Sum Capacity Maximization Research Articles

Joint Precoding Optimization for Multiuser Multi-Antenna Relaying Downlinks Using Quadratic Programming

This paper studies the optimization problem for joint precoding design in a multi-antenna downlink channel using relaying. We formulate the joint source and relay precoding design by aiming at sum capacity maximization. Since this problem is in general nonconvex, we first convert this problem into standard convex quadratic programs, and then propose an iterative joint precoding optimization algorithm by utilizing efficient quadratic programming approaches. We observe that the iterative method always yields optimal precoding matrices which diagonalize the compound channel of the backward (source-to-relay) and the forward (relay-to-destination) links at high SNR regimes. Motivated by this observation, we further develop an efficient structured precoding design. Simulation results are presented to verify the effectiveness of our proposed precoding schemes.

Resource allocation for multiuser cognitive OFDM networks with proportional rate constraints

In this paper we study the resource allocation problem for the multiuser orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) systems with proportional rate constraints. The mutual interference introduced by primary user (PU) and cognitive radio user (also referred to secondary user, SU) makes the optimization problem of CR systems more complex. Moreover, the interference introduced to PUs must be kept under a given threshold. In this paper, the highest achievable rate of each OFDM subchannel is calculated by jointly considering the channel gain and interference level. First, a subchannel is assigned to the SU with the highest achievable rate. The remaining subchannels are always allocated to the SU that suffers the severest unjustness. Second, an efficient bit allocation algorithm is developed to maximize the sum capacity, which is again based on the highest achievable rate of each subchannel. Finally, an adjustment procedure is designed to maintain proportional fairness. Simulation results show that the proposed algorithm maximizes the sum capacity while keeping the proportional rate constraints satisfied. The algorithm exhibits a good tradeoff between sum capacity maximization and proportional fairness. Furthermore, the proposed algorithm has lower complexity compared with other algorithms, rendering it promising for practical applications. Copyright © 2011 John Wiley & Sons, Ltd. (By jointly considering the channel gain and the interference level of the OFDM-based cognitive radio systems, the highest achievable rate of each subchannel can be calculated, which indicates the ability of carrying bits of the subchannel. Using the normalized cost index list, an efficient algorithm is proposed to maximize the sum capacity of the cognitive OFDM systems while keeping the proportional rate constraints satisfied.)

Adaptive Resource Allocation for a Two-Way OFDM Relay Network with Fairness Constraints

In this letter, we propose a new resource allocation scheme for a two-way OFDM relay network with fairness constraints. To maximize sum capacity, subcarriers and their power are successively allocated to the relays based on channel conditions. Also, the power constraint is imposed on each relay to achieve fairness for the relays. Simulation results show that the proposed scheme improves sum capacity and fairness significantly.

Joint Optimization of Source Power Allocation and Relay Beamforming in Multiuser Cooperative Wireless Networks

Relay beamforming techniques have been shown to significantly enhance the sum capacity of a multiuser cooperative wireless network through the optimization of the relay weights, where concurrent communications of multiple source-destination pairs are achieved via spatial multiplexing. Further optimization of the transmit power allocation over the source nodes is expected to improve the network throughput as well. In this paper, we maximize the sum capacity of a multiuser cooperative wireless network through the joint optimization of power allocation among source nodes and relay beamforming weights across the relay nodes. We consider a two-hop cooperative wireless network, consisting of single-antenna nodes, in which multiple concurrent links are relayed by a number of cooperative nodes. When a large number of relay nodes are available, the channels of different source-destination pairs can be orthogonalized, yielding enhanced sum network capacity. Such cooperative advantage is particularly significant in high signal-to-noise ratio (SNR) regime, in which the capacity follows a logarithm law with the SNR, whereas exploiting spatial multiplexing of multiple links yields capacity increment linear to the number of users. However, the capacity performance is compromised when the input SNR is low and/or when the number of relay nodes is limited. Joint optimization of source power allocation and relay beamforming is important when the input SNR and/or the number of relay nodes are moderate or the wireless channels experience different channel variances. In these cases, joint optimization of source power and distributed beamforming weights achieves significant capacity increment over both source selection and equal source power spatial multiplexing schemes. With consideration of the needs to deliver data from each source node, we further examine the optimization of global sum capacity in the presence of individual capacity requirements by maximizing sum capacity of the network subject to a minimum capacity constraint over each individual user.

