Der Einfluss nichtkohärenten Fadings auf Mehrbenutzerkommunikation
Zusammenfassung der Projektergebnisse
Virtually all mobile communication takes place over time-varying fading channels, whose realization is a priori unknown to the receiver. Nevertheless, neither the capacity nor the optimal input distribution for this class of channels are known. In recent years, advanced receivers using iterative code-aided channel estimation have been studied, where the channel estimation is not only based on pilot symbols, but additionally on the reliability information on the data symbols. However, to estimate the possible performance gain by using such an enhanced receiver processing, a detailed knowledge of the capacity of this class of channels is required. In this regard, we have derived different bounds on the achievable rate/capacity for stationary Rayleigh fading channels. First, we derived a new lower bound on the achievable rate when using an optimal joint processing of data and pilot symbols for multiple-input multiple-output (MIMO) systems. This bound gives an indication on the possible gains when using iterative code-aided channel estimation in comparison to conventional receivers with a channel estimation solely based on pilot symbols. The MIMO case is especially interesting as the degrees of freedom of the channel increases with the number of transmit and receive antennas additionally to the degrees of freedom given by the channel dynamic, yielding to an even more pronounced degradation of the capacity due to channel uncertainty. The new lower bound shows that the gain with joint processing of pilot and data symbols in comparison to separate processing strongly increases with the number of antennas even for small channel dynamics. Thus, especially for MIMO systems the use of joint processing is favorable. To understand how close systems based on pilot symbols approach the capacity, we further studied the achievable rate with i.i.d. Gaussian input symbols, which are capacity-achieving in the coherent case. We chose this input distribution as it approximates in the right SNR range very well the mutual information of complex discrete constellations like QAM, as they are typically used in wireless communications. In this regard, we proved a new upper bound on the achievable rate. For the construction of the proof we derived a new log-det inequality for random matrices which is fairly general and of interest on its own. We gave related deterministic inequalities of Muirhead- and Rado-type and applied the new inequality additionally to bound the capacity of a coherent fading channel with colored Gaussian noise. Moreover, in the context of studying the achievable rate with i.i.d. input symbols we have shown that the conditional per symbol entropy of the channel output given the input converges for almost every realization of an asymptotically mean stationary input process. This result is closely related to theorems by Barron, Orey, and Algoet and Cover, which establish a similar convergence for the unconditional case. Furthermore, we have studied the capacity pre-log factor of noncoherent continuous-time single user fading channels. The motivation for this study came from the observation that symbol rate sampling of the output of the continuous-time noncoherent stationary fading channel does not provide a sufficient statistic of the channel output with respect to the transmit symbol sequence. This led to the conjecture that the observed degradation of the capacity pre-log factor in case of noncoherent fading is an artefact of the symbol rate discrete-time channel model. We have been able to prove a corresponding result for the case of a continuous-time, time-selective Rayleigh block-fading channel. For the case of symbol rate sampling its capacity pre-log is given by 1 − Q /N where N is the number of symbols transmitted within one fading block, and Q is the rank of the covariance matrix of the discrete-time channel gains within each fading block. Differently, in case of two times oversampling with respect to the symbol rate, we have been able to show that one gets a capacity pre-log that is at least as large as 1 − 1/N. The remaining question is to understand the impact of noncoherent fading on multiuser settings. Due to the shift in the work plan to the study of the capacity pre-log of the continuous-time setup, which is an important prerequisite, the study of multiuser scenarios remains as future work.
Projektbezogene Publikationen (Auswahl)
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“On the gain of joint processing of pilot and data symbols in stationary Rayleigh fading channels,” IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 2963–2982, May 2012
M. Dörpinghaus, A. Ispas, and H. Meyr
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“On the achievable rate of stationary Rayleigh flatfading channels with Gaussian inputs,” IEEE Trans. Inf. Theory, vol. 59, no. 4, pp. 2208–2220, Apr. 2013
M. Dörpinghaus, H. Meyr, and R. Mathar
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“Oversampling increases the pre-log of noncoherent Rayleigh fading channels,” IEEE Trans. Inf. Theory, vol. 60, no. 9, pp. 5673–5681, Sept 2014
M. Dörpinghaus, G. Koliander, G. Durisi, E. Riegler, and H. Meyr
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“A log-det inequality for random matrices,” SIAM Journal on Matrix Analysis and Applications (SIMAX), J. Matrix Anal. & Appl., 36(3), 1164–1179. (16 pages) 2015
M. Dörpinghaus, N. Gaffke, L. Imhof, and R. Mathar
