The energy efficient joint source-relay power allocation problem is studied for the multi-input multi-output (MIMO) amplify-and-forward two-hop relaying system, in which the objective of the optimization is the number of the bits per second per hertz per Joule with the guarantee of the minimum spectral efficiency (SE). By assuming perfect channel state information at the transmitter, the MIMO channel is divided into several single-input single-output (SISO) subchannels via singular value decomposition (SVD). The problem is first established as an optimization subject to the minimum SE constraint, in which it is observed that both of the cost function and the constraint are not convex. By employing the high signal-to-noise ratio (SNR) approximation, the problem becomes suddenly a pseudo-convex optimization problem. Yet, the difficulty comes from solving the final Lagrangian equation, which is tackled by our proposed relaxation method according to the Jensen inequality. Finally, the analytical expression is derived for the energy efficient power allocations of the multiple antennas at the source and at the relay. Simulations demonstrate the effectiveness of the proposed method.

Energy Efficient MIMO Relay Transmissions via Joint Power Allocations

This paper studies the intercept behavior of an industrial wireless sensor network (WSN) consisting of a sink node and multiple sensors in the presence of an eavesdropping attacker, where the sensors transmit their sensed information to the sink node through wireless links. Due to the broadcast nature of radio wave propagation, the wireless transmission from the sensors to the sink can be readily overheard by the eavesdropper for interception purposes. In an information-theoretic sense, the secrecy capacity of the wireless transmission is the difference between the channel capacity of the main link (from sensor to sink) and that of the wiretap link (from sensor to eavesdropper). If the secrecy capacity becomes nonpositive due to the wireless fading effect, the sensor’s data transmission could be successfully intercepted by the eavesdropper and an intercept event occurs in this case. However, in industrial environments, the presence of machinery obstacles, metallic frictions, and engine vibrations makes the wireless fading fluctuate drastically, resulting in the degradation of the secrecy capacity. As a consequence, an optimal sensor scheduling scheme is proposed in this paper to protect the legitimate wireless transmission against the eavesdropping attack, where a sensor with the highest secrecy capacity is scheduled to transmit its sensed information to the sink. Closed-form expressions of the probability of occurrence of an intercept event (called intercept probability) are derived for the conventional round-robin scheduling and the proposed optimal scheduling schemes. Also, an asymptotic intercept probability analysis is conducted to provide an insight into the impact of the sensor scheduling on the wireless security. Numerical results demonstrate that the proposed sensor scheduling scheme outperforms the conventional round-robin scheduling in terms of the intercept probability.

Intercept Behavior Analysis of Industrial Wireless Sensor Networks in the Presence of Eavesdropping Attack

In this paper, we consider the pilot design based on the mutual incoherence property (MIP) for sparse channel estimation in orthogonal frequency-division multiplexing (OFDM) systems. With respect to the length of channel impulse response (CIR), we first derive a sufficient condition for the optimal pilot pattern generated from the cyclic different set (CDS). Since the CDS does not exist for most practical OFDM systems, we propose three pilot design schemes to obtain a near-optimal pilot pattern. The first two schemes, including stochastic sequential search (SSS) and stochastic parallel search (SPS), are based on the stochastic search. The third scheme called iterative group shrinkage (IGS) employs a tree-based searching structure and removes rows in a group instead of removing a single row at each step. We later extend our work to multiple-input–multiple-output (MIMO) systems and propose two schemes, i.e., sequential design scheme and joint design scheme. We also combine them to design the multiple orthogonal pilot patterns, i.e., using the sequential scheme for the first several transmit antennas and using the joint scheme to design the pilot pattern for the remaining transmit antennas. Simulation results show that the proposed SSS, SPS, and IGS converge much faster than the cross-entropy optimization and the exhaustive search and are thus more efficient. Moreover, SSS and SPS outperform IGS in terms of channel estimation performance.

