Optimal Power Allocation for Hybrid ARQ with Chase Combining in i.i.d. Rayleigh Fading Channels

Abstract

Abstract-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.

On the impact of HARQ on the throughput and energy efficiency using cross-layer analysis

“…In the PHY layer we assume the use of HARQ with Chase combining, in which previous erroneous transmission attempts are not discarded, but rather combined at the receiver [9], [15]. This scheme increases the chance of correct decoding by allowing up to M transmissions of the same packet in case of successive outage.…”

“…As a result, the use of HARQ may present a trade-off in terms of energy efficiency. In the literature, optimal power allocation for HARQ has been considered, e.g., in [9], [10], minimizing the necessary transmit power in block fading scenarios. Moreover, an energy and spectral efficiency trade-off was analyzed in [11] and a closedform expression for the energy efficiency is provided by [12].…”

Outage-optimal power adaptation and allocation for truncated HARQ

“…To solve the primal problem in (9), it is difficult to use the Karush-Kuhn-Tucker (KKT) conditions on the Lagrangian function (12) since it requires to solve analytically a system of an infinite number of equations where, in addition, closed form expressions of f k (for 2 ≤ k ≤ K) are unknown. To overcome these difficulties, we can solve the dual problem.…”

“…The case of long-term static channels was also studied in [10], where the authors determined the optimal power assignment strategy to minimize the total average transmission power subject to outage probability constraints. The optimization of energy efficiency with a packet error rate (PER) constraint was solved as a geometric programming problem in [11] for the case of space-time coded HARQ and in [12] for CC-HARQ over independent Rayleigh block fading channels. In [13], the authors derived an optimal power allocation scheme which minimizes the packet drop probability under a total average transmit power constraint for IR-HARQ with two transmissions.…”

“…The optimal solutions are given in parametrized closed form for an arbitrary number of transmissions. We note that only two transmissions were allowed in [13], while in [12] and [13] only Rayleigh block fading channels were considered. 3) We provide numerical results for practically interesting wireless channel models, comparing the outage probability with various power adaptation/allocation methods.…”