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Optimal Power Allocation for Hybrid ARQ with Chase Combining in i.i.d. Rayleigh Fading Channels
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7599-4367
2013 (English)In: IEEE Transactions on Communications, ISSN 0090-6778, E-ISSN 1558-0857, Vol. 61, no 5, 1835-1846 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
IEEE Press, 2013. Vol. 61, no 5, 1835-1846 p.
Keyword [en]
Hybrid-ARQ, diversity combining, optimal power allocation, outage probability, geometric programming.
National Category
Communication Systems Telecommunications
Identifiers
URN: urn:nbn:se:liu:diva-89650DOI: 10.1109/TCOMM.2013.032013.120422ISI: 000319752600019OAI: oai:DiVA.org:liu-89650DiVA: diva2:608658
Funder
eLLIIT - The Linköping‐Lund Initiative on IT and Mobile CommunicationsSwedish Foundation for Strategic Research Swedish Research Council
Available from: 2013-04-03 Created: 2013-02-28 Last updated: 2017-12-06Bibliographically approved
In thesis
1. HARQ Systems: Resource Allocation, Feedback Error Protection, and Bits-to-Symbol Mappings
Open this publication in new window or tab >>HARQ Systems: Resource Allocation, Feedback Error Protection, and Bits-to-Symbol Mappings
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Reliability of data transmission is a fundamental problem in wireless communications. Fading in wireless channels causes the signal strength to vary at the receiver and this results in loss of data packets. To improve the reliability, automatic repeat request (ARQ) schemes were introduced. However these ARQ schemes suffer from a reduction in the throughput. To address the throughput reduction, conventional ARQ schemes were combined with forward error correction (FEC) schemes to develop hybrid-ARQ (HARQ) schemes. For improving the reliability of data transmission, HARQ schemes are included in the present wireless standards like LTE, LTE-Advanced and WiMAX.

Conventional HARQ systems use the same transmission power and the same number of channel uses in different ARQ rounds. However this is not optimal in terms of minimizing the average transmit power or the average energy spent for successful transmission of a data packet. We address this issue in the first part of the dissertation, where we consider optimal resource allocation in HARQ systems with a limit on the maximum number of allowed transmissions for a data packet. Specifically, we consider the problem of minimizing the packet drop probability (PDP) under an average transmit power constraint or equivalently minimizing the average transmit power under a fixed PDP constraint. We consider both incremental redundancy (IR)-based and Chase combining (CC)-based HARQ systems in our work. For an IR-HARQ system, for the special case of two allowed transmissions for each packet, we provide a solution for the optimal number of channel uses and the optimal power to be used in each ARQ round. For a CC-HARQ system, we solve the problem of optimal power allocation in i.i.d. Rayleigh fading channels as well as correlated Rayleigh fading channels. For the CC-HARQ case, we also provide a low complexity geometric programming (GP) solution using an approximation of the outage probability expression.

HARQ systems conventionally use one bit acknowledgement (ACK)/negative ACK (NACK) feedback from the receiver to the transmitter. In the 3GPP-LTE systems, one method for sending these HARQ acknowledgement bits is to jointly code them with the other control signaling information using a specified Reed-Muller code consisting of 20 coded bits. Even though the resources used for sending this control signaling information can inherently provide a diversity gain, the Reed-Muller code with such a short block size is not good at extracting all of the available diversity. To address this issue, in the second part of this dissertation, we propose two new methods: i) based on complex-field coding (CFC), and ii) using repetition across frequency bands, to extract the inherent diversity available in the channel resources and improve the error protection for the HARQ acknowledgement bits along with the other control signaling information. In the second part of the dissertation, we also propose a new signal space diversity (SSD) scheme, which results in transmit signals having constant envelope (CE). The proposed CE-SSD scheme results in a better overall power efficiency due to the reduced back-off requirements on the radio frequency power amplifier. Moreover, the proposed CE-SSD technique can be useful for application scenarios involving transmission of small number of information bits, such as in the case of control signaling information transmission.

In conventional HARQ systems, during the retransmission phase, the channel resources are exclusively used for the retransmitted data packet. This is not optimal in terms of efficient resource utilization. For efficient utilization of channel resources during the retransmissions, a superposition coding (SPC) based HARQ scheme was proposed in the literature. In an SPC based HARQ system, an erroneous packet is transmitted together with a new data packet by superposition in the Euclidean space. In the final part of this dissertation, we study performance of different bits-to-symbol mappings for such an SPC based HARQ system.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. 43 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1526
Keyword
HARQ Systems, Resource Allocation, Geometric Programming, 3GPP-LTE, PUCCH Format 2, Complex-field coding, Signal Space Diversity, Optimization, Superposition Coding
National Category
Communication Systems Telecommunications
Identifiers
urn:nbn:se:liu:diva-96021 (URN)978-91-7519-574-2 (ISBN)
Public defence
2013-09-27, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:56 (English)
Opponent
Supervisors
Available from: 2013-09-11 Created: 2013-08-13 Last updated: 2017-01-13Bibliographically approved

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