A General Framework for Performance Analysis of Space Shift Keying (SSK) Modulation for MISO Correlated Nakagami-m Fading Channels

International audienceIn this paper, we offer an accurate framework for analyzing the performance of wireless communication systems adopting the recently proposed Space Shift Keying (SSK) modulation scheme. More specifically, we study the performance of a Nt×1 MISO (Multiple–Input–Single–Output) system setup with Maximum–Likelihood (ML) detection and full Channel State Information (CSI) at the receiver. The exact Average Bit Error Probability (ABEP) over generically correlated and non–identically distributed Nakagami–m fading channels is computed in closed–form when Nt=2, while very accurate and asymptotically tight upper bounds are proposed to compute the ABEP when Nt>2. With respect to current literature, our contribution is threefold: i) the ABEP is computed in closed–form without resorting to Monte Carlo numerical simulations, which, besides being computationally intensive, only yield limited insights about the system performance and cannot be exploited for a systematic optimization of it, ii) the framework accounts for arbitrary fading conditions and is not restricted to identically distributed fading channels, thus offering a comprehensive under standing of the performance of SSK modulation over generalized fading channels, and iii) the analytical framework could be readily adapted to study the performance over generalized fading channels with arbitrary fading distributions, since the Nakagami–m distribution is a very flexible fading model, which either includes or can closely approximate several other fading models. Numerical results show that the performance of SSK modulation is significantly affected by the characteristics of fading channels, e.g., channel correlation, fading severity, and power imbalance among the Nt transmit–receive wireless links. Analytical frameworks and theoretical findings are also substantiated via Monte Carlo simulations

Space Shift Keying (SSK) Modulation With Partial Channel State Information: Optimal Detector and Performance Analysis Over Fading Channels

International audienceSpace Shift Keying (SSK) modulation is a new and recently proposed transmission technology for Multiple–Input–Multiple–Output (MIMO) wireless systems, which has been shown to be a promising low–complexity alternative to several state–of–the–art MIMO schemes. So far, only optimal or heuristic transceivers with Full Channel State Information (F–CSI) at the receiver have been investigated, and their performance analyzed over fading channels. In this paper, we develop and study the performance of the optimal Maximum–Likelihood (ML) detector with unknown phase reference at the receiver (i.e., Partial–CSI, P–CSI, knowledge). A very accurate analytical framework for the analysis and optimization of this novel detector over generically correlated and non–identically distributed Nakagami–m fading channels is proposed, and its performance compared to the optimal receiver design with F–CSI. Numerical results will point out that: i) the performance of SSK modulation is significantly affected by the characteristics of fading channels, e.g., channel correlation, fading severity, and, particularly, power imbalance among the transmit–receive wireless links, and ii) unlike ordinary modulation schemes, there is a substantial performance loss when the receiver cannot exploit the phase information for optimal receiver design. This latter result highlights the importance of accurate and reliable channel estimation mechanisms for the efficient operation of SSK modulation over fading channels. Analytical frameworks and theoretical findings will also be substantiated via Monte Carlo simulations

Generation of bivariate Nakagami-m fading envelopes with arbitrary not necessary identical fading parameters

[EN] In this paper, a generation procedure of two correlated Nakagami-m random variables for arbitrary fading parameters values (not necessary identical) is described. For the generation of two correlated Nakagami-m samples, the proposed method uses the generalized Rice distribution, which appears in the conditional distribution of two correlated Nakagami-m variables. This procedure can be applied to simulate diversity systems such as selection combiners, equal-gain combiners, and maximal-ratio combiners as well as multiple-input multipleoutput (MIMO) receiver systems, in Nakagami-m channels.Contract/grant sponsor: Generalitat Valenciana; contract/grant number: GV04B/357.Reig, J.; Martínez Amoraga, MÁ.; Rubio Arjona, L. (2007). Generation of bivariate Nakagami-m fading envelopes with arbitrary not necessary identical fading parameters. Wireless Communications and Mobile Computing. 7(4):531-537. https://doi.org/10.1002/wcm.386S5315377

