential to have a readily invertible equation for different multiresolution modulation types in order to automatically execute an Adaptive Multiresolution Modulation (AMM) scheme. Exponential approximation was used for generating invertible expression for asymmetrical quadrature amplitude modulation. We also generated the curve fitting approximations for the average BER probability and individual BER for 4-PSK, 8-PSK, 16-QAM and 64-QAM by using the complementary error function approximation. In this article, we demonstrate the efficacy of the complimentary error function approximation as a better curve fitting approximation in comparison to exponential approximation. We also illustrated the benefits that can be gained from using the adaptive multiresolution modulation.