Nandana Rajatheva

Energy Detection of Unknown Signals in Fading and Diversity Reception

A comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed. For the no-diversity case and for the maximal ratio combining (MRC) diversity case, with either Nakagami-m or Rician fading, expressions for the probability of detection are derived by using the moment generating function (MGF) method and probability density function (PDF) method. The former, which avoids some difficulties of the latter, uses a contour integral representation of the Marcum-Q function. For the equal gain combining (EGC) diversity case, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2,3,4 and L >; 4, where L is the number of diversity branches. For the selection combining (SC) diversity, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2 and L >; 2. A discussion on the comparison between MGF and PDF methods is presented. We also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy. These results help quantify and understand the achievable improvement in the energy detectors performance with diversity reception. Numerical and simulation results are also provided.

Linear estimation of correlated data in wireless sensor networks with optimum power allocation and analog modulation

In this paper, we study the energy-efficient distributed estimation problem for a wireless sensor network where a physical phenomena that produces correlated data is sensed by a set of spatially distributed sensor nodes and the resulting noisy observations are transmitted to a fusion center via noise- corrupted channels. We assume a Gaussian network model where (i) the data samples being sensed at different sensors have a correlated Gaussian distribution and the correlation matrix is known at the fusion center, (ii) the links between the local sensors and the fusion center are subject to fading and additive white Gaussian noise (AWGN), and the fading gains are known at the fusion center, and (iii) the central node uses the squared error distortion metric. We consider two different distortion criteria: (i) individual distortion constraints at each node, and (ii) average mean square error distortion constraint across the network. We determine the achievable power-distortion regions under each distortion constraint. Taking the delay constraint into account, we investigate the performance of an uncoded transmission strategy where the noisy observations are only scaled and transmitted to the fusion center. At the fusion center, two different estimators are considered: (i) the best linear unbiased estimator (BLUE) that does not require knowledge of the correlation matrix, and (ii) the minimum mean- square error (MMSE) estimator that exploits the correlations. For each estimation method, we determine the optimal power allocation that results in a minimum total transmission power while satisfying some distortion level for the estimate (under both distortion criteria). The numerical comparisons between the two schemes indicate that the MMSE estimator requires less power to attain the same distortion provided by the BLUE and this performance gap becomes more dramatic as correlations between the observations increase. Furthermore, comparisons between power-distortion region achieved by the theoretically optimum system and that achieved by the uncoded system indicate that the performance gap between the two systems becomes small for low levels of correlation between the sensor observations. If observations at all sensor nodes are uncorrelated, the uncoded system with MMSE estimator attains the theoretically optimum system performance.An exact expression for the joint density of three correlated Rician variables is not available in the open literature. In this letter, we derive new infinite series representations for the trivariate Rician probability density function (pdf) and the joint cumulative distribution function (cdf). Our results are limited to the case where the inverse covariance matrix is tridiagonal. This case seems the most general one that is tractable with Miller¿s approach and cannot be extended to more than three Rician variables. The outage probability of triple branch selective combining (SC) receiver over correlated Rician channels is presented as an application of the density function.

Analysis of Equal Gain Combining in Energy Detection for Cognitive Radio over Nakagami Channels

This paper addresses the problem of energy detection of unknown deterministic signal of a primary user in a cognitive radio environment. As an extension to the previous works, we focus on equal gain combining technique when the wireless channel is modeled as Nakagami-m. We derive series form exact expressions for probability of detection and false alarm when the number of diversity branches are 1, 2, 3 and L ges 4. Finally, performance variation is shown against the number of diversity branches and the time bandwidth product in decision statistic with the aid of numerical results.

On the energy detection of unknown deterministic signal over Nakagami channelswith selection combining

Blind sensing for identifying unused frequency bands is of particular interest in cognitive radio and ultra wide-band applications. Energy detection is one such method proposed to identify the presence of an unknown band-limited deterministic signal. In this paper, by using an alternative series representation of the Marcum-Q function, the exact average detection probability over the Nakagami-m fading channel is derived. Moreover, we formulate the decision variable of a selection diversity combined energy detector and derive the exact average detection and false alarm probabilities.

An exact error probability analysis of OFDM systems with frequency offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for OFDM systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in frequency flat Rayleigh fading channel with BPSK and QPSK modulation schemes. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions

Unified Approach for Energy Detection of Unknown Deterministic Signal in Cognitive Radio Over Fading Channels

