Joint Power Constraint Research Articles

On the Capacity of Gaussian MIMO Channels Under the Joint Power Constraints

The capacity and optimal signaling over a fixed Gaussian MIMO channel are considered under the joint total and per-antenna power constraints. While the general case remains an open problem, a closed-form full-rank solution is obtained along with its sufficient and necessary conditions. The conditions for each constraint to be inactive are established. The high and low-SNR regimes are studied. Isotropic signaling is shown to be optimal in the former case while rank-1 signaling (beamforming) is not necessarily optimal in the latter case. Unusual properties of optimal covariance under the joint constraints are pointed out.

The Capacity of Gaussian MIMO Channels Under Total and Per-Antenna Power Constraints

The capacity of a fixed Gaussian multiple-input multiple-output (MIMO) channel and the optimal transmission strategy under the total power (TP) constraint and full channel state information are well known. This problem remains open in the general case under individual per-antenna (PA) power constraints, while some special cases have been solved. These include a full-rank solution for the MIMO channel and a general solution for the multiple-input single-output (MISO) channel. In this paper, the fixed Gaussian MISO channel is considered and its capacity and optimal transmission strategies are determined in a closed form under the joint total and PA power constraints in the general case. In particular, the optimal strategy is hybrid and includes two parts: first is equal-gain transmission and second is maximum-ratio transmission, which are responsible for the PA and TP constraints, respectively. The optimal beamforming vector is given in a closed form and an accurate yet simple approximation to the capacity is proposed. Finally, the above results are extended to the MIMO case by establishing the ergodic capacity of fading MIMO channels under the joint power constraints when the fading distribution is right unitary-invariant (of which i.i.d. and semi-correlated Rayleigh fading are special cases). Unlike the fixed MISO case, the optimal signaling is shown to be isotropic in this case.

Homotopy Approach for Energy-Efficient MIMO Systems With Zero-Forcing Transceivers

This paper addresses energy efficiency (EE) optimization problems for uplink multiuser multiple-input–multiple-output (MIMO) systems with zero-forcing (ZF) transceivers, subject to a joint power and rate constraint for each user. As the optimization problem considered in this paper is quite different from the traditional one, directly applying the Dinkelbach method to the new EE optimization problem cannot bring an advantage of low complexity. Hence, we try to propose a novel approach inspired by the homotopy algorithms, where we concentrate our attention on the solution path for the EE optimization. Making use of the piecewise-defined property between power allocations and the overall transmission power, we fit the entire path of solution for every value of the overall transmission power by replacing the search variable with a specially selected parameter. By checking only a finite number of breakpoints, we then try to propose a new homotopy-type algorithm to obtain the maximum EE in an exact closed form to reduce the computational complexity significantly. Simulation results verify the performance of the new method.

Secrecy Rates and Optimal Power Allocation for Full-Duplex Decode-and-Forward Relay Wire-Tap Channels

This paper investigates the secrecy rates and optimal power allocation schemes for a decode-and-forward wiretap relay channel where the transmission from a source to a destination is aided by a relay operating in a full-duplex (FD) mode under practical residual self-interference. By first considering static channels, we address the non-convex optimal power allocation problems between the source and relay nodes under individual and joint power constraints to establish closed-form solutions. An asymptotic analysis is then given to provide important insights on the derived power allocation solutions. Specifically, by using the method of dominant balance, it is demonstrated that full power at the relay is only optimal when the power at relay is sufficiently smaller when compared with that of the source. When the power at the relay is larger than the power at the source, the power consumed at the relay saturates to a constant for an effective control of self-interference. The analysis is also helpful to demonstrate that the secrecy capacity of the FD system is twice as much as that of the half-duplex system. The extension to fast fading channels with channel state information being available at the receivers but not the transmitters is also studied. To this end, we first establish a closed-form expression of the ergodic secrecy rate using simple exponential integrals for a given power allocation scheme. The results also show that with optimal power allocation schemes, FD can significantly improve the secrecy rate in fast fading environments.