On the Bivariate Nakagami-Lognormal Distribution and Its Correlation Properties

The bivariate Nakagami-lognormal distribution used to model the composite fast fading and shadowing has been examined exhaustively. In particular, we have derived the joint probability density function, the cross-moments, and the correlation coefficient in power terms. Also, two procedures to generate two correlated Nakagami-lognormal random variables are described. These procedures can be used to evaluate the robustness of the sample correlation coefficient distribution in both macro- and microdiversity scenarios. It is shown that the bias and the standard deviation of this sample correlation coefficient are substantially high for large shadowing standard deviations found in wireless communication measurements, even if the number of observations is considerable.This work was supported by the Spanish Ministerio de Ciencia e Innovacion TEC-2010-20841-C04-1.Reig, J.; Rubio Arjona, L.; Rodrigo Peñarrocha, VM. (2014). On the Bivariate Nakagami-Lognormal Distribution and Its Correlation Properties. International Journal of Antennas and Propagation. 2014:1-8. https://doi.org/10.1155/2014/328732S182014Rubio, L., Reig, J., & Cardona, N. (2007). Evaluation of Nakagami fading behaviour based on measurements in urban scenarios. AEU - International Journal of Electronics and Communications, 61(2), 135-138. doi:10.1016/j.aeue.2006.03.004Suzuki, H. (1977). A Statistical Model for Urban Radio Propogation. IEEE Transactions on Communications, 25(7), 673-680. doi:10.1109/tcom.1977.1093888Abu-Dayya, A. A., & Beaulieu, N. C. (1994). Micro- and macrodiversity NCFSK (DPSK) on shadowed Nakagami-fading channels. IEEE Transactions on Communications, 42(9), 2693-2702. doi:10.1109/26.317410Tjhung, T. T., & Chai, C. C. (1999). Fade statistics in Nakagami-lognormal channels. IEEE Transactions on Communications, 47(12), 1769-1772. doi:10.1109/26.809692Shankar, P. M. (2004). Error Rates in Generalized Shadowed Fading Channels. Wireless Personal Communications, 28(3), 233-238. doi:10.1023/b:wire.0000032253.68423.86Atapattu, S., Tellambura, C., & Jiang, H. (2011). A Mixture Gamma Distribution to Model the SNR of Wireless Channels. IEEE Transactions on Wireless Communications, 10(12), 4193-4203. doi:10.1109/twc.2011.111210.102115Reig, J., & Rubio, L. (2013). Estimation of the Composite Fast Fading and Shadowing Distribution Using the Log-Moments in Wireless Communications. IEEE Transactions on Wireless Communications, 12(8), 3672-3681. doi:10.1109/twc.2013.050713.120054Mukherjee, S., & Avidor, D. (2003). Effect of microdiversity and correlated macrodiversity on outages in a cellular system. IEEE Transactions on Wireless Communications, 2(1), 50-58. doi:10.1109/twc.2002.806363Zhang, R., Wei, J., Michelson, D. G., & Leung, V. C. M. (2012). Outage Probability of MRC Diversity over Correlated Shadowed Fading Channels. IEEE Wireless Communications Letters, 1(5), 516-519. doi:10.1109/wcl.2012.072012.120452Rui, Z., Jibo, W., & Leung, V. C. M. (2013). Outage probability of composite microscopic and macroscopic diversity over correlated shadowed fading channels. China Communications, 10(11), 129-142. doi:10.1109/cc.2013.6674217Abdel-Hafez, M., & Safak, M. (1999). Performance analysis of digital cellular radio systems in Nakagami fading and correlated shadowing environment. IEEE Transactions on Vehicular Technology, 48(5), 1381-1391. doi:10.1109/25.790511Shankar, P. M. (2009). Macrodiversity and Microdiversity in Correlated Shadowed Fading Channels. IEEE Transactions on Vehicular Technology, 58(2), 727-732. doi:10.1109/tvt.2008.926622MOSTAFA, M. D., & MAHMOUD, M. W. (1964). On the problem of estimation for the bivariate lognormal distribution. Biometrika, 51(3-4), 522-527. doi:10.1093/biomet/51.3-4.522Reig, J., Rubio, L., & Cardona, N. (2002). Bivariate Nakagami-m distribution with arbitrary fading parameters. Electronics Letters, 38(25), 1715. doi:10.1049/el:20021124Tan, C. C., & Beaulieu, N. C. (1997). Infinite series representations of the bivariate Rayleigh and Nakagami-m distributions. IEEE Transactions on Communications, 45(10), 1159-1161. doi:10.1109/26.634675Lien, D., & Balakrishnan, N. (2006). Moments and properties of multiplicatively constrained bivariate lognormal distribution with applications to futures hedging. Journal of Statistical Planning and Inference, 136(4), 1349-1359. doi:10.1016/j.jspi.2004.10.004Sørensen, T. B. (1999). Slow fading cross-correlation against azimuth separation of base stations. Electronics Letters, 35(2), 127. doi:10.1049/el:19990085Reig, J., Martinez-Amoraga, M. A., & Rubio, L. (2007). Generation of bivariate Nakagami-m fading envelopes with arbitrary not necessary identical fading parameters. Wireless Communications and Mobile Computing, 7(4), 531-537. doi:10.1002/wcm.386Lai, C. D., Rayner, J. C. W., & Hutchinson, T. P. (1999). Robustness of the sample correlation - the bivariate lognormal case. Journal of Applied Mathematics and Decision Sciences, 3(1), 7-19. doi:10.1155/s117391269900001