Pilot Design Schemes for Sparse Channel Estimation in OFDM Systems

Channel estimation for downlink millimeter wave (mmWave) multiuser multiple-input-multiple-output (MU-MIMO) communications over a time-varying channel is demandingly challenging. This is due to a massive number of channel coefficients to be estimated and the severe propagation loss of mmWave transmissions. To tackle this problem, this paper proposes an effective channel estimation scheme for time-varying mmWave channels. Discovering the property that the variations of angles of arrival/departure (AoAs/AoDs) are much slower than that of path gains, we propose a novel transmission frame structure, where the channel estimation is decoupled into two separated stages including AoAs/AoDs estimation followed by path gains estimation. In the first stage, the sparse nature of mmWave channels is leveraged to formulate the AoAs/AoDs estimation into a block-sparse signal recovery problem, and we develop an adaptive angle estimation algorithm to estimate the AoAs/AoDs. In the second stage, the pilot beamforming based on the estimated AoAs/AoDs is designed aiming for maximizing the desired pilot power so that the path gains can be accurately estimated. Simulation results demonstrate that the proposed scheme can effectively estimate the time-varying mmWave channels with a small number of pilots.

Time-Varying Channel Estimation for Millimeter Wave Multiuser MIMO Systems

This paper addresses the sparse channel estimation problem in multiple-input–multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems from the perspective of distributed compressed sensing (DCS). It is focused on deterministic pilot allocation of MIMO-OFDM systems to improve the performance of DCS-based channel estimation. By transforming the problem of DCS-based channel estimation to a problem of reconstructing block-sparse signals, a class of mutual coherence -related criteria is first proposed for optimizing pilot locations. By employing the proposed criteria, a genetic algorithm (GA)-based method of optimizing the pilot locations is then presented. Simulation results show that the DCS-based MIMO channel estimation with optimized pilot locations can improve the spectrum efficiency by nearly 36% and the bit error rate (BER) performance by 1.5 dB, as compared with the least squares (LS) channel estimation with equidistant pilot locations. Moreover, the DCS-based MIMO channel estimation yields a 4.7% improvement in spectrum efficiency under the same BER performance over the compressed sensing (CS)-based channel estimation.

Pilot Allocation for Distributed-Compressed-Sensing-Based Sparse Channel Estimation in MIMO-OFDM Systems

The frequency-selective channel-estimation problem in multi-input-multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems is investigated from the perspective of compressed sensing (CS). By minimizing the mutual coherence of the measurement matrix in CS theory, two pilot allocation methods for the CS-based channel estimation in MIMO-OFDM systems are proposed. Simulation results show that using the pilot patterns designed by the two proposed methods gives a much better performance than using other pilot patterns in terms of the mean square error of the channel estimate as well as the bit error rate of the system. Moreover, the optimal pilot patterns obtained by the proposed second method based on genetic algorithm and shift mechanism could offer a larger performance gain than those by the first method based on minimizing the largest element in the mutual coherence set possessed by pilot patterns for all multiple antenna ports.

Pilot Allocation for Sparse Channel Estimation in MIMO-OFDM Systems

The frequency selective channel estimation problem in orthogonal frequency division multiplexing (OFDM) systems is investigated from the perspective of compressed sensing (CS). By minimizing the mutual coherence or the modified mutual coherence of the measurement matrix in CS theory, two criteria for optimizing the pilot pattern for CS-based channel estimation are proposed. Simulation results show that using the pilot pattern designed by either of the two criteria gives a much better performance than using other pilot patterns in terms of the mean-squared error of the channel estimate as well as the bit error rate of the system. Moreover, the optimal pilot pattern designed by minimizing the modified mutual coherence offers a larger performance gain than that obtained by minimizing the mutual coherence.

Xueyun He

Papers

Pilot Allocation for Distributed-Compressed-Sensing-Based Sparse Channel Estimation in MIMO-OFDM Systems

Pilot Allocation for Sparse Channel Estimation in MIMO-OFDM Systems

Optimal Pilot Pattern Design for Compressed Sensing-Based Sparse Channel Estimation in OFDM Systems