Secrecy Rate and Optimal Power Allocation of the Amplify-and-Forward Relay Wire-Tap System

In this research work, we investigate the secrecy rate and optimal power allocation schemes for a half-duplex (HD) wire-tap Rayleigh fading channel in which a source wishes to communicate securely to a destination in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay. The secrecy capacity and the corresponding optimal power allocation schemes are examined under both individual and joint power constraints. Due to the absence of an insightful expression of the secrecy rate for a given power allocation scheme, determining such secrecy capacity is challenging. To overcome this issue, we first propose a novel method to calculate the expectation of an exponentially distributed random variable using the exponential integral function. By exploiting this calculation, we then establish the average secrecy rate of the considered AF relay channel in closed-form. By examining the quasi-concavity of the optimal power allocation problem, it is then concluded that the problem is quasi-concave. As such, the globally optimal solution exists and is unique for both individual and joint power constraints. A simple root finding method then can be applied into the derived close-formed formula to approximately calculate the optimal power allocation scheme to achieve the secrecy capacity. Numerical results are then provided to confirm the accuracy of the derived formula and the optimality of the proposed power allocation.

Optimal Power Allocation Schemes for the Single AF Relay and Jammer Wiretap Channels

This paper considers the wiretap channel in which a source node communicates with a destination node with the aid of a single helper and in the presence of an eavesdropper. The helper can apply either amplify-and-forward (AF) relaying or jamming. The secrecy capacity and respective optimal power allocation schemes at the source and the helper are investigated under both individual and joint power constraints. Given that the links among the nodes might not always be available for transmission (e.g., due to heavy shadowing), several network topologies are considered for relaying. To deal with the related nonconcave optimization problems in solving the optimal power allocation schemes, we first propose an analytical approach based on Descartes' rule of signs. Using this approach, optimal power allocation strategies are derived for some relay topologies and for the jamming system. Insights into the proposed schemes for different transmission power ranges and comparisons to the optimal information rate power allocations are also discussed. Simulation results are finally provided to quantify the optimality of the proposed schemes.

On Secrecy Rate and Optimal Power Allocation of the Full-Duplex Amplify-and-Forward Relay Wire-Tap Channel

We present the secrecy rate of a relay wire-tap channel in which a source node communicates securely to a destination node in the presence of an eavesdropper using an amplify-and-forward (AF) relay operating in full-duplex (FD) mode. We explicitly account for the residual self-interference due to FD transmission and compute the optimal power allocation (PA) that maximizes the secrecy rate under both individual and joint power constraints of the source and the relay nodes. For slowly varying fading channels, we show that the optimal PA problem is quasiconcave and, hence, determine the globally optimal solution. Applying the method of dominant balance to analyze the capacity and PA schemes in different high-power regimes, we demonstrate that full PA at the relay is only necessary when the power at the relay is sufficiently small compared to the power at the source. Our results show that FD relaying achieves a significantly higher secrecy rate than half-duplex (HD) relaying. We extend the results to ergodic fading channels where the channel gains are assumed to be available at the receivers but not the transmitters. To this end, we first calculate the expectation of linear functions of exponentially distributed random variables using the exponential integral function. This method allows us to obtain a closed-form expression for the ergodic secrecy rate. The bisection method can then be applied to find the optimal PA scheme. Numerical results also reveal the superiority of FD over HD relaying in channels with ergodic fading.

Robust Piecewise Linear Algorithm for Point-to-Point MIMO Systems

This letter considers a robust linear precoder optimization problem for point-to-point multiple-input multiple-output (MIMO) systems with imperfect channel state information (CSI), subject to a joint power constraint imposed on both sum-power and maximum eigenvalue power. Making use of the piecewise linear property between power allocations and sum-power, we derive a piecewise linear algorithm to obtain the optimal solution. As the optimal solution can be expressed analytically in terms of at most 2M candidates (M is the number of transmit antennas) whose expressions are all in closed forms, the proposed method can provide an exact closed-form solution.

A Framework for Transceiver Designs for Multi-Hop Communications With Covariance Shaping Constraints

For multiple-input multiple-output (MIMO) transceiver designs, sum power constraint is an elegant and ideal model. When various practical limitations are taken into account e.g., peak power constraints, per-antenna power constraints, etc., covariance shaping constraints will act as an effective and reasonable model. In this paper, we develop a framework for transceiver designs for multi-hop communications under covariance shaping constraints. Particularly, we focus on multi-hop amplify-and-forward (AF) MIMO relaying communications which are recognized as a key enabling technology for device-to-device (D2D) communications for next generation wireless systems such as 5G. The proposed framework includes a broad range of various linear and nonlinear transceiver designs as its special cases. It reveals an interesting fact that the relaying operation in each hop can be understood as a matrix version weighting operation. Furthermore, the nonlinear operations of Tomolision-Harashima Precoding (THP) and Decision Feedback Equalizer (DFE) also belong to the category of this kind of matrix version weighting operation. Furthermore, for both the cases with only pure shaping constraints or joint power constraints, the closed-form optimal solutions have been derived. At the end of this paper, the performance of the various designs is assessed by simulations.

