Complexity Comparison

The system complexity (measured in relative computation time) is shown in Fig- ure 6.5. This is measured as the percentage increase in computation time taken com- pared to the base case (iterative method and M = 6 for both figures and T_i = 200 and K = 1 for Figures 6.5(a) and 6.5(b) respectively). As expected, the iterative method has the lowest complexity of all schemes. Further, the number of UEs and/or RBs results in a large increase in complexity, while the datarate is shown to have negligible impact.

200 400 600 800 1000 1200 1400 1600 1800 2000 −12 −10 −8 −6 −4 −2 0 2 4 6 8

Datarate per ARQ slot (bits)

Average Applied Power ARQ Slot (dB)

Optimal − M=6 Optimal − M=10 Optimal − M=15 Iterative − M=6 Iterative − M=10 Iterative − M=15 Best−N − M=6 Best−N − M=10 Best−N − M=15

(a) versus Datarate (K=1)

1 1.5 2 2.5 3 3.5 4 4.5 5 −12 −10 −8 −6 −4 −2 0 2

Number of Users (UEs)

Average Applied Power Per ARQ Slot (dB)

Optimal − M=6 Optimal − M=10 Optimal − M=15 Iterative − M=6 Iterative − M=10 Iterative − M=15 Best−N − M=6 Best−N − M=10 Best−N − M=15

(b) versus Number of UEs

200 400 600 800 1000 1200 1400 1600 1800 2000 10−1 100 101 102 103 104

Datarate per ARQ slot (bits)

% Increase in Computation Time

Optimal − M=6 Optimal − M=10 Optimal − M=15 Iterative − M=6 Iterative − M=10 Iterative − M=15 Best−N − M=6 Best−N − M=10 Best−N − M=15

(a) versus Datarate (K=1)

1 1.5 2 2.5 3 3.5 4 4.5 5 100 101 102 103 104 105

Number of Users (UEs)

% Increase in Computation Time

Optimal − M=6 Optimal − M=10 Optimal − M=15 Iterative − M=6 Iterative − M=10 Iterative − M=15 Best−N − M=6 Best−N − M=10 Best−N − M=15

(b) versus Number of UEs

6.6

Chapter Summary

In this chapter we proposed a framework for energy efficient resource allocation in the SC-FDMA multi-user uplink. Firstly, we proposed an alternative method of selecting an appropriate scheduling epoch based on the impact of synchronous HARQ. By utilizing the proposed method, we can reduce the number of allocation procedures in time and ensure users can always initiate a new transmission during any frame (i.e..,

do not experience ARQ blocking).

Secondly, we proposed two sub-optimal power efficient resource allocation meth- ods. Both methods were compared to the optimal method in terms of complexity and power efficiency. We found that the sub-optimal methods closely obtain the power efficiency of the optimal allocation with reduced complexity. Further, we found that the efficiency of the power allocation scheme is dramatically reduced when static scheduling is employed for retransmissions.

One of the large drawbacks in this chapter, is the assumption on the availability of channel estimates for the duration of an ARQ slot. While this may be the case in a slow fading channel, this assumption will not hold in a fast fading environment. In future work, this issue should be addressed. The concept of an ARQ slot can be used to eliminate ARQ blocking, however allocation within the ARQ slot to individ- ual subframes for users can be based on estimates of the evolution of the channel. Details of this, and other related open problems are discussed under future work in Chapter 8.

Chapter 7

Energy Efficient QoS Constrained

Scheduler for SC-FDMA Uplink

In previous chapters we have independently looked at low complexity scheduling methods for both SC-FDMA and multiple users/streams with QSI. In this chap- ter, we introduce and demonstrate a method to extend this work to incorporate our energy efficiency multiple stream scheduling framework in the uplink SC-FDMA sce- nario. The remainder of this chapter is divided as follows. In Section 7.1 we overview the details of the employed uplink system model including the channel and schedul- ing models and in Section 7.2 we describe the scheduling ideology. In Section 7.3 simulation results are provided while in Section 7.4, conclusions are drawn on this work.

7.1

System Model

The system model is shown in Figure 7.1 and similar to the model presented in Chapter 6, however we do not consider the HARQ process. For clarity to the reader we briefly describe it again here.

