Masayoshi Nakamoto

Preamble and pilot symbol design for channel estimation in OFDM systems with null subcarriers

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 l2 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.

Design of a Data-Driven PID Controller using Operating Data

Abstract PID controllers have been widely used in a lot of process systems because a control structure is simple and physical meanings of PID parameters are clear. Among the methods for determining PID parameters, the VRFT (Virtual Reference Feedback Tuning) and the FRIT (Fictitious Reference Iterative Tuning) have gotten much attention as methods which determine control parameters directly by using a set of operating data in recent years. However, these methods target only linear systems, thus applicable scopes of these methods are narrow because most process systems have nonlinearity. On the other hand, a Data-Driven PID (DD-PID) controller has been proposed as an e ective method for nonlinear systems. In this method, PID parameters are recursively tuned based on a large database. Moreover, a database can store new operating data in an on-line manner, thus PID parameters are tuned flexibly even if a system has nonlinearity. However, the method needs a lot of experimental trials to obtain an initial set of PID parameters in a database, and it has been pointed out as a weak point of this method. In this research, an o -line updating method of a DD-PID controller by using the FRIT is proposed. According to this method, a DD-PID controller is able to update an initial set of PID parameters in a database by only using a set of operating data. Moreover, this method can expand applicable scopes of the FRIT to nonlinear systems. In this research, the e ectiveness of the proposed method is numerically evaluated by some simulations.

Design of Multi-Band Digital Filters and Full-Band Digital Differentiators Without Frequency Sampling and Iterative Optimization

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.

Pilot symbol assisted channel estimation for OFDM-based cognitive radio systems

In this article, challenges regarding the provision of channel state information (CSI) in non-contiguous orthogonal frequency division multiplexing (NC-OFDM) cognitive radio (CR) systems are addressed. We propose a novel scheme that utilizes cross entropy (CE) optimization together with an analytical pilot power distribution technique to design pilot symbols that minimizes the channel estimate mean squared error (MSE) of frequency-selective channels. The optimal selection of pilot subcarriers is a combinatorial problem that requires heavy computations. To reduce the computational complexity, the CE optimization is utilized to determine the position of pilot subcarriers. Then, for a given pilot placement obtained by the CE algorithm, a closed form expression to obtain optimal pilot power distribution is employed. Simulation results indicate that, the proposed pilot symbol design provides better channel estimate MSE as well as the bit error rate (BER) performance when compared with the conventional equal powered pilot design.

Combined channel estimation and PAPR reduction technique for MIMO-OFDM systems with null subcarriers

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.

Finite wordlength design for IIR digital filters based on the modified least-square criterion in the frequency domain

The filter design problem is often formulated in real space (or complex space) whose word length is infinite. However, when implementing a filter in hardware, the frequency characteristic can be degraded caused by finite word-length effect. In this paper, we formulate the filter design problem based on modified least square criterion in the frequency domain. Here the problem is expressed as quadratic form and we optimize the filter coefficients by using branch and bound method in discrete space. In the branch and bound method, we calculate the relaxation solution based on the Lagrange multiplier method and search in the domain in which good possible solutions exist. In this method, the stable solutions whose poles are all inside the unit circle are just acceptable, so the stability of the filter can be guaranteed. Finally, numerical example is given to illustrate the utility of the proposed method.

Design of frequency-selective digital differentiators without frequency sampling and iterative optimization

We introduce the design scheme of frequency-selective digital differentiators which is the hybrid class between frequency-selective filter (band-pass filter) and differentiator. The response of the frequency-selective digital differentiators is more flexible than that of frequency-selective Alter or full-band differentiators. Hence, the frequency-selective digital differentiators are often more beneficiated than full-band differentiators in some applications. The features of the proposed method are as follows. First, the design problem can be formulated in the quadratic form without any frequency sampling. Second, thanks to the quadratic form, the solution is unique and the optimization scheme does not require any iterative optimization in order to get the solution. Accordingly, the procedure of the design of the frequency-selective differentiators is very simple. Also, the frequency-selective differentiators obtained by the proposed method have a robust stability since the maximum pole radius can be prescribed. To demonstrate the effectiveness of the proposed method, we show the numerical examples in the cases of low-pass differentiator and high-pass differentiator.

Training Symbol Design for Channel Estimation and IQ Imbalance Compensation in OFDM Systems

In this paper, training symbol designs for estimation of frequency selective channels and compensation of in-phase (I) and quadrature (Q) imbalances on OFDM transmitters and receivers are studied. We utilize cross entropy (CE) optimization techniques together with convex optimization to design training sequence that minimizes the channel estimate mean squared error (MSE) as well as estimating the effect of I/Q mismatch while lowering the peak power of the training signals. The proposed design provide better channel estimate MSE and bit error rate (BER) performances. The efficacies of the proposed designs are corroborated by analysis and simulation results.

Closed-form approximation of linear phase IIR digital filters with guaranteed stability

We develop a closed-form approximation algorithm for designing IIR digital filters with linear phase and guaranteed stability. In this algorithm, the stopband and passband edge frequency can be specified in the frequency domain and the filter coefficients can be easily obtained for approximating the given frequency response. Additionally, there is a property that the maximum of absolute values of all poles can be controlled, so we can avoid the risk that the designed filters under finite word-length effects become unstable. Finally, a numerical example is given to illustrate the utility of the proposed method.

How many known symbols are required for linear channel estimation in OFDM

Training sequences for estimation of channel parameters have been well designed under the condition that the number of the unknown channel parameters is not greater than the number of the known symbols. Without the condition, we develop a method to obtain the optimal number of known pilot symbols for pilot-aided linear channel estimation in orthogonal frequency division multiplexing (OFDM). We derive an expression for channel estimation error covariance from which performance measures can be numerically evaluated to obtain the optimal number of pilot symbols. Using capacity lower bound as a performance measure, we demonstrate that for channels with exponential power profiles, it is better to estimate a truncated version of the channel response, which reveals the disadvantage of the existing design based on the condition.