We consider Hybrid Automatic Repeat & reQuest with Chase-combining (HARQ-CC) for uplink spectral efficiency enhancement in a multicell system with base- stations (BSs) using large antenna arrays. Each BS uses a zero-forcing receiver and knows only the channel gains of users in its own cell. We first derive the outage probability and long-term average transmission rate (LATR) of the proposed HARQ-CC while limiting the number of retransmissions. We then formulate the optimal rate-selection problem for the proposed scheme and provide a method to find a solution. Since the optimal-rate selection method for the HARQ-CC scheme is computationally intensive, we develop a sub-optimal rate-selection technique that has a LATR performance close to that of the optimal method. Illustrative results show that the HARQ-CC requires less number of antennas than the non-HARQ scheme to achieve the same LATR performance.

We consider hybrid automatic repeat and request (HARQ) schemes in the uplink of a multicell multiuser single-input multiple-output system with large-scale antenna arrays at the base station (BS) for improving the spectral efficiency while limiting the number of retransmissions. Assuming a zero-forcing receiver at each BS and that each BS knows only the channel gains of users in its own cell, we derive the expressions for the outage probability and long-term average transmission rate (LATR) of the Type-I HARQ, HARQ with chase-combining (HARQ-CC), and HARQ with incremental redundancy (HARQ-IR). We then formulate the optimal rate-selection problems for the three schemes and provide methods to find a solution. Since the optimal-rate selection methods for the HARQ-CC and HARQ-IR schemes are computationally intensive, we propose sub-optimal rate-selection methods, which yield a closer LATR performance to that of the optimal methods. For the Type-I HARQ and HARQ-IR, we also present a parameterization-based method showing the approximate relation between the expressions of the optimized-LATR, optimal rate, and number of antennas. Illustrative results show that the HARQ-IR has significant gain over HARQ-CC and Type-I HARQ in terms of LATR, while Type-I HARQ yields practically similar performance to HARQ-CC as the number of antennas at the BS increase.

We consider progressive hybrid precoder design for packet retransmissions in large-scale multiple-input multiple-output (MIMO) systems with perfect channel state information (CSI) knowledge at the transmitter. To exploit time diversity provided by packet retransmissions, we propose a two-step approach to optimize both the radio-frequency (RF) precoder and the corresponding baseband precoder with the objective of maximizing the mutual information. During each retransmission attempt, we choose the RF precoder matrix columns from the set of transmit array response vectors. For a given RF precoder, we show that the optimal baseband precoder is a function of the generalized eigen-matrix of the Gram matrices of the effective channel matrix and the RF precoding matrix. The optimal baseband precoder for each transmission round includes appropriate power loading, selection and reverse pairing of the singular values of the previous transmission attempts with the ratio of the elements obtained by the diagonalization of the Gram matrices of the effective channel matrix and the RF precoding matrix using a generalized eigen-matrix. Illustrative results show that the proposed progressive hybrid precoder design achieves a performance close to that of the optimal progressive digital precoder (OPDP).

This paper deals with energy-efficient adaptive power allocation for an incremental multiple-input multiple-output (IMIMO) system employing hybrid automatic repeat request (HARQ) with Chase combining (CC), to minimize its rate-outage probability under a constraint on average energy consumption per data packet. We first provide the rate-outage probability expressions for the considered IMIMO system, and use Gauss-Legendre approximation to convert them into a tractable form and formulate a non-convex optimization problem that can be solved by an interior-point algorithm for finding a local optimum. Next, to further reduce the solution complexity, using an asymptotically equivalent approximation of the rate-outage probability expression, we approximate the non-convex optimization problem as a geometric programming problem (GPP), for which a solution can be obtained using convex optimization algorithms. Illustrative results indicate that the proposed power allocation (PPA) offers significant gains in energy savings as compared to the equal-power allocation (EPA), and the less complex GPP approach can provide a closer performance to the exact method at lower values of rate-outage probability.