ARQ by Subcarrier Assignment for OFDM-Based Systems

We consider two automatic repeat request (ARQ) schemes based on subcarrier assignment in orthogonal frequency-division multiplexing (OFDM)-based systems: single ARQ subcarrier assignment (single ARQ-SA) and multiple ARQ-SA. In single ARQ-SA, data transmitted on a subcarrier in a failed transmission are repeated on a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">assigned</i> subcarrier in the ARQ transmission. In multiple ARQ-SA, the data are repeated on <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">assigned</i> subcarriers in the ARQ transmission. At the receiver, maximum ratio combining is performed on subcarriers that carry the same data. Our goal is to optimize certain system utility functions (such as to minimize bit error rates or to maximize sum capacity) through the choice of the subcarrier assignment. We show that a large class of reasonable system utility functions that we wish to maximize are characterized as Schur-concave. For this class of utility functions, we obtain the optimum subcarrier assignment for single ARQ-SA and propose a suboptimum (heuristic) subcarrier assignment scheme for multiple ARQ-SA. Further, to lower the overhead of signaling the subcarrier assignment information, we consider subcarrier grouping methods. Numerical results indicate that substantial throughput improvement can be achieved by appropriate assignments, especially with the use of incremental redundancy at high signal-to-noise ratios.

Jointly Optimal Signature Sequences and Power Allocation for CDMA Systems

The problems of designing signature sequences and power allocation policy for code-division multiple access (CDMA) are important and have been the subject of intensive research in recent years. Taking the maximization of the system information theoretic sum capacity as the design criterion, most of the previous works only consider the optimizations of signature sequences and power allocation separately. In contrast, this letter presents a jointly optimal design of signature sequences and power allocation for a CDMA system with fixed, but unequal channel gains and under the sum power constraint. The proposed design is of closed-form, and applicable for the general case of correlated signals and colored noise. Numerical results verify the superiority of the proposed design over the existing ones.

Downlink resource allocation in multi-carrier systems: frequency-selective vs. equal power allocation

This paper revisits equal power allocation from the viewpoint of asymptotic network utility maximization (NUM) problem in multi-carrier systems. It is a well-known fact that the equal power allocation is near optimal to the sum capacity maximization problem in high SNR (signal-to-noise ratio) regime, i.e., optimal water-filling approximates to equal power allocation in that case. Due to this property together with its simplicity, the equal power allocation has been adopted in several researches, but its performance in other problems has not been clearly understood. We evaluate the suitability of equal power allocation in NUM problem which turns into various resource sharing policies according to utility functions. Namely, our conclusion is that in frequency selective channels, the equal power allocation is near optimal for efficiency-oriented resource sharing policy, but when fairness is emphasized, its performance is severely degraded and thus frequency-selective power allocation is necessary. For this, we develop a suboptimal subcarrier and frequency-selective power allocation algorithm for asymptotic NUM problem using the gradient-based scheduling theory and compare the performance of equal power allocation and the developed algorithm. Extensive simulation results are presented to verify our arguments.

A low complexity user scheduling algorithm for uplink multiuser MIMO systems

A low complexity user scheduling algorithm based on a novel adaptive Markov chain Monte Carlo (AMCMC) method is proposed to achieve the maximal sum capacity in an uplink multiple-input multiple-output (MIMO) multiuser system. Compared with the existing scheduling algorithms, our algorithm is not only more efficient but also converges to within 99% of the optimal capacity obtained by exhaustive search. We demonstrate the convergence of the proposed scheduling algorithm and study the tradeoff between its complexity and performance.