Homotopy Algorithm for Energy-Efficient MIMO Systems with Joint Power Constraints

This paper considers an energy efficiency (EE) optimization problem for multiple-input multiple-output (MIMO) systems, subject to a realistic power constraint jointly imposed on both sum-power and maximum eigenvalue. Inspired by an existing Homotopy-type algorithm for the optimal precoder design of MIMO systems, we fully investigate the usefulness of the piecewise linear property between power allocations and sum-power, and then derive a piecewise-defined algorithm to obtain the maximum EE in a closed form. To the best of our knowledge, it is the first time to present such a closed-form solution for the EE optimization in MIMO systems.

On the Capacity of the Static Half-Duplex Non-Orthogonal AF Relay Channel

In this paper, we analyze the capacity of the static half-duplex single-relay amplify-and-forward (AF) system under both per-node and joint power constraints. Different from multiple-input multiple-output systems, the channel matrix of the cooperative AF system is a function of the parameters to be optimized and hence water-filling over the square of the singular values is no longer optimal. Furthermore, given that the mutual information of the AF system is not a concave function, conventional optimization methods cannot be applied. Instead, by deriving and comparing all local solutions, we characterize the optimal input covariance matrix at the source and the optimal power allocation scheme at the relay that maximize the achievable rate. First, for the individual power constraint scenario, it is shown that the capacity of the AF system is achieved by either a direct transmission (DT) scheme, a non-orthogonal AF (NAF) beamforming (BF) protocol with a unit-rank covariance matrix, or a NAF system using a specific full-rank covariance matrix. Then, for the global power constraint scenario, it is shown that only a DT or a NAF-BF protocol can achieve the capacity. In both cases, orthogonal transmission is strictly suboptimal. The capacity of the AF system is finally analyzed for some concrete examples, such as under asymptotically high and low transmission powers and for several network models.

Linear Precoder Optimization for MIMO Systems with Joint Power Constraints

This paper considers linear precoder optimization problems for multiple-input multiple-output (MIMO) systems. In addition to the conventionally used sum-power constraint, maximum eigenvalue constraint on the precoding matrix is also considered so as to account for power limitations imposed on each antenna by the linearity of its own power amplifier in practical implementations. A framework employing directional derivative is developed to obtain optimal precoder designs for different criteria including maximizing the information rate and minimizing the sum of mean-square error (MSE). It turns out that power allocations in such situations are piecewise linear in sum-power space. The piecewise linear property allows us to generate the entire path of solution through finding out a finite number of breakpoints. A Homotopy-type algorithm is then proposed to obtain the solution for an arbitrary sum-power constraint. The number of breakpoints to be determined in our exact piecewise linear solution is in fact only about two times of the number of transmit antennas, so that our method is super fast and outperforms existing approximate solutions in the literature in both effectiveness and efficiency. Simulated experiments are performed to verify our theoretical analysis.

A Study of Optimization Problem for Amplify-and-Forward Relaying over Weibull Fading Channels with Multiple Antennas

We consider power allocation (PA) and relay positioning in a dual-hop regenerative relaying system with multi-antenna destination node in Weibull fading environment. With the fixed relay location, adaptive PA at the source and relay nodes under joint power constraint and with the aim to minimize the average error probability at high signal-to-noise ratios (SNRs) is presented. Then considering fixed PA, the optimal relay location is derived. Thereafter, we propose to jointly optimize the PA and relay positioning. Numerical simulations are also provided to validate the analytical results, and comparisons between the different optimization schemes and their performance are presented. Results show that optimum PA brings only coding gain, while optimum relay positioning yields diversity gains as well. Also, joint optimization improves both, the diversity gain and the coding gain. Furthermore, results illustrate that the proposed adaptive algorithms outperform uniform schemes.

