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) undera total average transmit power constraint, and (ii) minimizingthe 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 work, we first provide an exact closed-form expression for the packet drop probability (PDP) in incremental redundancy (IR) based hybrid automatic repeat request (HARQ) schemes with a limit on the maximum number of transmissions. In the later part, we extend our work in [5], and consider the optimal resource allocation problem of minimizing the PDP under the constraints of an average transmit power and total number of channel uses. We provide two approaches to solve this optimization problem and compare their performance with the solution given in [5].

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 problem of minimizing the packet drop probability (PDP) under an average transmit power constraint for Chase combining (CC)-based hybrid-automatic repeat request (HARQ) schemes in correlated Rayleigh fading channels. We propose a method to find a solution to the non-convex optimization problem using an exact expression of the outage probability. However, the complexity of this method is high. Therefore, we propose an alternative approach in which we use an asymptotically equivalent expression for the outage probability and reformulate it as a geometric programming problem (GPP), which can be efficiently solved using convex optimization algorithms.

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 physical uplink control channel (PUCCH) format 2 control signaling. We derive optimal detectors for both the conventional method and the proposed precoding method for different cases of channel state information (CSI) and noise variance information at the receiver. With a single receive antenna, the proposed method offers significant gains compared to the coding currently used in 3GPP-LTE for all the different scenarios considered in this work. However the gains are relatively less with two receive antennas.

We propose improvements for the physical uplink control channel (PUCCH) format 2 control signaling in 3GPP-LTE systems. These improvements can be useful for low-cost UE design and optimization planned for the future LTE releases. In the proposed method, instead of repeating a single QPSK symbol across the 12 subcarriers in each OFDM symbol of a resource block as done in the current release of the standard, we pick two QPSK symbols from two independent resource blocks and repeat them across 6 subcarriers each. The proposed method has a performance gain of about 5.5 dB and 1.85 dB over the conventional method with one and two receiving antennas at the base station, respectively. These gains can be achieved without the use of any additional transmission power, time-frequency resources or receiver complexity.

The cell-specific QPSK sequences specified in the standard for PUCCH transmission are chosen according to the conventional repetition across the 12 subcarriers, hence we suggest new cell-specific QPSK sequences which minimize the peak-to-average-power ratio (PAPR) of the PUCCH signal with the proposed method.

We propose a nonlinear signal space diversity (SSD) precoding techniquethat 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 twomethods for construction of CE signal set. While the proposed CESSDscheme is inferior to the conventional SSD designs in termsof coding gain performance, it performs better in terms of overallpower efficiency because of the reduced back-off requirement of thepower 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 thanthe 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.