In this work, copula models for fitting bivariate response data with Weibull marginal distributions are studied, which are motivated by the need of model fading channels in signal applications. The analytical expressions for the joint probability density function (p.d.f.), and joint cumulative distribution function (c.d.f.) are utilized as the bivariate distribution of the fading channels data with not necessarily identical fading parameters and average powers. The performances of outage probability employing diversity receivers, called as selection combining (SC), equal-gain combining (EGC), and maximal-ratio combining (MRC) of two diversity receivers under bivariate copula models with Weibull marginal distributions are presented. They are also compared with the results in Sagias (2005) where the data assumed to follow the bivariate Weibull distribution. It will be demonstrated that the copula models can approximate the bivariate Weibull distribution used in Sagias (2005) very closely with suitable copula model, and the computations for obtaining the performances of outage probability under SC are much simplified. Keywords and phrases: equal-gain combining, maximal-ratio combining, selection combining

ITC/USA 2010 Conference Proceedings / The Forty-Sixth Annual International Telemetering Conference and Technical Exhibition / October 25-28, 2010 / Town and Country Resort & Convention Center, San Diego, California / This work explores aeronautical telemetry communication performance with the SOQPSK- TG ARTM waveforms when frequency-selective multipath corrupts received information symbols. A multi-antenna equalization scheme is presented where each antenna's unique multipath channel is equalized using a pilot-aided optimal linear minimum mean-square error filter. Following independent channel equalization, a maximal ratio combining technique is used to generate a single receiver output for detection. This multi-antenna equalization process is shown to improve detection performance over maximal ratio combining alone.

In the cooperative communications, the users relay each other¡¦s signal and thus forming multiple transmission paths to the destination and therefore the system can achieve spatial diversity gain. Decode-and-forward and amplify-and-forward are the most popular relaying strategies in the literature due to their simplicity. However, in practice, cooperative users acting as relays may not always normally operated or trustworthy. When the relay misbehavior is present in the cooperative networks, the communication performance may degrade dramatically and the users may be even better off without cooperation. Therefore, it is necessary for the destination to determine the misbehaving relays and to take appropriate actions to ensure that cooperative advantages are preserved. In this thesis, we focus on developing a misbehaving relay detection method to detect whether or not the system is in the presence of some misbehaving relays. After performing misbehaving relay detection, the destination removes the signals from the un- reliable paths and then uses maximal ratio combing to achieve spatial diversity. The simulation results conducted by the thesis show that the proposed method is more robust as compared with those without employing misbehaving relay detection when the system is in the presence of some misbehaving relays.

In the cooperative communications, the users relay each other's signal and thus form multiple transmission paths to the destination and therefore the system can achieve spatial diversity gain. Most studies in the literature assumed that cooperative users acting as the relays are normally operated and trustworthy. However, this may not always be true in practice. When the relay misbehaviors are present in the cooperative communications, the communication performance may degrade dramatically and the users may be even better off without cooperation. Therefore, it is necessary for the destination to determine the misbehaving relays and to take appropriate actions to ensure that cooperative advantages are preserved. This thesis considers both models in which the cooperative communications are with direct path (WDP) and without direct path (WODP). Utilizing the proposed Kolmogorov-Smirnov test mechanism, the destination identifies the misbehaving relays within the cooperative communications and then excludes their transmitting messages when performing the diversity combining to infer the symbols of interest sent by the source. In addition, this thesis provides the bit error rate (BER) analysis of the cooperative communications employing the proposed misbehaving relay detectors. The simulation results demonstrate that the proposed methods have robust performance when the relay misbehaviors are present in the cooperative communications.

Approved for public release; distribution is unlimited. / In military operations, covertness of operation is of paramount importance. The transmission power of the data link must be kept to the minimum to maintain a low probability of detection (LPD) from the adversary. However, a reduction in the transmitted power implies a reduction in the operating range, though the detection range by the enemy is also reduced. Therefore, to reduce the enemy’s detection range while maintaining operating distance, this thesis explores strategies to discriminate gain against an adversary’s sensor. The strategies involve using processing gain, directional antennas, polarization and the natural environment as a transmission shield. The processing gain strategy analyzed in this thesis uses a diversity technique called Maximal Ratio Combining (MRC) applied to an IEEE 802.16a link. Sinclair D. Smith carried out a study on the possible processing gain derivable from this technique and this thesis will bring his results to practical applications via link analyses. In the event that the link is detected and the enemy decides to carry out jamming, the thesis explores a possible anti-jamming (AJ) strategy by using MRC and a directional antenna. Daniel P. Zastrow carried out a study on the AJ capability of MRC and this thesis brings his results to practical applications via link analyses. / Major, Republic of Singapore Airforce