Cooperative Amplify-and-Forward Beamforming with Multiple Multi-Antenna Relays

In this paper, we consider beamforming (BF) for cooperative networks with one multi-antenna source, multiple multi-antenna amplify-and-forward (AF) relays, and one single-antenna destination. The source BF vector and the AF-BF matrices at the relays are optimized for maximization of the signal-to-noise ratio (SNR) at the destination under three different power constraints. In particular, we consider individual relay power constraints, a joint relay power constraint, and a joint power constraint for the source and the relays. We solve the associated optimization problems in two stages. In the first stage, we find the optimal AF-BF matrices for a given BF vector at the source. For the cases of individual and joint relay power constraints, closed-form solutions for the AF-BF matrices are provided, respectively. Furthermore, for the case of a joint source-relay power constraint, the AF-BF matrices are obtained in closed form up to a scalar power allocation factor and an efficient numerical algorithm for the power allocation between the source and the relays is given. In the second stage, the optimal source BF vectors are computed. Thereby, we show that for the joint relay and the joint source-relay power constraints, the resulting problem can be transformed into a non-convex polynomial programming problem which allows for an exact solution for small-scale networks. For large-scale networks and networks with individual relay power constraints, we propose efficient suboptimal optimization methods for the source BF vector. Simulation results show the benefits of having multiple antennas at the source and/or multiple multi-antenna relays and illustrate the performance differences introduced by the three different power constraints.

Energy-Efficient Transmission Scheduling With Strict Underflow Constraints

This paper considers a single source transmitting data to one or more receivers/users over a shared wireless channel. Due to random fading, the wireless channel conditions vary with time and from user to user. Each user has a buffer to store received packets before they are drained. At each time step, the source determines how much power to use for transmission to each user. The source's objective is to dynamically allocate power in a manner that minimizes total power consumption and packet holding costs, while satisfying strict buffer underflow constraints and a joint power constraint in each slot. The primary application motivating this problem is wireless media streaming. For this application, the buffer underflow constraints prevent the user buffers from emptying, so as to maintain playout quality. In the case of a single user, a state-dependent modified base-stock policy is shown to be optimal with linear power-rate curves, and a state-dependent finite generalized base-stock policy is shown to be optimal with piecewise-linear convex power-rate curves. When certain technical conditions are satisfied, efficient methods to compute the critical numbers that complete the characterizations of the optimal control laws in each of these cases are presented. The structure of the optimal policy for the case of two users is then analyzed.

</title> </titles> <publication_date> <month>06</month> <year>2007</year> </publication_date> <pages> <first_page>1</first_page> <last_page>1</last_page> </pages> <publisher_item> <item_number item_number_type='arNumber'>4200699</item_number> </publisher_item> <doi_data> <doi>10.1109/JSTSP.2007.897064</doi> <resource>http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4200699</resource> </doi_data> </journal_article> <journal_article> <titles> <title><![CDATA[Information Theoretic Adaptive Radar Waveform Design for Multiple Extended Targets

In this paper, we use an information theoretic approach to design radar waveforms suitable for simultaneously estimating and tracking parameters of multiple extended targets. Our approach generalizes the information theoretic water-filling approach of Bell to allow optimization for multiple targets simultaneously. Our paper has three main contributions. First, we present a new information theoretic design criterion for a single transmit waveform using a weighted linear sum of the mutual informations between target radar signatures and the corresponding received beams (given the transmitted waveforms). We provide a family of design criteria that weight the various targets according to priorities. Then, we generalize the information theoretic design criterion for designing multiple waveforms under a joint power constraint when beamforming is used both at the transmitter and the receiver. Finally, we provide a highly efficient algorithm for optimizing the transmitted waveforms in the cases of single waveform and multiple waveforms. We also provide simulated experiments of both algorithms based on real targets and comment on the generalization of the proposed technique for other design criteria, e.g., the linearly weighted noncausal MMSE design criterion

Asymptotic Results for Decentralized Detection in Power Constrained Wireless Sensor Networks

In this paper, we study a binary decentralized detection problem in which a set of sensor nodes provides partial information about the state of nature to a fusion center. Sensor nodes have access to conditionally independent and identically distributed observations, given the state of nature, and transmit their data over a wireless channel. Upon reception of the information, the fusion center attempts to accurately reconstruct the state of nature. Specifically, we extend existing asymptotic results about large sensor networks to the case where the network is subject to a joint power constraint, and where the communication channel from each sensor node to the fusion center is corrupted by additive noise. Large deviation theory is used to show that having identical sensor nodes, i.e., each node using the same transmission scheme, is asymptotically optimal. Furthermore, a performance metric by which sensor node candidates can be compared is established. We supplement the theory with examples to illustrate how the results derived in this paper apply to the design of practical sensing systems.

Performance of DS Spread-Spectrum Receiver Employing Interference-Suppression Filters Under a Worst-Case Jamming Condition

In this paper, the worst-case power spectral density of a narrow-band Gaussian jammer operating in a direct sequence (DS) spread-spectrum system employing an interference-rejection filter is derived under a joint power and bandwidth constraint on the jammer. The effectiveness of the suppression filter under these conditions is examined and average probability of error results for the system's performance are presented.