Optimal Training for Time-Selective Wireless Fading Channels Using Cutoff Rate
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Optimal Training for Time-Selective Wireless Fading Channels Using Cutoff Rate Saswat Misra,1, 2 Ananthram Swami,1 and Lang Tong2 1 The
Army Research Laboratory, Adelphi, MD 20783, USA of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14850, USA
2 Department
Received 1 June 2005; Revised 11 December 2005; Accepted 13 January 2006 We consider the optimal allocation of resources—power and bandwidth—between training and data transmissions for singleuser time-selective Rayleigh flat-fading channels under the cutoff rate criterion. The transmitter exploits statistical channel state information (CSI) in the form of the channel Doppler spectrum to embed pilot symbols into the transmission stream. At the receiver, instantaneous, though imperfect, CSI is acquired through minimum mean-square estimation of the channel based on some set of pilot observations. We compute the ergodic cutoff rate for this scenario. Assuming estimator-based interleaving and MPSK inputs, we study two special cases in-depth. First, we derive the optimal resource allocation for the Gauss-Markov correlation model. Next, we validate and refine these insights by studying resource allocation for the Jakes model. Copyright © 2006 Saswat Misra et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
In wireless communications employing coherent detection, imperfect knowledge of the fading channel state imposes limits on the achievable performance as measured by, for example, the mutual information, the bit-error rate (BER), or the minimum mean-square error (MMSE). Typically, a fraction of system resources—bandwidth and energy—is devoted to channel estimation techniques (known as training) which improve knowledge of the channel state. Such schemes give rise to a tradeoff between the allocation of limited resources to training on one hand and data on the other, and it is natural to seek the optimal allocation of resources between these conflicting requirements. Such optimization is of particular interest for rapidly varying channels, where the energy and bandwidth savings of an optimized scheme can be significant. In this context, the pilot symbol assisted modulation (PSAM) [1, 2] has emerged as a viable and robust training technique for rapidly varying fading channels. In PSAM, known pilot symbols are multiplexed with data symbols for transmission through the communications channel. At the receiver, knowledge of these pilots is used to form channel estimates, which aid the detection of the data both directly (by modifying the detection rule based on the channel estimate) and indirectly (e.g., by allowing for estimator-directed modulation, power control, and media access). PSAM has been
incorporated into standards for IEEE 802.11, Global System for Mobile Communication (GSM), Wideband CodeDivision Multiple-Access (WCDMA), and military protocols, and many the
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