Optimal Training Signals Research Articles

Amplify-and-forward relay identification using joint Tx/Rx I/Q imbalance-based device fingerprinting

Relay identification is necessary in many cooperative communication applications such as detecting the presence of malicious relays for communication security, selecting the intended relays for signal forwarding, and tracing a specific relay. However, this identification task becomes extremely challenging for amplify-and-forward (AF) relaying systems since AF relays usually have no capability of adopting traditional identification methods implemented above the physical layer. This paper proposes a physical-layer AF relay identification scheme based on the exploitation of the device-specific in-phase and quadrature-phase imbalance (IQI) feature. Given that IQI estimation is mandatory in most present receivers for compensation, it is cost-effective to make use of these estimation results for fingerprinting AF relays. A generalized likelihood ratio test-based fingerprint differentiation technique is adopted to detect the minor difference between two range-limited IQI fingerprints. Using this differentiation technique, a whitelist-based identification algorithm consisting of fingerprint registration, update, and identification is proposed. Furthermore, the optimal training signals that lead to the maximal detection probability are derived for the typical quadrature amplitude modulation and phase-shift keying modulation schemes. The simulation results validate our derivations and confirm that the proposed method can accurately identify AF relays.

On the optimality of training signals for MMSE channel estimation in MIMO-OFDM systems

In this paper, we investigate the optimality of training signals for linear minimum mean square error (LMMSE) channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) with frequency-selective fading channels. This is a very challenging problem due to its mathematical intractability and has not been analytically solved in the literature. Using the Lagrange multiplier method, we derive the optimality conditions for training signal design. Important findings revealed on optimal training signals are twofold: (i) the energies of the training signals on each subcarrier are equal, and (ii) on each subcarrier, the training signals transmitted from the different antennas are orthogonal and of equal energy. We verify that our results are in line with the design principles that have been derived in single-carrier MIMO systems. Two types of optimal training signal examples that satisfy the optimality conditions are presented for practical implementations in MIMO-OFDM systems. Simulation results show that the training signals based on the optimality conditions outperform other non-optimal training signals in terms of channel estimation performance.

Robust channel estimation in the Rician distributed flat fading multiple-input–multiple-output channel

In this paper, the mean square error (MSE) of the new technique, the shifted scaled least squares (SSLS), and the minimum MSE (MMSE) estimator is analysed in the Rician distributed flat fading multiple-input–multiple-output (MIMO) channels. First, the closed form expressions are obtained for MSE of the estimators using the estimated and the actual mathematical expectation matrix of the channel and the matrix of channel covariances. It is analytically and numerically shown that the performance of the estimators is less sensitive to the erroneous estimation of the Rice factor at the receiver. On the other hand, it is shown that the performance of the MMSE estimator is quite sensitive to the erroneous estimation of the channel correlation coefficient. In order to estimate the channel Rice factor, two algorithms are also proposed in this paper. These algorithms work based on the optimal training signal and least squares (LS) technique. Finally, the estimated Rice factor is used in the SSLS and MMSE estimators. Simulation results confirm the efficiency of the algorithms and the robustness of the above-mentioned estimators to the erroneous estimation of Rice factor.

Virtual Simulation Technology of Wireless Sensor Neural Network in Basketball Movement Distribution

With the innovation of computer hardware technology and software technology, virtual simulation technology has been applied in various fields, including sports training and basketball teaching process. In this paper, the basketball technology actions optimization system is designed by using MATLAB virtual simulation method, and the initial signal calculus model of basketball technology actions is established by using wireless sensor signal transmission principle, and then using the trained neural network method carries on processing for the initial signal, combining the approximation degree of optimal training signal and original signal determine the validity and reliability of the simulation. Through the simulation, we finally get the optimization allocation effect of the number of neurons’ best basketball technology actions, which provides a new computer method for the exploration of basketball training new method.

Optimal Training Signal Design for Estimation of Correlated MIMO Channels in Two-Way Amplify-and-Forward Relay Systems

In this study, we design a training signal for a correlated two-way amplify-and-forward (AF) relay channel, where the relay system consists of two sources and one relay, and each terminal is equipped with multiple antennas. In the system, given that a mean square error (MSE) exists at each source, we minimize the sum of the two MSEs. In particular, we first derive a linear minimum MSE channel estimator with an arbitrary training signal. Second, we formulate the training signal design problem to minimize the sum of the MSEs of the two sources. Finally, we present the optimal structure of the training signal. The optimal training signal is obtained numerically, and a suboptimal training signal is obtained in a closed form. The simulation results show that the MSE performance of the closed-form training signal is almost the same as that of the optimal training signal.