Detection of an unknown deterministic signal by using an energy detector is of promising for cognitive radio networks. In this paper, a new approach is proposed to analyze the performance of the energy detector. It is based on the contour integral representation of the Marcum-Q function and the use of the moment generating function (MGF) of the signal-to-noise ratio (SNR). A new decision variable is constructed for the case of maximal ratio combining (MRC) reception. With its help and the MGF based approach, the performance of the MRC energy detector over i.i.d. Rician fading channels is analyzed. This case is intractable with the conventional probability density function (PDF) based approach. Further the detection probability of MRC combined energy detector over Nakagami-m fading branches is derived. The simulation results are presented to support the developed MGF based method, decision variable formulation and derivations. The detector performance is evaluated over different fading and diversity parameters with the help of numerical and simulation examples. I. INTRODUCTION Cognitive radio technology allows unlicensed users (sec- ondary users) to dynamically use unoccupied free spectrum bands of primary users (licensed users), while avoiding in- terference to primary users. Energy detection can be used to explore the presence of primary user transmissions and hence to identify the available spectrum holes. When using this technique, the energy detector of the secondary user treats the received primary user transmission as an unknown deterministic signal. Hence, secondary users do not requires unauthorized, irrelevant details of the primary transmissions. Due to this application, the performance of the energy detector using diversity reception techniques and over various wireless fading environments is of interest. The technique of detecting an unknown deterministic signal by using an energy detector is introduced in (1). It is shown that the detection problem is a test of binary hypotheses and statistics of the decision variable is chi-square distributed, irre- spective of whether the process model is lowpass or bandpass. Kostylev (2) extends the formulation to fading channels. In his work, average detection (Pd) and false alarm (Pf ) probabilities over Rayleigh, Rician and Nakagami-m fading channels are presented. But the Nakagami-m channel result is limited to an integral form expression. In (3) Nakagami-m and Rician fading channels are considered. But the derivation of Nakagami-m is restricted to integer values of the shape parameter (m) while the result of Rician fading channel is limited to unity time bandwidth product (u) in the decision variable. Maximal ratio, selection and switch and stay diversity detectors are analyzed over i.i.d. Rayleigh fading channels in (3). Expressions of Pd over i.i.d. and correlated Rayleigh fading channels with square-law combining is derived in

Unified Performance Analysis of Two-Hop Amplify-and-Forward Relay Systems with Antenna Correlation

We present a unified performance analysis of a system in which the source and the destination are equipped with multiple antennas and communicating via a single antenna relay. Our studies can be divided into two parts. First we consider a system with maximal ratio transmission (MRT) at the source and maximal ratio combining (MRC) at the destination by assuming general correlation structures with arbitrary eigenvalue multiplicities at the source and the destination. Then a system with transmit antenna selection (TAS) at the source with uncorrelated antennas and MRC at the destination with correlated antennas is investigated. The exact closed form expressions for outage probability, average symbol error rate (SER), generalized higher moments of SNR for both channel state information (CSI)-assisted and fixed gain relaying are derived and an analysis of the ergodic capacity is provided. Hence, our new results cover several previously reported cases as well as new additional ones. Further, we present the asymptotic analysis which gives an insight of the system performance and the diversity gain in each case. To verify the analytical results we provide Monte Carlo simulations at the end.

Infinite series representations of the trivariate and quadrivariate nakagami-m distributions

In this paper, we derive new infinite series representations for the quadrivariate Nakagami-m distribution and cumulative distribution functions (cdf). we make use of the Millers approach and the Dougalls identity to derive the joint density function. The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of our joint density function. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function and cdf for an arbitrary correlation matrix is also derived from our main result. Bounds on the error resulting from truncation of the infinite series are also presented. Finally, numerical results are presented to verify the accuracy of our formulation.

Envelope and phase distribution of two correlated gaussian variables

Probability density functions (pdfs) are derived for the phase and amplitude (envelope) of the complex gain X +jY (j = radic-1), where X and Y are two correlated non zero-mean Gaussian random variables. The pdf of the amplitude is derived as an infinite series, but reduces to a closed-form expression when the means are zero. The classical Rayleigh and Rician pdfs turn out to be special cases of the derived pdf. This pdf is used to analyze the error performance of non-coherent binary frequency shift keying (BFSK) with in-phase/quadrature(I/Q) imbalance over an additive white Gaussian noise (AWGN) channel. The resulting bit error rate (BER) expression is derived as an infinite series. The analytical expressions are validated by simulation, and the I/Q imbalance related performance degradation is quantified. Convergence of the PDF series and the BER series is established.

Dynamic spreading code selection method for PAPR reduction in OFDM-CDMA systems with 4-QAM modulation

We present a new dynamic spreading code selection technique to obtain low peak-to-average-power ratio (PAPR) of an orthogonal frequency-division multiplexing code-division multiple-access (OFDM-CDMA) system with 4-QAM modulation for the down-link in mobile communication. In this method, initially, each user is assigned a low and a high PAPR spreading code, which allows selecting one when the system is operating. The spreading code of each user is dynamically selected so that total PAPR level of the whole user group present in the system is minimized. With the proposed technique, the PAPR level of a system with 10 users and 64 sub-carriers using 64 chip Walsh-Hadamard (WH) codes, can be limited to 15 dB while the worst case theoretical maximum could go up to 28.1 dB. Although 64 chip WH codes are employed to evaluate the performance it can be generalized to all other sets of spreading codes.