We assume that there are K users (denoted as UEs) within a single cell, com- municating with a single base station (denoted as an eNB). Since we are concerned with resource allocation within a single cell, for the purpose of our work, it is as- sumed that intercell interference is negligible. The cell spectrum is divided intoN_sub

subcarriers which are grouped into M resource blocks. Each resource block (RB) is comprised of 12 equivalent subcarriers. Without loss of generality we assume there is an Integer number (M) of RBs available for allocation. The system is assumed to be operating in FDD mode.

There are Nsym symbols per subcarrier in a given subframe where the exact

number of subcarriers depends on the uplink configuration. The physical uplink shared channel (PUSCH) is used for transmission of uplink data and comprises a portion of symbols along with other controls channels. For the purpose of our work, it is assumed the PUSCH occupies Nsym −Nctrl symbols per subcarrier, per sub-

frame where N_ctrl is the number of symbols used for all other physical channels and signalling.

Each UE receives uplink traffic from upper layers of their protocol stack des- tined for transmission to the eNB. Each UE’s traffic has associated QoS parameters

{D_i, L_i, λ_i, B_i, δ_i} which denotes the maximum tolerable average delay, SDU length, average arrival rate, buffer size at the radio link control (RLC) layer and maximum tolerable packet loss rate respectively for that stream. Each stream may represent a broad service class (such as voice over IP or video) or a particular application-layer stream being used at the time. Each incoming stream is stored in a finite-length first-in, first-out (FIFO) buffer where incoming packets are dropped when the buffer is full.

The scheduling horizon is divided into subframes consisting of 2 LTE time slots (of duration 1ms). During each subframem, users can transmit up toT_i bits of data as determined by the eNB. On average each user will receive a service rate of µ_i

packets per second.

During each frame, each of the K users can transmit a single transport block ofT_i(m) bits. For now, it is assumed that eligible transport block sizes are an integer number of SDUs plus a header (i.e.,no SDU segmentation is required by the RLC). In this case, the scheduling objective for the MAC is to determine either a priori or online, a way to allocate each user a quantity of data to transmit T_i(m) for all subframes m to meet the individual loss, delay and throughput requirements of all users and while minimizing the average weighted energy expenditure. The MAC layer scheduling decision is as follows. For each user, design the set of scheduling policy decisions to minimize the long-term average allocated transmission power.

The MAC allocation component is formulated as a constrained Markov decision process where the system state of user i is denoted by its buffer level and the action

RLC

RLC SDUs of size Li

ci(m)={0,1,…,Zi}

SDUci(m) …. SDU1

PDU Header + ci(m)SDUs

MAC

Figure 7.1: SC-FDMA Uplink System Model: (a) Each UE, (b) Overall System. space describes the number of packets that can be transmitted during a subframe subject to a randomized policy. The solution to the problem for any scheduling policy

Ω is a random policy which described by the distribution θ_i(c_i, u_i|Ω) which denotes the probability of choosing the actionc_i as the number packets for transmission given that queue i is in state ui. The aforementioned policy is derived for all users. The

goal of the optimization formulation is to findθ_i(c_i, u_i|Ω) for allc_i, u_i,as well asithat minimizes the average applied transmission power. The resultant policy is coupled by

Ωwhich defines the scheduling actions for each queueiand each queue stateui ∈ Ui.

Using this policy, in each subframe m, T_i(m) bits are chosen for transmission from UE i (where T_i(m) = L_ic_i(m) +L_hdr) and c_i(m) is c_i chosen randomly at time m

subject with probability defined by θ_i(c_i, u_i|Ω).

For anytimem,_{c_i(m)_|0_≤c_i(m)_≤Z_i,_∀i_}denotes the joint action space taken for all UEs. The set of all feasible joint action spaces is _C (known a priori). In order to solve for the aforementioned policy Ω to minimize transmission power, one must

first determine the power cost of taking each joint action c _{∈ C}. This is handled by the physical (PHY) layer component.

Firstly, we clarify the following assumptions

• The CSI matrix corresponding to the channel between each UE and the eNB over all RBs is available at the eNB error free.

• The eNB feedback channel informs UEs in advance of the resource blocks and quantity of data for transmission for a user during any uplink subframe.

• The eNB has knowledge about buffer occupancy levels and QoS parameters of each UE.