Constrained Optimization of MIMO Training Sequences
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Research Article Constrained Optimization of MIMO Training Sequences Justin P. Coon and Magnus Sandell Toshiba Telecommunications Research Laboratory, 32 Queen Square, Bristol BS1 4ND, UK Received 30 May 2006; Revised 22 November 2006; Accepted 11 January 2007 Recommended by Erchin Serpedin Multiple-input multiple-output (MIMO) systems have shown a huge potential for increased spectral efficiency and throughput. With an increasing number of transmitting antennas comes the burden of providing training for channel estimation for coherent detection. In some special cases optimal, in the sense of mean-squared error (MSE), training sequences have been designed. However, in many practical systems it is not feasible to analytically find optimal solutions and numerical techniques must be used. In this paper, two systems (unique word (UW) single carrier and OFDM with nulled subcarriers) are considered and a method of designing near-optimal training sequences using nonlinear optimization techniques is proposed. In particular, interior-point (IP) algorithms such as the barrier method are discussed. Although the two systems seem unrelated, the cost function, which is the MSE of the channel estimate, is shown to be effectively the same for each scenario. Also, additional constraints, such as peak-to-average power ratio (PAPR), are considered and shown to be easily included in the optimization process. Numerical examples illustrate the effectiveness of the designed training sequences, both in terms of MSE and bit-error rate (BER). Copyright © 2007 J. P. Coon and M. Sandell. 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.
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INTRODUCTION
Future wireless systems can offer substantially higher data rates than current systems by using new, sophisticated technologies. One of the most promising technologies is multiple-input multiple-output (MIMO) transmission [1, 2], where spatial multiplexing [3, 4], or more advanced space-time codes [5–7], can increase the spectral efficiency by using the spatial domain. One drawback with MIMO systems is that channel estimation becomes more important. Not only are MIMO decoders more sensitive to channel estimation errors than their single-antenna counterparts, the overhead in terms of required training sequences is also increased. Thus, it is important to make training as efficient as possible. For a MIMO system with M transmit antennas, the simplest form of training sequence is to transmit from only one antenna at a time. This method, however, requires M slots, which in some cases can be a large overhead. One technique that has been applied in MIMO orthogonal frequency division multiplexing (OFDM) systems (see, e.g., [8] for an overview of OFDM) to reduce this overhead is to exploit the channel dimensions. Since OFDM systems design the data in the frequency domain, channel estimates are required for
all K subcarriers. However, the time-do
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