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Combined Cross-Layer Design and HARQ for TDD Multiuser systems with Outdated CSIT. Rui Wang & Vincent K. N. Lau Dept. of ECE The Hong Kong University of Science & Technology. Outline. Model of Multiuser System with HARQ-IR Cross-Layer Problem Formulation Cross-Layer Scheduler Design
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Combined Cross-Layer Design and HARQ for TDD Multiuser systems with Outdated CSIT Rui Wang & Vincent K. N. Lau Dept. of ECE The Hong Kong University of Science & Technology
Outline • Model of Multiuser System with HARQ-IR • Cross-Layer Problem Formulation • Cross-Layer Scheduler Design • Discussions & Simulation Results • Conclusions
Encoder: Information Coded Packet Tx: 1st Tx 2nd Tx 3rd Tx 4th Tx Rx: MRC Combining Achieve larger receiving SNR Encoder: Information Subpacket Subpacket Subpacket Subpacket Tx: 1st Tx 2nd Tx 3rd Tx 4th Tx Rx: Subpacket Subpacket Subpacket Subpacket Protect the packet by redundancy HARQ • Generally speaking, HARQ (Hybird Automatic Retransmission reQuest) is a retransmission technique to improve the packet receiving. • There are two schemes of HARQ retransmission: • Chase Combining (CC): the retransmit packets are exactly the same, while the receiver combines the multiple copies of the packet to obtain a higher post-combining SNR. • Incremental Redundancy (IR): the information is first encoded into a long mother code, and then punctured into multiple blocks where the blocks will be sent in subsequent retransmission. • We consider the scheme of incremental redundancy in this paper.
User 1 BS User 2 User 3 Noise Channel gain Received symbol System Model • We consider downlink transmission of a multiuser system with one BS and K mobile users. • At each packet transmission, BS should select one mobile as target receiver. • HARQ-IR is supported, hence, if the target receiver cannot decode the packet, a NAK will be feed back to the BS. • The BS should retransmit the failed packet until the ACK feedback is received or the maximum number of transmission is reached. • Let X be the transmitted symbol, the receiver symbol of the user k is given by the following equation. • We consider slow fading channel where the channel gain is quasi-static within a transmission event (the duration one packet transmission).
Estimated CSIT CSIT Error Actual CSI Model of Outdated CSIT --- Practical Issues • In order to perform scheduling in the downlink transmission, the BS should have the knowledge of channel state information (CSIT). • However, the CSIT estimated at the BS is usually outdated. • A general model of CSIT error is given below:
Packet Error Model --- Subsequent of Outdated CSIT • In slow fading channels, there are two reasons of packet error • Finite block length of channel coding [channel noise effect] • Transmitted data rate exceeding the instantaneous mutual information of the channel [channel outage] • By applying strong channel coding (e.g. LDPC) with reasonable block length (e.g. 2k byte), it can be shown that Shannon’s limit can be achieved to within 0.05dB for a target FER of 10^{-2}. the effect of channel noise can be ignored with strong coding. • Yet, the second factor (channel outage) is systematic and will be the major contributor of packet error (esp when strong coding is used). Hence, we assume Packet Error Rate = Pr [r > mutual information]. • To account for penalty of packet errors, we shall consider system goodput (b/s/Hz successfully delivered to the mobiles) as our optimization objective.
Date rate I[] is 1 when the event is true and 0 otherwise. Summation due to IR retransmission Average number of transmissions per transmission event Average System Goodput • The instantaneous throughput of a transmission event is • The average system throughput of a transmission event is • Since each transmission event may contain multiple channel use, we use the normalized average throughput (named as average goodput) as the system optimization objective.
Outline • Model of Multiuser System with HARQ-IR • Cross-Layer Problem Formulation • Cross-Layer Scheduler Design • Discussions & Simulation Results • Conclusions
Diagram of Scheduler Selected user CSIT Cross-Layer Scheduler Data rate Power for each transmission We shall formulate this box as an optimization problem
Policies --- Actions of Scheduler • The average system goodput is a function of the user selection policy A, power allocation policy P and rate allocation policy R. • User selection policy A: determine the active user for each packet transmission according to the CSIT • Power allocation policy P: determine the transmit power for active users according to the CSIT. • Rate allocation policy R: determine the transmit data rate for active users according to the CSIT.
Average power per transmission event Maximum number of transmission Packet error rate after j-1 transmissions Power of j-th transmission Problem Formulation • The optimal user selection policy A*, the optimal power allocation policy P* as well as the optimal rate allocation policy R* are given by: • Subject to the following constraint: • PER constraint: the packet error probability after the maximum number of transmissions should be ε. • Average power constraint: the average transmit power cannot be large than P0.
Outline • Model of Multiuser System with HARQ-IR • Cross-Layer Problem Formulation • Cross-Layer Scheduler Design • Discussions & Simulation Results • Conclusions
Power constraint Outage probability of the j-1 th transmission Constant related to L Target outage probability Estimation error Cross-layer Scheduler Design • The asymptotical optimally scheduler design for sufficiently small target outage probability and sufficiently large SNR on each transmission is given by: • User selection: • Power allocation (power for j-th transmission): • Rate allocation:
Outline • Model of Multiuser System with HARQ-IR • Cross-Layer Problem Formulation • Cross-Layer Scheduler Design • Discussions & Simulation Results • Conclusions
O(lnK) O(lnL) Discussions • The average system goodput is given by • Goodput vs. Number of users K: The average system goodput scales in the order of ln(K), for small number of users K. • Goodput vs. Maximum number of transmissions L: The average system goodput scales in the order of ln(L).
Conclusions • In this paper, we study the combined design of cross-layer scheduling and HARQ for TDD multiuser systems with outdated CSIT in slow fading channel. • We obtain the closed-form expressions for the average system goodput. • average system goodput scales in the order of O(ln L) at small K and target PER ε. • the average system goodput also scales in the order of O(ln K) for small K.