PEP-Based Optimal Training for MIMO Systems in Wireless Channels

Pair-wise error probability (PEP) is analyzed in the presence of channel estimation error (CEE) for orthogonal frequency division multiplexing (OFDM) in a quasi-static Rayleigh fading channel. Subcarriers in OFDM are grouped in an equi-spaced manner with the number of subcarriers in a group equal to the number of channel taps. One group is dedicated for training and the rest are for data transmission. A linear minimum mean square error (LMMSE) based channel estimation for coherent detection is considered in this paper. This enables the signal dependent CEE to be uncorrelated to the data. Since ML decoding employed with perfect CSI becomes suboptimal in the presence of CEE, an optimal ML decoding is derived. It is observed from our training-based PEP expression that the CEE does not reduce the diversity order but contributes to a loss of coding gain. Moreover, a code design criterion is established. To reduce the loss of coding gain, an optimal training scheme is developed, based on the PEP expression. Loss of performance due to an imperfect channel estimate is quantified in terms of bounds on bit error probability (BEP) for high SNR. Our analytical findings are corroborated by simulation examples.

This paper investigates the optimal precoder design and power allocation between the source and relay for a half-duplex single-relay non-orthogonal amplify-and-forward (NAF) system. Based on the pair-wise error probability (PEP) analysis, an optimal class of 2 × 2 precoders is first derived for the traditional power allocation scheme, where one-third of the system power is spent at the relay node, while two-thirds are spent at the source node. Different from optimal unitary precoders proposed earlier, the derived class of precoders indicates that the source should spend all its power transmitting a superposition of the symbols in the broadcast phase, while being silent in the cooperative phase, for optimal asymptotic performance. We then further address the problem of jointly optimal precoder and power allocation for the system under consideration. It is shown that the total power should be equally distributed to the source and the relay, and the source should again spend no power during the cooperative phase for the best asymptotic performance. Analytical and simulation results reveal that the proposed precoders not only exploit full cooperative diversity, but also provide significant coding gain over the optimal unitary precoders. For instance, a coding gain of around 1dB can be attained at the practical BER level of 10 − 5 for various modulation schemes.

To improve the bandwidth efficiency, a semi-blind channel estimation method using data nulling superimposed pilots (DNSP) is designed for orthogonal frequency division multiplexing (OFDM) system without data rate loss. However, the data distortion is introduced by rank-deficient precoding. To minimize the data distortion, the optimal precoder is found to minimize the Euclidean distance between precoded sequence and source sequence. Further, the impact of power allocation between training sequence and data information on effective signal noise ratio (SNR) is analytically derived, effective SNR is found to be a quadratic function for the percentage allocated for training sequence, and the optimal power allocation is provided to maximize the effective SNR. Simulation results show that our optimal precoder design and power allocation scheme obtain the optimal performance of symbol detection.

For data services over satellite networks, the efficient management of satellite downlink communication resources is crucial for economic competitiveness of the medium. To support a broad spectrum of users with small terminals at high rates, narrow transmit spotbeams on the satellite will be used. Since satellite transmitter resources are expensive and there can be many spotbeam-coverage cells within the satellite service area, it is attractive to use some form of agile scanning beam system and to time-share these precious resources. An optimized design of the multibeam antenna pattern and scheduling can further improve the efficiency of transmission and power management. In this paper, the advantage of parallel multibeams in terms of spectral efficiency and power gain is shown, and the issue of multibeam power allocation based on traffic demands and channel conditions over satellite downlinks with power and delay constraints is addressed. The study indicates that the use of a parallel multibeam scheme with optimum power allocation can achieve a substantial power gain and reasonable proportional fairness. By coupling power allocation with multibeam scheduling when the number of active beams is smaller than the number of cells, the authors show that a modest number of active parallel beams are sufficient to cover many cells efficiently.

In the pursuit of ever increasing demand of higher data rates, modern wireless communication systems are resorting to tighter frequency reuse patterns thereby leading to interference-limited systems. Recently proposed interference-aware receiver [1] is a low complexity and efficient receiver design for interference mitigation in cellular systems. However this advanced receiver necessitates the channel knowledge of both the desired and interfering signals which may not be available in a practical system. In this paper, we investigate the performance of interference-aware receiver under imperfect channel state information (CSI). We consider uncorrelated Rayleigh flat fading channels and model the estimation error as independent complex Gaussian random variables. We derive upper bound on the pair wise error probability (PEP) and show that the interference-aware receiver is characterized by full diversity in the presence of channel estimation errors. We compare the performance of interference-aware receiver with that of MMSE receiver and show that the degradation in the performance of MMSE receiver is much more pronounced than that of interference-aware receiver under imperfect CSI.

In this paper, we consider an optimal power allocation problem that maximizes the sum-rate of a single-cell MISO broadcast channel with regularized channel inversion (RCI) beamforming at the base station (BS). Unlike the channel inversion or zero forcing beamforming, the optimal power allocation with RCI precoding at the base station is a nonlinear non-convex optimization problem with many local optima. Here, we investigate this problem in the large system limit, i.e., when the number of users K and antennas at the base station N tend to infinity with their ratio β = K/N being held constant. We assume each user has data symbol with power p k , and slow-varying path-loss a k . In this setting, we first derive the expression for the signal to interference plus noise ratio (SINR). Then, we divide all K users into L groups where all users in each group are assumed to be co-located or to have approximately the same distance from the BS. In other words, the users in each group have the same path-loss which is distance dependent. Moreover, in each group, we assume that the power allocated to each user is the same. Based on this system model, we investigate optimal power allocation schemes that maximize the sum-rate per antenna, firstly under average power constraint, and then under both average and per-user power constraints. We show that both problems are convex and the power allocation mainly follows the well-known water-filling strategy.