This report, presents an analytical framework for analyzing two-branch diversity systems for a Rayleigh fading channel. In many cases the fading received at both branches (i.e. a two-antenna element system) is correlated because of the proximity of the antenna elements to each other. It is also not uncommon for a diversity system to use antennas with different patterns or polarizations, this usually results in differences in average signal-to-noise ratios at both branches depending on which element is better matched to the signal environment. As will be shown, the performance of a diversity system depends greatly on the envelope correlation, average power imbalance and the combining scheme used on both branches. An analytical expression for the probability density function of the signal-to-noise ratio at the output of a two-branch maximal ratio and selection diversity system is developed in this report. The two branches are assumed to be Rayleigh fading, correlated, as well as of unequal signal-to-noise ratios. Measurements were made in Rayleigh fading channels and compared to the analytical results. The analytical cumulative distribution functions (derived using probability distributions) were found to be within 1 dB of the measured results (statistics obtained from time combining) for both maximal ratio and selection diversity attesting to the validity of the analytic results. Also developed in this report are the exact analytical average probabilities of symbol error for coherent BPSK and coherent QPSK before and after maximal ratio combining for this environment. The diversity gain for selection, maximal ratio, and equal gain combining for the 10% probability level is presented as a function of power imbalance and correlation between branches for a two-branch Rayleigh diversity system / Master of Science

Recently multiple antenna systems have received significant attention from researchers as a means to improve the energy and spectral efficiency of wireless systems. Among many classes of schemes, Space-Time Block codes (STBC) and Space-Time Trellis codes (STTC) have been the subject of many investigations. Both techniques provide a means for combatting the effects of multipath fading without adding much complexity to the receiver. This is especially useful in the downlink of wireless systems. In this thesis we investigate the impact of channel estimation error on the performance of both STBC and STTC. Channel estimation is especially important to consider in multiple antenna systems since (A) for coherent systems there are more channels to estimate due to multiple antennas and (B) the decoupling of data streams relies on correct channel estimation. The latter effect is due to the intentional cross-talk introduced into STBC. / Master of Science

Mobile arrays employing diversity combining and adaptive beamforming techniques overcome multipath fading, improve coverage, and increase capacity in wireless communications systems. In this thesis, diversity combining and adaptive beamforming performance of different four element arrays for mobile (vehicular speed) and portable (pedestrian speed) terminals is investigated. The performance of four element arrays with different configurations and with different element patterns is compared using the square array of four half-wave dipole elements as the baseline. Results from diversity and beamforming measurements, performed in urban and suburban environments for both line-of-sight (LOS) and obstructed multipath channels are used to analyze and compare the performances of different four element arrays. At cumulative probabilities of 10%, 1% and 0.1%, diversity gain and improvement in signal-to-interference-plus-noise-ratio (SINR) are calculated from the diversity combining measurements and interference rejection measurements respectively. Experimental results illustrating the dependence of diversity gain on power imbalance, envelope correlation and diversity-combining scheme are presented. Measurements were performed at 2.05 GHz using the handheld antenna array testbed (HAAT). Low profile linear arrays are shown to provide diversity gain values of 5 to 8 dB and 11 to 16 dB, respectively for switched and maximal ratio combining at the 99% reliability level in non-line-of-sight urban channel. Interference cancellation of 24 to 28 dB was recorded in urban and suburban line-of-sight (LOS) channels for the sectorized square array. Results of vehicular measurements with the arrays mounted on a ground plane supported above the vehicle roof are also reported. / Master of Science

