136 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 1, JANUARY 2004 Power-Allocation Policy and Optimized Design of Multiple-Antenna Systems With Imperfect Channel Estimation Enzo Baccarelli and Mauro Biagi, Student Member, IEEE Abstract—We here focus on the optimized design and per- formance of Rayleigh-faded multiple-antenna multiple-input– multiple-output systems when both transmitter and receiver share imperfect (i.e., error impaired) channel estimates computed via training sequences. In particular, according to the emerging principle of the so-called synchronized detection, for this operating scenario we propose a simple water-filling (WF)-like strategy for allocating power over transmit antennas and test its actual performance. Afterward, we introduce and evaluate some related figures of merit summarizing the overall system’s performance and use these last for noting effective system’s design guidelines. In particular, some optimized solutions for power- versus-bandwidth efficiency tradeoff are presented and their validity limits are debated. All the developed results explicitly take into account the actual reliability of the achievable channel estimates. Index Terms—Bandwidth-versus-power tradeoff, channel esti- mation, multiple antenna, optimized system design, power-alloca- tion policy, synchronized detection, water filling. I. INTRODUCTION M ULTIPLE-ANTENNA systems are able to exploit space diversity for increasing conveyed throughputs without wasting bandwidth and power resources [1], [4], [10] so that, at the present, these systems are an appealing candidate for emerging fourth-generation wireless local area networks (WLANs) [12], [16]. In principle, information throughput of multiple-antenna sys- tems may be further increased via an optimized allocation of the available power over transmitting antennas. As is well known, when the multiple-input–multiple-output (MIMO) channel is perfectly estimated by the receiver and this (perfect) estimate is fed back to the transmitter via an ideal link, then the optimal policy for power allocation is the so-called water-filling (WF) one [2], [8], [14], [15], [17]. Unfortunately, due to users’ mobility and fading effects, the above-stated assumption of perfect channel estimates becomes quite unrealistic in emerging WLANs [5], [12]. A more-real- istic assumption reflecting expected operating conditions of emerging WLANs [12], [16] consists of assuming that both transmitter and receiver share an imperfect (i.e., noisy) MIMO channel estimate whose reliability depends upon the effective- Manuscript received March 22, 2002; revised April 22, 2003, September 16, 2003, and October 8, 2003. The authors are with the INFO-COM Department, Università di Roma La Sapienza, Rome 00184, Italy (e-mail: enzobac@infocom.uniroma1.it; m.biagi@ieee.org). Digital Object Identifier 10.1109/TVT.2003.822025 ness of the employed channel estimator [5], [7]. Unfortunately, barring some recent contributions [3], the performance eval- uation, optimized design, and power-allocation strategy for multiple-antenna systems when both transmit/receiver share imperfect channel estimates appears to have received little attention [10], [13], [19], [22], [23]. On the basis of the above considerations, in this contribution we focus on some aspects concerning optimized design of mul- tiple-antenna systems with imperfect channel estimates avail- able at both transmitter and receiver. A. Pursued Approach of the Synchronized Detection The approach we follow for developing the proposed power- allocation strategy relies on the emerging principle of the synchronized detection [18], [23]. Roughly speaking, this principle is based on the observation that, due to implementa- tion complexity considerations, most wireless communication modems achieve adaptive data detection by cascading two steps [18], [23]. The first consists in computing (generally imperfect) channel estimates of the underlying wireless channel by exploiting transmission of known training pilots. In the second, the system utilizes these (imperfect) channel estimates for data detection, treating them as if they were the exact channel estimates [18], [23]. Although intuitive and, at first glance, elementary, this prin- ciple relies on sound information-theoretic foundation [18] and its merits have been recently detailed in several contributions [18]; [19], Section V; [21]; [22], Section III; [23]. However, all these works focus on communication systems in which the (im- perfectly computed) channel estimates are available only at the receiver. Thus, it is still an open question of how the principle of synchronized detection affects power allocation and the re- sulting information throughput of multiple-antenna transceivers equipped with feedback links for communicating back to the transmitter channel estimates computed at the receiver. B. Main Contributions of This Work The aim of this paper is to shed some light on these still- unanswered questions. For this purpose and according to the abovementioned principle of the synchronized detection, at first we develop a WF-like power-allocation strategy that relies only on available channel estimates. We then test its actual effectiveness on several application scenarios of practical interest. Afterward, by exploiting the developed analytical tool, we introduce and evaluate some figures of merit that 0018-9545/04$20.00 © 2004 IEEE