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...g-based capacity with the assumption that all training symbols or pilot tones have the same energy. For OFDM systems, the optimal placement of pilot tones is equal spacing in the frequency domain. In =-=[10]-=-, optimal design and placement of pilot symbols for frequency-selective block-fading channel estimation are addressed for single-input single-output (SISO) as well as multiple-input multiple-output (M...

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...methods treat unknown data as nuisance parameters that can either be marginalized or estimated jointly with a channel. These semiblind approaches improve the estimation performance for a given amount of training. Because it is desirable that the design of an optimal Training for MIMO communications 9 training scheme does not depend on the specific algorithm used at the receiver, the Cramer-Rao bound (CRB) (Van Trees, 1968) is a natural choice as a figure of merit in this case. Semiblind CRB’s have been developed under deterministic and stochastic data assumption (de Carvalho and Slock, 1997; Dong and Tong, 2002), and for MIMO channels (Sadler et al., 2001b; Kozick et al., 2003). For semiblind channel estimation, the position of training symbols makes a difference since both training and data are modelled in estimation. Using the CRB as metric, training design has been investigated for linear finite impulse response (FIR) MIMO channels (Dong and Tong, 2002), for orthogonal space-time coded systems (Budianu and Tong, 2002), and for FIR MIMO systems using affine precoding (Vosoughi and Scaglione, 2004, 2003). Multiple transmitting antennas are also considered for multicarrier systems (Bolcskei et al., ...

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...ion matrix [25]. For large L where the law of large numbers applies, the scaled version of Φ would converge to the expectated value of the correlation matrix. A similar technique has been employed in =-=[43]-=-. 8 The choice of an appropriate circulant matrix to approximate a Toeplitz matrix is not unique [28], and here the circulant matrix ˜ Φ is constructed through the inverse Fourier transform [30]. or w...

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...ns of optimal complex sequences were discussed in [5]–[8] and references therein. Recent treatments of the optimal training structure and training signal design for channel estimation can be found in =-=[9]-=-–[11] and references therein. Training sequence design for timing synchronization was discussed in [12] in the context of the minimum-shift keying signal. For timing synchronization, [13] presented th...

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...6], or, minimizing the channel mean-square error (MSE) [17]–[19]. Pilot optimization for single-carrier transmissions has also been investigated in [15], [20]–[22] based on these two criteria, and=-= in [23] by-=- minimizing the Cramér–Rao bound on the channel MSE. As error probability directly determines the reliability of a communication link, our use of SER as a criterion is certainly of practical intere...