There has been phenomenal interest in applying space-time coding techniques in wireless communications in the last two decades. In general, the benefit of applying space-time codes in multiple-input, multiple-output (MIMO) wireless channels is an increase in transmission reliability or system throughput (capacity). However, such a benefit cannot be obtained in some wireless systems where size or other constraints preclude the use of multiple antennas. As such, wireless relay communications has recently been proposed as a means to provide spatial diversity in the face of this limitation. In this approach, some users or relay nodes assist the transmission of other users information. This dissertation contributes to the advancement of wireless relay communications by investigating the performance of various relaying signal processing methods under different practical fading environments. In particular, it examines two main relaying methods, namely decode-and-forward (DF) and amplify-and-forward (AF).<p> For DF, the focus is on the diversity analysis of relaying systems under various practical protocols when detection error at relays is taken into account. In order to effectively mitigate the phenomenon of error propagation, the smart relaying technique proposed by Wang et al. in [R1] is adopted. First, diversity analysis of a single-relay system under the scenario that only the relay is allowed to transmit in the second time slot (called Protocol II) is carried out. For Nakagami and Hoyt generalized fading channels, analytical and numerical results are provided to demonstrate that the system always obtains the maximal diversity when binary phase shift keying (BPSK) modulation is used. Second, a novel and low-complexity relaying system is proposed when smart relaying and equal gain combing (EGC) techniques are combined. In the proposed system, the destination requires only the phases of the channel state information in order to detect the transmitted signals. For the single-relay system with M-ary PSK modulation, it is shown that the system can achieve the maximal diversity under Nakagami and Hoyt fading channels. For the K-relay system, simulation results suggest that the maximal diversity can also be achieved. Finally, the diversity analysis for a smart relaying system under the scenario when both the source and relay are permitted to transmit in the second time slot (referred to as Protocol I) is presented. It is shown that Protocol I can achieve the same diversity order as Protocol II for the case of 1 relay. In addition, the diversity is very robust to the quality of the feedback channel as well as the accuracy of the quantization of the power scaling implemented at the relay.<p> For AF, the dissertation considers a fixed-gain multiple-relay system with maximal ratio combining (MRC) detection at the destination under Nakagami fading channels. Different from the smart relaying for DF, all the channel state information is assumed to be available at the destination in order to perform MRC for any number of antennas. Upperbound and lowerbound on the system performance are then derived. Based on the bounds, it is shown that the system can achieve the maximal diversity. Furthermore, the tightness of the upperbound is demonstrated via simulation results. With only the statistics of all the channels available at the destination, a novel power allocation (PA) is then proposed. The proposed PA shows significant performance gain over the conventional equal PA.

There has been phenomenal interest in applying space-time coding techniques in wireless communications in the last two decades. In general, the benefit of applying space-time codes in multiple-input, multiple-output (MIMO) wireless channels is an increase in transmission reliability or system throughput (capacity). However, such a benefit cannot be obtained in some wireless systems where size or other constraints preclude the use of multiple antennas. As such, wireless relay communications has recently been proposed as a means to provide spatial diversity in the face of this limitation. In this approach, some users or relay nodes assist the transmission of other users information. This dissertation contributes to the advancement of wireless relay communications by investigating the performance of various relaying signal processing methods under different practical fading environments. In particular, it examines two main relaying methods, namely decode-and-forward (DF) and amplify-and-forward (AF).<p> For DF, the focus is on the diversity analysis of relaying systems under various practical protocols when detection error at relays is taken into account. In order to effectively mitigate the phenomenon of error propagation, the smart relaying technique proposed by Wang et al. in [R1] is adopted. First, diversity analysis of a single-relay system under the scenario that only the relay is allowed to transmit in the second time slot (called Protocol II) is carried out. For Nakagami and Hoyt generalized fading channels, analytical and numerical results are provided to demonstrate that the system always obtains the maximal diversity when binary phase shift keying (BPSK) modulation is used. Second, a novel and low-complexity relaying system is proposed when smart relaying and equal gain combing (EGC) techniques are combined. In the proposed system, the destination requires only the phases of the channel state information in order to detect the transmitted signals. For the single-relay system with M-ary PSK modulation, it is shown that the system can achieve the maximal diversity under Nakagami and Hoyt fading channels. For the K-relay system, simulation results suggest that the maximal diversity can also be achieved. Finally, the diversity analysis for a smart relaying system under the scenario when both the source and relay are permitted to transmit in the second time slot (referred to as Protocol I) is presented. It is shown that Protocol I can achieve the same diversity order as Protocol II for the case of 1 relay. In addition, the diversity is very robust to the quality of the feedback channel as well as the accuracy of the quantization of the power scaling implemented at the relay.<p> For AF, the dissertation considers a fixed-gain multiple-relay system with maximal ratio combining (MRC) detection at the destination under Nakagami fading channels. Different from the smart relaying for DF, all the channel state information is assumed to be available at the destination in order to perform MRC for any number of antennas. Upperbound and lowerbound on the system performance are then derived. Based on the bounds, it is shown that the system can achieve the maximal diversity. Furthermore, the tightness of the upperbound is demonstrated via simulation results. With only the statistics of all the channels available at the destination, a novel power allocation (PA) is then proposed. The proposed PA shows significant performance gain over the conventional equal PA.