Superimposed training for channel estimation of OFDM modulated amplify-and-forward relay networks

This paper is concerned with the problem of channel estimation for amplify-and-forward (AF) cooperative relay networks with orthogonal frequency division multiplexing (OFDM) modulation. The algorithm is based on both the least square (LS) and minimum mean square error (MMSE) technique with a superimposed training strategy. Specifically, both the source and relay superimpose their own training signal onto data stream prior to transmission so as to estimate the separate channel state information of the source to relay link and the relay to destination link. We also present the performance analysis and derive the approximated closed-form expressions for the MSE of separate channel estimation of source to relay link and the relay to destination link, respectively, from which we compute the optimal training signal as well as the relay power-amplification factor. To further improve the performance of channel estimation, we adopt a weighted average process to enhance the estimation performance over multiple OFDM blocks, from which we compute the optimal tracking factor. Simulation results are provided to corroborate the proposed scheme.

Training signal designs for spatially correlated multi-user multi-input multi-output with orthogonal frequency-division multiplexing systems

Optimal training design and channel estimation for spatially correlated multi-user multi-input multi-output with orthogonal frequency-division multiplexing (MIMO-OFDM) systems is still an open research topic of great interest. This study first applies tractable semi-definite programming (SDP) to obtain the optimal training signal for the general case of spatial channel correlations for multi-user MIMO-OFDM. In order to reduce the computational complexity of the SDP-based solution, an approximate solution in closed-form is then presented. For a special case of transmit correlations, an optimal solution in closed-form expression is also derived. Analytical and simulation results demonstrate the excellent performance of the proposed designs and their performance advantage over the existing equi-powered training designs.

Least square identification of alias components of linear periodically time-varying systems and optimal training signal design

A least-squares (LS) method for identifying alias components of discrete linear periodically time-varying (LPTV) systems is proposed. The authors apply a periodic input signal to a finite impulse response (FIR) - LPTV system and measure the noise-contaminated output. The output of this LPTV system has the same period as the input when the period of the input signal is a multiple of the period of the LPTV system. The authors show that the input and the output can be related by using the discrete Fourier transform. In the frequency domain, an LS method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR) - LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.

Optimal training signals for MIMO OFDM channel estimation in the presence of frequency offset and phase noise

We develop robust mean-square error (MSE)-optimal training signal designs for multiple-input multiple-output orthogonal frequency-division multiplexing channel estimation with frequency offset and phase noise (PN), and present analytical and simulation results for the frequency-offset and PN effects on channel estimation. The proposed designs are more advantageous for moderate-to-high values of signal-to-noise ratio (SNR), residual frequency offset, and PN level. At SNR = 10 dB, the normalized MSE reductions of our proposed training signals at normalized frequency offset |v|=0.1,0.5 are about 9 and 19 dB, respectively, for one transmit antenna, and 6 and 11 dB for two transmit antennas

Optimal Periodic Training Signal for Frequency Offset Estimation in Frequency-Selective Fading Channels

This paper addresses an optimal periodic training signal design for frequency offset estimation in frequency-selective multipath Rayleigh fading channels. For a fixed transmitted training signal energy within a fixed-length block, the optimal periodic training signal structure (the optimal locations of identical training subblocks) and the optimal training subblock signal are presented. The optimality is based on the minimum Cramer-Rao bound (CRB) criterion. Based on the CRB for joint estimation of frequency offset and channel, the optimal periodic training structure (optimality only in frequency offset estimation, not necessarily in joint frequency offset and channel estimation) is derived. The optimal training subblock signal is obtained by using the average CRB (averaged over the channel fading) and the received training signal statistics. A robust training structure design is also presented in order to reduce the occurrence of outliers at low signal-to-noise ratio values. The proposed training structures and subblock signals achieve substantial performance improvement

Optimal training signals for MIMO OFDM channel estimation

This paper presents general classes of optimal training signals for the estimation of frequency-selective channels in MIMO OFDM systems. Basic properties of the discrete Fourier transform are used to derive the optimal training signals which minimize the channel estimation mean square error. Both single and multiple OFDM training symbols are considered. Several optimal pilot tone allocations across the transmit antennas are presented and classified as frequency-division multiplexing, time-division multiplexing, code-division multiplexing in the frequency-domain, code-division multiplexing in the time-domain, and combinations thereof. All existing optimal training signals in the literature are special cases of the presented optimal training signals and our designs can be applied to pilot-only schemes as well as pilot-data-multiplexed schemes.

Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals

In this paper, we study the performance of multiple-input multiple-output channel estimation methods using training sequences. We consider the popular linear least squares (LS) and minimum mean-square-error (MMSE) approaches and propose new scaled LS (SLS) and relaxed MMSE techniques which require less knowledge of the channel second-order statistics and/or have better performance than the conventional LS and MMSE channel estimators. The optimal choice of training signals is investigated for the aforementioned techniques. In the case of multiple LS channel estimates, the best linear unbiased estimation (BLUE) scheme for their linear combining is developed and studied.