Wireless Network Design: Optimization Models and Solution ...

330 Nitin Salodkar and Abhay Karandikar
14.3.2 Energy Efficient Scheduling
Apart from maximizing throughput, energy efficiency is also an important concern
in wireless communications. As is evident from the foregoing discussion on capacity,
the power required for error free communication in Shannon’s sense at a rate u
when the channel state is x is given by
P(x,u) = N0
x (eu − 1), (14.25)
where N0 is the thermal noise power spectral density. Note that for a giver x, the
transmission power is an increasing and strictly convex function of u.
Even for practical digital communication systems, the power required to transmit
at a rate u for a specified bit error rate (BER) is given by
P(x,u) =
N0
Γ (BER) x (eu − 1), (14.26)
where Γ (BER) denotes the signal to noise ratio (SNR) gap corresponding to a practical
modulation and coding setting. Even in this case, the power is convex and
strictly increasing function of u.
The convex power-rate relationship implies that if we want to, say, double the
rate, we may have to transmit at more than double the power. Thus to transmit u
packets, the scheduler can transmit u
u
2 packets in one slot and 2 packets in the next
slot instead of u packets in one slot (if the rate permits). This strategy saves the
power, albeit, at a cost of delay of one slot. This suggest that the scheduler should
transmit the data in opportunistic chunks for energy efficiency.
Note that packets (hence bits) arrive randomly and may be subjected to buffering.
Hence to maximize throughput or to minimize energy, opportunistic or energy
efficient scheduling has to contend with network layer issues like fairness, packet
delay and queue stability. This leads to formulating the scheduling problem as a
control problem which exploits fading state information to maximize (or minimize)
a given utility function subject to some constraints such as fairness, delay, stability.
In the rest of the chapter, we focus on such formulations. We begin by discussing
the system model in more detail in the next section.
14.3.3 System Model for Centralized Scheduling
We consider a multiuser wireless system where N users communicate with a base
station. On the uplink, as depicted in Figure 14.5, users communicate with the base
station using TDMA, i.e., time is divided into slots of equal duration and only one
user can transmit in a slot. We assume that the slot duration is normalized to unity.
The base station is the centralized entity that makes the scheduling decision and the
user scheduled by the base station transmits in a slot.