On the Dual-Decomposition-Based Sum Capacity Maximization for Vector Broadcast Channels

The dual-decomposition-based sum capacity maximization algorithm for the vector broadcast channels consists of the following two nested loops: The inner loop is an iterative water-filling-like algorithm that optimizes the covariance matrices for a fixed water level, and the outer loop finds the optimum water level by using a bisection search. Recently, an improved version has been proposed, where the inner loop is optimized only to a certain tolerance that still guarantees algorithm convergence. This requires tracking the instantaneous error of the inner loop, and this issue has not yet been addressed. In this paper, we provide a tight upper bound of the instantaneous error of the inner loop, which can be used to construct a nonheuristic stopping criterion. Specifically, we derive the Lagrange dual function of the inner optimization problem and provide a method to obtain a feasible dual variable from which a tight upper bound of the instantaneous error can easily be computed. We also show that the rate of convergence of the global algorithm can substantially be improved by introducing a covariance normalization step between two successive outer iterations.

Interference Avoidance and Multiaccess Vector Channels

In this paper we present application of interference avoidance in the context of a general multiple access vector channel model. We show that this monotonically increases sum capacity, and discuss algorithms for code division multiple access (CDMA) codeword optimization based on this procedure. A greedy interference avoidance algorithm for multiaccess vector channels is presented in the paper, for which we discuss convergence to a class of codeword ensembles that satisfy a simultaneous water filling solution and maximize sum capacity. Numerical results obtained from simulations that corroborate our analytical results are also presented.

Adaptive Resource Allocation and Capacity Comparison of Downlink Multiuser MIMO-MC-CDMA and MIMO-OFDMA

In this paper, we examine and compare the potential maximum sum capacity of downlink multiple-input-multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) and multiple-input-multiple-output multicarrier code division multiple access (MIMO-MC-CDMA) in a single-cell multiuser environment with channel side information at the transmitter, with and without a fairness constraint. The resource allocation is formulated as a cross-layer optimization framework and optimal power allocation and user selection algorithms are proposed for both scenarios. We find that for delay-sensitive applications, where fairness is imposed, the performance gain of OFDMA over MC-CDMA is quite large at moderate path loss exponents and number of antennas. However, for delay-insensitive applications, the benefits of OFDMA over MC-CDMA are significantly reduced when the path loss exponent or the number of antennas is large

Sequences that maximize the symmetric capacity under the requirement of quasi-scalability

We examine the symmetric capacity of quasi-scalable systems under the equal average input energy constraint. It turns out that the maximum achievable symmetric capacity is equal to the maximum achievable sum capacity. Moreover, the multiple-OCDMA signature sets, which are known to maximize the sum capacity under the constraint of quasi-scalability, actually achieve this maximum symmetric capacity.

Sequences that maximize the symmetric capacity under the requirement of quasi-scalability

We examine the symmetric capacity of quasi-scalable systems under the equal average input energy constraint. It turns out that the maximum achievable symmetric capacity is equal to the maximum achievable sum capacity. Moreover, the multiple-OCDMA signature sets, which are known to maximize the sum capacity under the constraint of quasi-scalability, actually achieve this maximum symmetric capacity.

Adaptive resource allocation in multiuser OFDM systems with proportional rate constraints

Multiuser orthogonal frequency division multiplexing (MU-OFDM) is a promising technique for achieving high downlink capacities in future cellular and wireless local area network (LAN) systems. The sum capacity of MU-OFDM is maximized when each subchannel is assigned to the user with the best channel-to-noise ratio for that subchannel, with power subsequently distributed by water-filling. However, fairness among the users cannot generally be achieved with such a scheme. In this paper, a set of proportional fairness constraints is imposed to assure that each user can achieve a required data rate, as in a system with quality of service guarantees. Since the optimal solution to the constrained fairness problem is extremely computationally complex to obtain, a low-complexity suboptimal algorithm that separates subchannel allocation and power allocation is proposed. In the proposed algorithm, subchannel allocation is first performed by assuming an equal power distribution. An optimal power allocation algorithm then maximizes the sum capacity while maintaining proportional fairness. The proposed algorithm is shown to achieve about 95% of the optimal capacity in a two-user system, while reducing the complexity from exponential to linear in the number of subchannels. It is also shown that with the proposed resource allocation algorithm, the sum capacity is distributed more fairly and flexibly among users than the sum capacity maximization method.

