Title:Resource allocation for multi-user downlink MISO OFDMA-URLLC systems
Author:Walid R. Ghanem, Vahid Jamali, Yan Sun, and Robert Schober
Target:
系统架构：single cell, multiuser, downlink, OFDMA（创新）,MISO
优化目标：最大化加权系统总吞吐量
约束：发送bit数，packet error probability, delay
资源：
作用：作为次优低复杂度的性能上界
仿真结论：证明多天线可以减低时延，提高可靠性，当时延需求不同时，优于两种比较算法，接近于最优算法结果
数学问题：非凸问题，通过monotonic优化解决

Related work

the performance limits of short packet communication (SPC) ：
optimal power allocation in a multi-user time division multiple access
(TDMA) URLLC system was considered in

Y. Hu, M. Ozmen, M. C. Gursoy, and A. Schmeink, “Optimal power
allocation for QoS-constrained downlink multi-user networks in the
finite blocklength regime,” IEEE Trans. Wireless Commun, vol. 17, no. 9, pp. 5827–5840, Sept 2018.
J. Chen, L. Zhang, Y. Liang, X. Kang, and R. Zhang, “Resource
allocation for wireless-powered IoT networks with short packet communication,” IEEE Trans. Wireless Commun, vol. 18, no. 2, pp. 1447–1461, Feb 2019.
S. Xu, T. H. Chang, S. C. Lin, C. Shen, and G. Zhu, “Energy-efficient packet scheduling with finite blocklength codes: convexity analysis and efficient algorithms,” IEEE Trans. Wireless Commun, vol. 15, no. 8, pp. 5527–5540, Aug 2016.

the energy efficiency was maximized by optimizing the antenna configuration, bandwidth allocation, and power control= under latency and reliability constraints.

C. Sun, C. She, C. Yang, T. Q. S. Quek, Y. Li, and B. Vucetic, “Optimizing resource allocation in the short blocklength regime for ultra-reliable and low-latency communications,” IEEE Trans. Wireless Commun, vol. 18, no. 1, pp. 402–415, Jan 2019.

a cross-layer framework based on the effective bandwidth was proposed for optimal resource allocation under QoS constraints.

C. She, C. Yang, and T. Q. S. Quek, “Cross-layer optimization for ultrareliable and low-latency radio access networks,” IEEE Trans. Commun, vol. 17, no. 1, pp. 127–141, Jan 2018.

the joint uplink and downlink transmission design for URLLC in MISO systems.

C. Shen, T. Chang, H. Xu, and Y. Zhao, “Joint uplink and downlink transmission design for URLLC using finite blocklength codes,” in Proc. ISWCS 2018, Lisbon, Portugal, August 28-31, 2018, 2018, pp. 1–5.

a hybrid automatic repeat request (HARQ) scheme for URLLC systems

A. Avranas, M. Kountouris, and P. Ciblat, “Energy-latency tradeoff in ultra-reliable low-latency communication with retransmissions,” IEEE J. Sel. Areas Commun, vol. 36, no. 11, pp. 2475–2485, Nov 2018.
D. Qiao, M. C. Gursoy, and S. Velipasalar, “Throughput-delay tradeoffs with finite blocklength coding over multiple coherence blocks,” IEEE Trans. Commun, pp. 1–1, 2019.

System model

single-cell downlink OFDMA system, single BS with NT antennas,using 5G NR standard (such as typical sub-carrier bandwidth of 15kHz, Ts is 66us and to meet the delay requirement of URLLC N has to be smaller than 7),operates in a time-division duplex (TDD) mode.
NTN_TNT : BS antennas
K: Number of URLLC users with single antenna.
M: the numbers of the orthogonal sub-carriers indexed by m∈1,...Mm \in{ {1,...M}}m∈1,...M
TfT_fTf:duration of resource frame with the unit of seconds
NsN_sNs:numbers of subframes
N: time slots of each subframe indexed by n

one OFDMA symbol spans one time solt ,and in total M*N resource elements assigned to K users in each subframe.

Assumption: delay requirements of all users are known at the BS;only users whose delay requirements can potentially be met in the current resource block are admitted into the system.
Channel model
Received signal of k-th user on sub-carrier m in time slot n, linear transmit precoding at BS------->SINR of user k

Resource Allocation problem formulation

Achievable rate for SPC

Maximum number of bits conveyed in packet comprising L symbols: its an approximation result . Eq.,(6) is the base of the resource allocation algorithm.
ϵ\epsilonϵ: decoding packet error probability
i: the i-th symbol
L:=M*N, the total resource elements

channel dispersion

Qos and system performance metric

Qos requirments of URLLC user

minimum number of received bits, Bk
target packet error probability, ϵk\epsilon_kϵk
maximum number of time slots available for transmission of the users packet, Dk (delay requirements of user k can be met by assigning all symbols of user k to the first Dk time slots)

total number of bits transmitted over the resources allocated to user k(based on Eq.(6))

where, wk\bold w_kwk: collection of all beamforming vectors
weighted sum throughput
To control the fairness among all users

μk\mu_kμk: weight factor, larger of the factor, the higher priority of the user and the higher throughput
It can be specified in the MAC layer and is assumed to be given in this paper.

Optimization problem formulation

C1: guarantees the minimum number of Bk bits to k-th user;
C2:total power budget constraint of BS
C3: delay requirements.
Its a non-convex problem due to the non-convexity of SINR and Eq(8)

Optimal solution

Using monotonic optimization to lead the optimization problem to an iterative resource allocation algorithm and with a semi-definite relaxation problem in each iteration.
If need, focus on the mathematical process.

Performance evaluation

Simulation parameters

The path loss: 35.3+37.6log10(dk)35.3+37.6log_{10}(d_k)35.3+37.6log10(dk), dk is the distance from BS to user k
all user weights are set to μk=1\mu_k=1μk=1

Performance metric
sum throughput

averaging R over all channel realizations ----average sum throughput

Performance bound

Shannon’s capacity formula is adopted in problem(14).

Baseline

Scheme1: solution obtained for shannons capacity formula is used to compute the sum throuthput.
Scheme2: employ maximum ration transmission beamforming,

Simulation results

Convergence
different numbers of sub-carriers M and different numbers of user K
sum throughput as a function of the numbers of iterations
Result: converge to the global optimum solution;
average sum throughput versus the maximum transmit power at BS

for different antennas and different delay requirements.
S0: scenario 0, none of the users has delay restrictions,Dk=N=4
S1: two users have strict delay D1=D2=2, the remaining users Dk=4

1.more antennas at the BS considerably increases the average system sum throughput;2. the stricter delay requirements for S1 reduce the average system sum throughput compared to S0 because the BS is forced to allocate more power to the two delay sensitive users even if their channel conditions are poor to ensure their delay requirements are met
average system sum throughput versus the number of antennas
average sum throughput vs. different delay requirement

-average system sum throughput versus the number of users for different delay scenarios

the average system sum throughput versus the packet error probability

impact of imperfect CSI

model
using normalized mean squared error NMSE to quantify the quality of the CSI
modify optimal problem by adding a safety margin to the feasible region
form Bk to (1+bk)Bk, bk is a positive parameter refering to as a back-off parameter.
The consraint C1 in (14) is
The backoff bk can be adjusted according to the accuracy of channel estimation. More accurate of the estimation, the smaller bk, which means that bk is 0 for perfect CSI.

depending on the adopted value of bk, a minimum channel estimation quality is required for the proposed resource allocation scheme to achieve a high performance.

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