This letter considers the effect of channel estimation errors on the performance of space-time coded (STC) systems with transmit and receive antenna selection over quasi-static flat fading channels. By performing pairwise error probability analysis and presenting numerical examples, we show that the diversity order achieved with perfect channel state information (CSI) is still achievable with imperfect CSI used both at the antenna selection and the space-time decoding processes. We note that our results apply to general STC systems with both transmit and/or receive antenna selection based on largest received powers which can be estimated by any channel estimator.

In this paper, spatial modulation (SM) is used in a cooperative decode-and-forward (DF) cognitive radio system in order to enhance the overall spectral efficiency. In particular, a multi- antenna secondary transmitter communicates with a single antenna secondary receiver with the help of DF secondary relays in the presence of multiple primary users (PUs). To study the secondary system performance, we derive a closed-form expression for the average pairwise error probability (PEP) over Rayleigh fading channels assuming limited feedback from the PUs. A tight upper bounded average bit error rate is obtained using the PEP expression. Moreover, simple approximate expressions are obtained to get insights on the system diversity and estimation errors effects. Numerical results, which match simulations, show the effectiveness of SM in improving the overall secondary performance in the presence of channel estimation errors.

This paper presents an optimal energy-efficient power allocation scheme for a point-to-point multicarrier link over frequency-selective fading channel subject to a delay-outage probability constraint. For a target delay-outage limit, the energy efficiency (EE) objective function is formulated as the ratio of the achieved link effective capacity to the total expenditure power, expressed in units of b/J/Hz. We first prove that this objective function is quasi-concave in the transmission power, and, hence, the global maximum solution of the underlying optimization problem can be obtained using fractional programming. Subsequently, we develop a two-step optimal power allocation algorithm by first obtaining the average sum power level corresponding to the maximum achievable EE, followed by jointly distributing this obtained average power over time and frequency. Analytical results show that the EE-based power allocation has a structure similar to that of the QoS-driven spectral-efficient scheme, but with a different cut-off threshold below which no transmission power is allocated. Simulation results show that the proposed joint optimal power allocation scheme provides significant EE gains over the simple independent subcarrier optimization scheme, where these performance advantages become more pronounced with tighter delay constraints and in fading channels with more severe frequency selectivity.

Novel closed form formulae of iterative optimal power control and allocation, and a criterion for optimal subcarrier allocation, are derived for uplink of multicarrier non-orthogonal multiple access (MC-NOMA) systems. Our new formulae provide intuitive insights on how to optimally allocate subcarriers and power to MC-NOMA (and as a special case, MC-OMA) users. In particular, the novel water-filling power allocation formulae provide a mean to iteratively compute optimal power allocation for a general NOMA cluster size. Convergence of the iterative algorithm and sum rate performance of MC-NOMA system are presented and compared with MC-OMA system.

In this letter, a novel approach for outage probability analysis of the multinode amplify-and-forward relay network is provided. It is shown that the harmonic mean of two exponential random variables can be approximated, at high signal-to-noise ratio (SNR), to be an exponential random variable. The single relay case considered before is a special case of our analysis. Based on that approximation, an outage probability bound is derived which proves to be tight at high SNR. Based on the derived outage probability bound, optimal power allocation is studied. Simulation results show a performance improvement, in terms of symbol error rate, of the optimal power allocation compared to the equal power-allocation scheme

Novel closed form formulae of iterative optimal power control and allocation, and criterion for optimal subcarrier allocation are derived for downlink of multicarrier non-orthogonal multiple access (MC-NOMA) systems. For the first time, we present closed form water-filling formulae that quantify exactly the following effects of multiple access interference for optimal power allocation of MC-NOMA downlink: (i) Each user should take into account the sum of interference from other stronger users plus the receiver Gaussian noise as an equivalent interference in each subcarrier; (ii) The sum of each user’s interference to other weaker users should be accounted as factors which determine the distinct water levels in each subcarrier of each of the other weaker users. We also propose novel iterative water-filling algorithm and projected conjugate gradient algorithm that facilitate iterative computation of optimal power allocation for MC-NOMA downlink.

We propose an iterative detection scheme for Turbo-BLAST system with optimal power allocation in the presence of channel state information imperfection. The proposed scheme uses the channel estimation matrix for detection and treats the interference caused by channel estimation errors and additive white Gaussian noise as equivalent noise where the channel estimation matrix and the statistical characteristic of channel estimation errors are necessitated. Simulation results show the proposed algorithm is effective to improve bit error rate (BER) performance through iterative detection for modified Turbo-BLAST system with optimal power allocation in the presence of imperfect channel state information.

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

Power and code allocation across two adjacent cells is studied for the downlink of a code-division multiple-access voice network. Each user has a utility function that measures the user's willingness to pay, or utility, as a function of the received signal-to-interference-plus-noise-ratio. The objective is to maximize the total utility over the two cells subject to code and power constraints. When all active users receive the same utility, the optimal allocation is characterized by a pair of threshold radii for the two cells, where each radius specifies the set of active users in that cell. The behavior of the optimal radii are characterized as a function of load and available resources (power and codes). The corresponding optimal power allocation can be achieved through a pricing scheme, in which each base station announces a price for each resource, and each user responds by requesting the amount of resources that maximizes the user's surplus (utility minus cost). We show that, depending on the load and resource constraints, the two cells may have to coordinate, or exchange information, in order to maximize the total utility.