Optimal Sequences and Sum Capacity of Symbol Asynchronous CDMA Systems

The optimal signature sequences that maximize the sum capacity of a direct sequence code-division multiple-access (CDMA) system are characterized in the general case of symbol delay profile and user power constraints. It is shown that the optimal sum capacity of the symbol asynchronous system equals that of the symbol synchronous system with the same user power constraints. With the optimal signature sequence set, the maximum sum capacity is achieved with white Gaussian input signals. The existence of the optimal signature sequence set is proved by the proposal of an explicit construction method for arbitrary user delay profiles and power constraints.

Sum Capacity of Equal-Power Users in Overloaded Channels

We consider the sum capacity of code-division multiple-access (CDMA) signature-sequence sets in overloaded channels that contain an orthogonal subset of dimension N. We introduce a family of signature-sequence sets that consists of a hierarchy of orthogonal subsets (HOS), and show that various signature-sequence sets designed for channel overloading belong to this family. Assuming an equal average energy (EAE) constraint on the user signals, an expression for the sum capacity of the HOS family is derived. We point out that the maximum sum capacity over the HOS family is achieved by the multiple-orthogonal (m-O) CDMA sequence sets. The sum capacity of m-O is only slightly less than the upper bound imposed by the Gaussian multiple-access channel. Moreover, m-O is superior to a system with N orthogonal sequences and (K-N) pseudonoise (PN) sequences (PN/O), which, in turn, outperforms a system with K PN sequences. Both for PN/O and sequence sets over HOS, there is no additional loss in sum capacity if we require the sequences to consist of chips that are binary or quaternary valued.

The Maximum Squared Correlation, Sum Capacity, and Total Asymptotic Efficiency of Minimum Total-Squared-Correlation Binary Signature Sets

The total squared correlation (TSC), maximum squared correlation (MSC), sum capacity (C/sub sum/), and total asymptotic efficiency (TAE) of underloaded signature sets, as well as the TSC and C/sub sum/ of overloaded signature sets are metrics that are optimized simultaneously over the real/complex field. In this present work, closed-form expressions are derived for the MSC, C/sub sum/, and TAE of minimum-TSC binary signature sets. The expressions disprove the general equivalence of these performance metrics over the binary field and establish conditions on the number of signatures and signature length under which simultaneous optimization can or cannot be possible. The sum-capacity loss of the recently designed minimum-TSC binary sets is found to be rather negligible in comparison with minimum-TSC real/complex-valued (Welch-bound-equality) sets.

Greedy SINR Maximization in Collaborative Multibase Wireless Systems

We present a codeword adaptation algorithm for collaborative multibase wireless systems. The system is modeled with multiple inputs and multiple outputs (MIMO) in which information is transmitted using multicode CDMA, and codewords are adapted based on greedy maximization of the signal-to-interference-plus-noise ratio. The procedure monotonically increases the sum capacity and, when repeated iteratively for all codewords in the system, converges to a fixed point. Fixed-point properties and a connection with sum capacity maximization, along with a discussion of simulations that corroborate the basic analytic results, are included in the paper.

Comments on "Symmetric capacity and signal design for L-out-of-K symbol-synchronous CDMA Gaussian channels

For original paper see A. A. Alsugair and R. S. Cheng, ibid., vol. 41, p. 1072-1082 (July, 1995). We show that the signature sequences set that maximizes the lower bound on symmetric capacity derived in the above paper also maximizes the sum capacity of the Gaussian synchronous code-division multiple-access (CDMA) channel. This is done by relying on the equivalence of the eigenvalues of energy-weighted correlation matrices. This result establishes the missing link between the above paper and the sum capacity maximization result by Viswanath et al. (1999).

Sum Capacity and TSC Bounds in Collaborative Multibase Wireless Systems

We consider a wireless system with base stations which collaborate, and derive bounds on sum capacity and total squared correlation for uniform channels between users and bases. The correspondence also investigates structural properties which must be satisfied by user transmit covariance matrices at the optimal sum capacity/total squared correlation (TSC) point, and shows that for multibase systems, maximizing sum capacity and minimizing TSC are, in general, not equivalent problems.