Manav R. Bhatnagar

Cooperative Spectrum Sensing in Multiple Antenna Based Cognitive Radio Network Using an Improved Energy Detector

Performance of cooperative spectrum sensing with multiple antennas at each cognitive radio (CR) is discussed in this paper. The CRs utilize selection combining of the decision statistics obtained by an improved energy detector for making a binary decision of the presence or absence of a primary user (PU). The improved energy detector uses an arbitrary positive power p of amplitudes of samples of the PUs signals. The decision of each CR is orthogonally forwarded over imperfect reporting channels to a fusion center, which takes the final decision of a spectrum hole. We derive expressions of the probabilities of false alarm and missed detection of the proposed cooperative spectrum sensing scheme. By minimizing the total error rate (sum of the probability of missed detection and the probability of false alarm) we derive a closed-form solution of the optimal number of CRs required for cooperation. It is shown by simulations that by using multiple antennas at the CRs, it is possible to significantly improve reliability of spectrum sensing with extremely low interference levels to the PU at very low (much less than 0 dB) signal-to-noise ratio of the PU-CR link.

Performance Analysis of Decode-and-Forward Relaying in Gamma-Gamma Fading Channels

We analyze performance of the decode-and-forward (DF) protocol in the free space optical (FSO) links following the Gamma-Gamma distribution. The cumulative distribution function (cdf) and probability density function (pdf) of a random variable containing mixture of the Gamma-Gamma and Gaussian random variables is derived. By using the derived cdf and pdf, average bit error rate of the DF relaying is obtained.

Performance Analysis of AF Based Hybrid Satellite-Terrestrial Cooperative Network over Generalized Fading Channels

In this paper, the transmission of signals in a hybrid satellite-terrestrial link is considered. In particular, we address the problem of amplify-and-forward (AF) relaying in a hybrid satellite-terrestrial link, where a masked destination node receives the relayed transmission from a terrestrial link and direct transmission from the satellite link. The satellite-relay and satellite-destination links are assumed to follow the Shadowed-Rician fading; and the channel of the terrestrial link between the relay and destination is assumed to follow the Nakagami-m fading. The average symbol error rate of the considered AF cooperative scheme for M-ary phase shift keying constellation is derived for these generalized fading channels. Moreover, analytical diversity order of the hybrid system is also obtained.

On the Capacity of Decode-and-Forward Relaying over Rician Fading Channels

In this letter, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the minimum of two non-central Chi-square random variables with two degrees of freedom in terms of power series. With the help of the derived PDF and CDF, we obtain the exact ergodic capacity of the following adaptive protocols in a {decode-and-forward} (DF) cooperative system over dissimilar {Rician} fading channels: (i) constant power with optimal rate adaptation; (ii) optimal simultaneous power and rate adaptation; (iii) channel inversion with fixed rate. By using the analytical expressions of the capacity, it is observed that the optimal power and rate adaptation provides better capacity than the optimal rate adaptation with constant power from low to moderate signal-to-noise ratio values over dissimilar Rician fading channels. Despite low complexity, the channel inversion based adaptive transmission is shown to suffer from significant loss in capacity as compared to the other adaptive transmission based techniques over DF Rician channels.

ML Decoder for Decode-and-Forward Based Cooperative Communication System

Decode-and-forward (DF) protocol based cooperative communication is vulnerable to the erroneous relaying by the relay. In this paper, we derive a maximum-likelihood (ML) decoder for the DF protocol utilizing arbitrary complex-valued constellations including M-PSK, M-PAM, and M-QAM. A set-up of a single pair of source and destination with one relay is studied. The source and the relay utilize orthogonal uncoded transmissions. The relay performs ML decoding and forwards the decoded symbol to the destination, and it might commit errors in decoding the data. The ML decoder at the destination is obtained by maximizing the probability density function (p.d.f.) of the data received during two orthogonal transmissions at the destination under the assumption that the average probability of error of the source-relay link is known at the destination. The proposed ML decoder is a generalized decoder which is applicable to arbitrary constellations, whereas, one existing DF cooperative decoder is applicable to the real valued constellations like BPSK and M-PAM. One existing decoder is also applicable to M2-QAM constellations. We also derive a low-complexity piecewise linear (PL) decoder for arbitrary complex-valued M-point constellations which performs similar to the ML decoder for all signal-to-noise ratio values. An approximate expression of the symbol error rate (SER) of the PL decoder for M-PSK constellation is derived. By using the approximate SER expressions, it is proved that the proposed ML and PL decoders achieve full diversity of two in the cooperative system studied.