Mobile to mobile channel modelling for wireless communications

Wireless communication has been experiencing many recent advances in mobile to mobile (M2M) applications. M2M communication systems differ from conventional fixed to mobile systems by having both transmitter and receiver in low elevation and in motion. This raises the need to come up with new channel models and perform statistical analysis on M2M communication channels looking from a different perspective. This need motivated us to perform the research outlined in this thesis. In reviewing the literature we found that though in general the M2M channel models are sparse, a major gap exists in the non geometrical stochastic based mathematical channel models. In filling this gap, we develop a novel mathematical non geometrical stochastic multiple input multiple output (MIMO) M2M channel model for two dimensional (2D) and three dimensional (3D) scattering environments. This model is based on the underlying physics of free space wave propagation and can be used as a framework for any environment by selecting suitable complex scattering gain functions. In addition, we extend this novel model to multicarrier M2M which is the first multicarrier channel model in the non geometrical stochastic M2M category. Based on our novel M2M channel model, we carry out an extensive analysis in space-time correlation, space-frequency correlation and second order channel statistics. With the choice of suitable parameters, this analysis and channel model can be used for any wireless environment. Thus, we claim that our novel channel model together with the analysis performed in this thesis can be taken as a generalized framework. A significant contribution of our analysis is the consideration of the impact of transmitter and receiver speed to space-time and space-frequency correlation, which is not available in the literature. Using a von Mises-Fisher distribution as the angular power distribution, the usefulness of the derived temporal correlation function is discussed. The simulation results corroborate the fact that both space-time and space-frequency correlations are reduced when transmitter or receiver speed increases. The rate of reduction of space-time correlation in von Mises-Fisher distribution scattering environment is more than in the isotropic environment. Under second order channel statistics, we consider Rice, Rayleigh and Nakagami fading channels in four different non-isotropic scattering environments with angle of departure (AoD) and angle of arrival (AoA) distributions given by (i) separable Truncated Gaussian, (ii) separable von-Mises, (iii) truncated Gaussian bivariate and (iv) truncated Laplacian bivariate distributions. We show that the major second order statistics, namely, the level crossing rate (LCR) and the average fade duration (AFD), in different fading channels can be expressed in terms of known scattering coefficients of the AoD and AoA distributions. As the channel models and their respective measurements provide reliable knowledge of the channel for the design and analysis of M2M systems, the proposed channel model and the corresponding analysis will be useful for the design, testing and performance evaluation of future M2M communication systems

HARQ Feedback in Spectrum Sharing Networks

This letter studies the throughput and the outage probability of spectrum sharing networks utilizing hybrid automatic repeat request (HARQ) feedback. We focus on the repetition time diversity and the incremental redundancy HARQ protocols where the results are obtained for both continuous and bursting communication models. The channel data transmission efficiency is investigated in the presence of both secondary user peak transmission power and primary user received interference power constraints. Finally, we evaluate the effect of secondary-primary channel state information imperfection on the performance of the secondary channel. Simulation results show that, while the throughput is not necessarily increased by HARQ, substantial outage probability reduction is achieved in all conditions.Comment: Published in IEEE Communications Letter

Reinforcement-based data transmission in temporally-correlated fading channels: Partial CSIT scenario

Reinforcement algorithms refer to the schemes where the results of the previous trials and a reward-punishment rule are used for parameter setting in the next steps. In this paper, we use the concept of reinforcement algorithms to develop different data transmission models in wireless networks. Considering temporally-correlated fading channels, the results are presented for the cases with partial channel state information at the transmitter (CSIT). As demonstrated, the implementation of reinforcement algorithms improves the performance of communication setups remarkably, with the same feedback load/complexity as in the state-of-the-art schemes.Comment: Accepted for publication in ISWCS 201