IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 11, NOVEMBER 2008 4739 Design of an Adaptive MIMO System using Linear Dispersion Code Mabruk Gheryani, Zhiyuan Wu, and Yousef R. Shayan Abstract—In this paper, we present a new adaptation scheme for MIMO systems using linear dispersion code. The statistics of signal-to-interference-noise for a MIMO transceiver using linear dispersion code and linear minimum-mean-square-error (MMSE) receiver over a Rayleigh fading channel is studied. The associated probability density function of the signal-to- interference-noise is derived and veriﬁed. The average BER over MIMO fading channel for a given constellation using the MMSE receiver is calculated numerically. The numerical and simulation results match very well. With the statistics as a guideline, we study new design of selection-mode adaptation using a linear dispersion code. A new adaptive parameter, called space-time symbol rate, can be applied due to the use of linear dispersion code. An adaptive algorithm for the selection-mode adaptation is proposed. Based on the proposed algorithm, two adaptive techniques using constellation and space-time symbol rate are studied, respectively. If constellation and space-time symbol rate are considered jointly, more selection modes can be available. Theoretical analysis demonstrates that the average transmission rate of selection-mode adaptation can be improved in this case. Simulation results are provided to show the beneﬁts of our new design. Index Terms—MIMO, LDC, space-time codes, adaptive tech- niques, channel state information. I. I NTRODUCTION T HE current demand for bandwidth efﬁciency in wireless communications is unprecedented and will continue to grow. A signiﬁcant advancement employed to improve radio spectrum efﬁciency is the use of multiple-input-multiple- output (MIMO) technology [1] [2]. The use of Space-time (ST) codes in turn is the most promising technique for MIMO systems [3] [4]. Due to battery life and device size, the power available for radio communications is limited. Under this power constraint, adaptive technique can cooperate with MIMO technology to further exploit radio spectrum [5] [6]. In an adaptive system, a feedback channel is utilized to provide channel state information (CSI) from the receiver to the transmitter. Using this feedback information, the trans- mitter can adjust transmission parameters, such as power allocation, modulation, coding rate, etc. This is conditioned by the fact that the channel stays relatively constant before the transmitter receives the CSI and then transmits next data block. In other words, the channel is “slow”. Many of adaptive MIMO schemes have been proposed, such as water-ﬁlling- based schemes [1] [7]- [10] and various beamforming schemes Manuscript received September 27, 2007; revised May 1, 2008; accepted October 21, 2008. The associate editor coordinating the review of this paper and approving it for publication was X.-G. Xia. The authors are with Concordia University, Department of Electri- cal Engineering, Montreal, Quebec, Canada (e-mail: {m gherya, zy wu, yshayan}@ece.concordia.ca). Digital Object Identiﬁer 10.1109/T-WC.2008.071074 [6] [11]- [14]. These proposed schemes require near-perfect CSI feedback for adaptation calculation and consume large feedback bandwidth. In practice, the channel estimation will exhibit some inaccuracy depending on the estimation method. In addition the receiver needs time to process the CSI and there are delays associated with the feedback transmission. Likewise the transmitter needs time to choose a proper code, and there can be errors in the feedback channel. These factors add inaccuracies to the CSI at the transmitter. Another prevalent problem is that the feedback bandwidth is often limited. To overcome the shortfalls in these adaptive schemes, we propose using a set of discrete transmission modes which we call “selection-mode” adaptation. At the receiver, the channel state information and channel noise are measured and then chooses the transmission mode that offers the highest transmission rate while meeting the bit error rate (BER) requirement. The optimal mode is then fed back to the transmitter. For selection-mode MIMO adaptation for uncoded systems, a convenient adaptive parameter is the constellation size. For example, a constellation adaptation such as 2 η -QAM is applied to space-time block code (STBC) [15] and to space-time trellis code (STTC) [16]. A disadvantage of these schemes is that they are not ﬂexible for different rates. Rate ﬂexibility is a key requirement in the future wireless communications. Moreover, the gap between the available transmission rates are often very large due to the use of discrete constellations [12]. In this paper, we propose to apply a linear dispersion code (LDC) [17] [18] for adaptation because LDC subsumes many existing block codes as its special cases. This allows suboptimal linear receivers with greatly reduced complexity and provides ﬂexible rate-versus-performance tradeoff [17]- [19]. The LDC breaks the data stream into sub-streams that are dispersed over space and time and then combined linearly at the transmitter [17]. Since the LDC is combined linearly from sub-streams, it makes the ST symbol rate available for adaptation and also makes the adaptation simple and ﬂexible. By adjusting this new parameter together with constellation size, more transmission modes can be made available. Hence, the throughput under a power constraint can be further im- proved while the target bit error rate (BER) is achieved. Due to simplicity and good performance [20] [21], a linear MMSE detector is more attractive to LDC. However, the performance analysis in this case is still deﬁcient. Most of the related works address only the V-BLAST [22]- [24] scheme, a special case of the full-rate LDC. For example, the case of two transmit antennas was analyzed in [25] and the distribution of the angle between two complex Gaussian vectors was pre- sented. The layer-wise signal-to-interference-plus-noise ratio 1536-1276/08$25.00 c  2008 IEEE