2868 IEICE TRANS. COMMUN., VOL.E94–B, NO.10 OCTOBER 2011 LETTER Regional Diversity-Multiplexing Tradeoff * Won-Yong SHIN † , Nonmember and Koji ISHIBASHI †† a) , Member SUMMARY The concept of regional diversity-multiplexing tradeoff (DMT) is introduced by extending the asymptotic outage probability ex- pression for multiple-input multiple-output (MIMO) channels. It is shown that for both Rayleigh and Rician MIMO channels, the regional diversity gain is a linear function of the regional multiplexing gain and that the orig- inal DMT curve can be obtained from the set of regional DMT lines. As a result, vital information for capturing both finite and infinite signal-to-noise ratio characteristics in terms of DMT is provided. key words: multiple-input multiple-output (MIMO), outage, regional diversity-multiplexing tradeoff (DMT), Rician 1. Introduction Multiple-input multiple-output (MIMO) antenna systems have recently stimulated a large amount of research activ- ity, as they can offer a dramatic increase in the transmis- sion rates [1] and reliability of wireless links [2] over single- antenna systems. However, their design requires some cau- tion because there is a tradeoff between diversity and mul- tiplexing gain. Zheng and Tse [3] have discovered a funda- mental tradeoff between the two gains, in which outage anal- ysis plays an important role, under the following assump- tions: the channel is independent and identically distributed (i.i.d.) Rayleigh and quasi-static, the signal-to-noise ratio (SNR) approaches infinity, and perfect channel state infor- mation (CSI) is available at the receiver but not at the trans- mitter. This work has led to a number of research efforts to extend the optimal diversity-multiplexing tradeoff (DMT) for other practical channel models [4]–[7]. Asymptotic out- age performance [8] and the DMT for finite SNR [5], [9] have also been characterized. In this paper, we would first like to illuminate the work in [8], where the other aspects not shown in DMT [3] were examined and thus foster an understanding of the relation- ship among the outage probability, target rate, and SNR. We take into account a more realistic MIMO channel model, in- cluding the Rician factor which represents the degrees of channel uncertainty. It is then analyzed that the asymp- totic outage expression for Rayleigh channels [8] also holds Manuscript received March 24, 2011. Manuscript revised June 20, 2011. † The author is with the School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA. †† The author is with the Department of Electrical and Elec- tronic Engineering, Shizuoka University, Hamamatsu-shi, 432- 8561 Japan. ∗ This work was supported in part by KAKENHI (21760284). a) E-mail: koji@ieee.org (corresponding author) DOI: 10.1587/transcom.E94.B.2868 for Rician channels. Based on this result, the concept of regional DMT is introduced and the relation between the regional DMT and the original DMT is carefully charac- terized. While the regional DMT is derived for high SNR regime, as in [3], it is shown that its lines are different from the conventional DMT curve since it partially informs finite SNR characteristics according to various operating regions. The rest of this paper is organized as follows. Section 2 describes the system and channel models. In Sect. 3, the original DMT is briefly reviewed and then some asymptotic outage behaviors are shown. Section 4 characterizes the regional DMT. Finally, Sect.5 summarizes the paper with some concluding remarks. 2. System and Channel Models Consider a MIMO system with n T transmit antennas and n R receive antennas over a flat fading channel. The received signal vector y ∈ C n R of the MIMO system is given by y =  ρ n T Hx + n, (1) where ρ is the average SNR at each receive antenna, H ∈ C n R ×n T is the channel matrix whose element h ij represents the complex channel gain between the jth transmit antenna and the ith receive antenna, x ∈ C n T is the transmitted signal vector, and n ∈ C n R is an additive white Gaussian noise vec- tor. For notational convenience, we define m = min{n T , n R } and n = max{n T , n R }. When the channel is Rician, H can be expressed as H =  K K + 1 ¯ H +  1 K + 1 H w , (2) where K denotes the Rician factor (K ≥ 0), ¯ H is a deter- ministic matrix representing line-of-sight components and is normalized as tr( ¯ H ¯ H † ) = n R n T , and H w consists of zero-mean complex Gaussian random variables with unit- variance. Hence, the channel is normalized such that E[tr(HH † )] = n R n T . It is assumed that the channel H w is known at the receiver, but not known at the transmitter. Both the transmitter and the receiver know ¯ H. 3. DMT and Outage Behavior In this section, the DMT for Rayleigh channels is briefly re- viewed. Then, asymptotic outage probabilities of Rayleigh Copyright c  2011 The Institute of Electronics, Information and Communication Engineers