Performance of an amplify-and-forward dual-hop asymmetric RF–FSO communication system

In this work, the performance and the capacity analysis of a fixed-gain amplify-and-forward (AF)-based dual-hop asymmetric radio frequency-free space optical (RF-FSO) communication system is performed. The RF link experiences Nakagami-m fading and the FSO link experiences Gamma-Gamma turbulence. For this mixed RF-FSO cooperative system, novel and finite power series-based mathematical expressions for the cumulative distribution function, probability density function, and moment generating function of the end-to-end signal-to-noise ratio are derived. Using these channel statistics new finite power series-based analytical expressions are obtained for the outage probability, the average bit error rate (BER) for various binary and M-ary modulation techniques, and the average channel capacity of the considered system. The same analysis is also performed for the scenario when the FSO link undergoes significant pointing errors along with the Gamma-Gamma distributed turbulence. As a special case analytical expressions for the outage probability, BER, and channel capacity are also presented for a dual-hop asymmetric RF-FSO system where the RF link is Rayleigh distributed. Simulation results validate the proposed mathematical analysis. The effects of fading, turbulence, and pointing error are studied on the outage probability, average BER, and the channel capacity.

Beamforming and Combining in Hybrid Satellite-Terrestrial Cooperative Systems

In this paper, we consider the transmission of signals in a hybrid satellite-terrestrial cooperative system. In particular, we address the problem of beamforming and combining based amplify-and-forward (AF) relaying in a hybrid satellite-terrestrial cooperative system. In this set-up, a multiple antenna based relay node forwards the received satellite signals to the destination, by using a beamforming vector, and multiple antenna based destination node uses maximal ratio combining. The approximate average symbol error rate of the considered beamforming and combining based hybrid AF cooperative scheme for M-ary phase shift keying constellation is derived; analytical diversity order of the hybrid system is also obtained. Moreover, diversity calculations for some specific antenna configurations are shown for providing useful insight of the proposed scheme, at high signal-to-noise ratio.

Decode-and-Forward-Based Differential Modulation for Cooperative Communication System With Unitary and Nonunitary Constellations

In this paper, we derive a maximum-likelihood (ML) decoder of the differential data in a decode-and-forward (DF)-based cooperative communication system utilizing uncoded transmissions. This decoder is applicable to complex-valued unitary and nonunitary constellations suitable for differential modulation. The ML decoder helps to improve the diversity of the DF-based differential cooperative system using an erroneous relaying node. We also derive a piecewise linear (PL) decoder of the differential data transmitted in the DF-based cooperative system. The proposed PL decoder significantly reduces the decoding complexity, as compared with the proposed ML decoder, with no significant degradation in the receiver performance. Existing ML and PL decoders of the differentially modulated uncoded data in the DF-based cooperative communication system are only applicable to binary modulated signals like binary phase shift keying and binary frequency shift keying, whereas the proposed decoders are applicable to complex-valued unitary and nonunitary constellations suitable for differential modulation under uncoded transmissions. We derive a closed-form expression of the uncoded average symbol error rate (SER) of the proposed PL decoder with M phase-shift keying constellation in a cooperative communication system with a single relay and one source-destination pair. An approximate average SER by ignoring higher order noise terms is also derived for this setup. It is analytically shown on the basis of the derived approximate SER that the proposed PL decoder provides full diversity of second order. In addition, we also derive the approximate SER of the differential DF system with multiple relays at asymptotically high signal-to-noise ratio (SNR) of the source-relay links. It is shown by simulations that the proposed PL decoder in the differential DF cooperative system with more than one relay also achieves the maximum possible diversity.

On the Closed-Form Performance Analysis of Maximal Ratio Combining in Shadowed-Rician Fading LMS Channels

In this paper, the maximal ratio combining (MRC) scheme in Shadowed-Rician (SR) fading land mobile satellite (LMS) channels is studied. The MRC scheme for SR fading LMS channels has been studied in existing literature; however, most of the existing analytical results are in the form of infinite power series, which are not in closed-form. In this paper, we derive approximate closed-form expressions of the probability density function and cumulative distribution function of the received signal-to-noise ratio of the MRC based receiver in SR fading LMS channels. Then we provide approximate closed-form expressions of the bit error rate (BER), outage probability, and capacity of the considered scheme. One of the derived closed-form BER expressions is found useful for obtaining the analytical diversity order and coding gain of the considered MRC scheme.

Average BER Analysis of Differential Modulation in DF Cooperative Communication System over Gamma-Gamma Fading FSO Links

In this letter, we study differential modulation for decode-and-forward (DF) based free space optical (FSO) cooperative communication system over Gamma-Gamma fading channels. We derive exact bit error rate (BER) of the differential DF FSO system in terms of power series. The diversity order and coding gain of the differentially modulated DF FSO system are analytically obtained. It is demonstrated by analysis and simulation that the differential DF FSO system is able to achieve significant performance gain over a non-cooperative direct transmission based differential FSO system.