In this article, design of preamble for channel estimation and pilot symbols for pilot-assisted channel estimation in orthogonal frequency division multiplexing system with null subcarriers is studied. Both the preambles and pilot symbols are designed to minimize the l 2 or the l ∞ norm of the channel estimate mean-squared errors (MSE) in frequency-selective environments. We use convex optimization technique to find optimal power distribution to the preamble by casting the MSE minimization problem into a semidefinite programming problem. Then, using the designed optimal preamble as an initial value, we iteratively select the placement and optimally distribute power to the selected pilot symbols. Design examples consistent with IEEE 802.11a as well as IEEE 802.16e are provided to illustrate the superior performance of our proposed method over the equi-spaced equi-powered pilot symbols and the partially equi-spaced pilot symbols.

Most design problems of digital filters (or differentiators) are formulated with a set of grid point in the frequency region (frequency sampling). These problems are usually difficult to solve, and often require iterative optimization. The objective of this paper is to provide an efficient and simplified design approach to multi-band filters (including low-pass filters or high-pass filters) as well as full-band differentiators. The proposed method does not require frequency sampling and iterative optimization to compute the coefficients of the filters or that of the differentiators. The magnitude and phase specifications are simultaneously approximated, and the errors in the specified frequency bands are controlled by using frequency-weighting factors. In addition, a maximum pole radius, which corresponds to a stability margin, can be specified to robustly ensure the stability of the filters or the differentiators. To evaluate the efficiency of proposed method, we compare the proposed method with several established methods. Simulation results show that, although the propose method does not utilize frequency sampling and iterative optimization, the designed filters and differentiators have sufficient performance.

In this paper, challenges regarding the provision of channel state information (CSI) and carrier frequency synchronization for orthogonal frequency division multiplexing (OFDM) systems with null subcarriers are addressed. We propose novel maximum likelihood (ML) based schemes that estimate the aggregate effects of the CFO and channel by using two successive OFDM preambles. In the presented scheme, CFO is estimated by considering the phase rotation between two consecutive received OFDM preambles. Both single input single output (SISO) as well as multiple input multiple output (MIMO) OFDM systems are considered. The mean squared errors (MSE) of the channel and CFO are used to evaluate the performance of our proposed scheme. By using two successive OFDM preambles, the estimation of channel and the estimation of CFO are decoupled, which leads to a simple estimation method. Simulation results show that the BER performance of the proposed estimators is comparable to that of known channel state information and the CFO MSE performance achieves the Cramer-Rao bound (CRB) of the fully loaded OFDM system.

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In this article, we address the challenges regarding the provision of channel state information as well as reducing peak-to-average power ratio (PAPR) of a multiple input multiple output orthogonal frequency multiplexing (MIMO-OFDM) system. The mean squared error (MSE) of the channel estimate is adopted as the optimization criterion to design pilot symbols for channel estimation in MIMO-OFDM systems with null subcarriers. We design the placement and power distribution to the pilot symbols for multiple transmit antennas to minimize the MSE of the least square (LS) channel estimates. To reduce interference of the pilot symbols transmitted from different antennas, an algorithm to guarantee that pilot symbols are disjoint from any other transmitter pilot set is proposed. To efficiently reduce the PAPR of the MIMO-OFDM signals, a method that mixes dummy symbols and phase information of the pilot symbols is presented. Simulation results based on IEEE 802.16e are presented to illustrate the superior performance of our proposed channel estimation method over the existing standard and the partially equi-spaced pilot symbols. We also demonstrate that, by mixing the dummy symbols and phase information of the pilot symbols, the PAPR of the MIMO-OFDM signals can significantly be reduced.