Combined Cross-Layer Design and HARQ for TDD Multiuser systems with Outdated CSIT

Combined Cross-Layer Design and HARQ for TDD Multiuser systems with Outdated CSIT Rui Wang & Vincent K. N. Lau Dept.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Estimated CSIT CSIT Error Actual CSI Model of Outdated CSIT --- Practical Issues • In order to perform scheduling in the downlink transmission, the BS should have the knowledge of channel state information (CSIT). • However, the CSIT estimated at the BS is usually outdated.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Packet Error Model --- Subsequent of Outdated CSIT • In slow fading channels, there are two reasons of packet error • Finite block length of channel coding [channel noise effect] • Transmitted data rate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.

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.

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:

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).

Simulations

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.

Thank You !

Combined Cross-Layer Design and HARQ for TDD Multiuser systems with Outdated CSIT