We consider the power allocation and relay selection for rate maximization in a two-path amplify-and-forward (AF) relay network with inter-relay interference (IRI) consideration. We first investigate the power allocation with only a pair of relays under both the individual and global power constraints. To find the global optimum solution to this nonconvex problem, we develop a three-step approach using the rate-profiling technique together with a reformulation of the sum-rate maximization problem as a set of power-minimization geometric programming problems (GPPs). For reduced complexity, we further convert the optimization problem into a set of GPPs in a single-step by using a high signal-to-interference-plus-noise ratio approximation. Next, we consider the relay pair selection and propose an algorithm in which the achievable rate of each pair of relays with the proposed power allocation is compared. This selection criterion outperforms the conventional selection scheme in terms of the achievable rate. We further propose two low-complexity selection criteria for low and moderate IRI. For moderate IRI, the ratio of the source-relay and relay-destination channel power product to the square of inter-relay channel power can be used for relay selection to achieve a performance close to that of the selection based on the proposed power allocation.

We propose a nonlinear signal space diversity (SSD) precoding technique that produces transmit signals that have constant envelope (CE) in discrete time, resulting in low peak-to-average power ratio (PAPR) waveforms after pulse-shape filtering. We propose two methods for construction of CE signal set. While the proposed CE-SSD scheme is inferior to the conventional SSD designs in terms of coding gain performance, it performs better in terms of overall power efficiency because of the reduced back-off requirement of the power amplifier (PA).

We consider the mapping of bits-to-superimposed constellation symbols in terms of the achievable rate on the channel for the HARQ system using superposition coding as proposed in [2]. We show that using a Gray mapping of bits-to-superimposed constellation symbols has better performance than the conventional natural mapping that results from superposition in signal space, for all the values of the superposition ratio. We also show through link-level simulations that the predicted gains in terms of achievable rate can be realized in practice using LDPC codes. Furthermore, we show that the optimal superposition ratio for the Gray mapping case results in conventional higher order constellation symbols after the superposition operation.

We consider the optimization of Chase combining (CC)-based hybrid-automatic repeat request (HARQ) schemes with a limit on the maximum number of retransmissions. We formulate two optimization problems: (i) minimizing the packet drop probability (PDP) under a total average transmit power constraint, and (ii) minimizing the average transmit power under a fixed PDP constraint. Towards solving these equivalent optimization problems, we provide a closed-form expression for the outage probability of a CC-HARQ scheme. We then show that solving the optimization problems using an exact expression of the outage probability becomes complex with an increase in the maximum number of retransmissions. We propose an alternative approach in which we approximate the optimization problems by using an approximate outage probability expression and formulate the two optimization problems as two equivalent geometric programming problems (GPPs), which can be solved efficiently even for a large limit on the maximum number of retransmissions. The results show that the optimal power allocation solution provides significant gains over the equal power allocation solution. For PDP values below 10-3, the optimal solution provided by the GPP approach has a performance close to that of the solution provided by solving the optimization problem exactly using nonlinear optimization techniques.

We consider the optimization of power in incremental redundancy (IR) based hybrid automatic repeat request (HARQ) schemes when the maximum number of (re)transmissions is fixed. We formulate two optimization problems: (i) minimizing the packet drop probability (PDP) under a total average transmit power constraint, and (ii) minimizing the average transmit power under a fixed PDP constraint. We consider in detail the special case of only two allowed transmissions, and we prove that the two optimization problems are equivalent. For this special case, we also provide a sub-optimal root-finding solution and compare its performance with the optimal solution obtained through an exhaustive search. The results show that the optimal power allocation can provide significant gains over the equal power solution in terms of average transmit power spent. The performance of the proposed root-finding solution is practically the same as that of the optimal solution.

In this paper, we study retransmission strategies for the symmetric relaying scenario when the number of retransmissions for a data packet is limited. We propose a retransmission scheme based on superposition modulation and give the exact packet drop probability expression for it when only one retransmission is allowed. We compare the performance of the proposed retransmission scheme with retransmission schemes based on classical decode-and-forward (DF) relaying and non-cooperative transmission. When only two retransmissions are allowed, the proposed scheme has a performance gain of 3 dB in SNR over the retransmission scheme based on classical DF relaying. Through simulations, we also study the effect of varying the superposition ratio for the retransmissions.

We study the uplink control signaling in 3GPP-Long Term Evolution (LTE) systems. Specifically, we propose a precoding method that uses complex-field coding (CFC) to improve the performance of the PUCCH format 2 control signaling. In the case of perfect channel state information (CSI) at the receiver and with a single receive antenna, the proposed method offers significant gains compared to the coding currently used in 3GPP-LTE. However the gains are marginal with two receive antennas. In order to examine the impact of channel estimation errors, we also derive the optimal detector for the case of imperfect receiver CSI, both for conventional coding and for the proposed CFC method.