Energy-delay trade-offs in wireless networks

In many wireless networks energy management is an important issue for reducing the size and cost of communication devices and/or extending a device's usable life-time. Often, the required transmission power is one of the main energy consumers in a wireless device; consequently, there has been much interest in efficiently utilizing this resource. A basic technique is transmission power control, i.e. adapting the transmission power over time in an attempt to not use any more energy than needed to communicate reliably. With data traffic, in addition to adjusting the transmission power, energy efficiency can be further improved by adjusting the transmission rate or equivalently the transmission time per packet, for example, by using adaptive modulation and coding. Such approaches exploit the well-known fact that the required energy per bit needed for reliable communication is decreasing in the number of degrees of freedom used to send each bit. In a fading channel, another benefit of adapting the transmission rate and power is that it enables the transmitter to be "opportunistic" and send more data during good channel conditions, which again reduces the required average energy per bit. In the past few years, there have been a number of energy-efficient scheduling schemes studied, which exploit these effects including [1], [4], [3], [2]. This talk will survey some of this work with an emphasis on the basic model introduced in [2]. In this model, data randomly arrives from some higher layer application and is placed into a transmission buffer. Periodically, data is removed from the buffer, encoded and transmitted over the fading channel. Two possibilites are introduced regarding the coding of each message. In one case each codeword is sent over a fixed number of channel uses, but different codewords may be of different rates. In the second case codewords are of variable length and a message is not decoded until sufficient reliability is accumulated at the receiver. After a codeword is received, it is decoded and sent on to the corresponding higher layer application at the receiver. The transmitter can vary the transmission power and rate based on both the channel state and the buffer occupancy. For a given arrival and fading process, let P* (D) denote the optimal power delay trade-off, i.e. the minimum long-term average power under any scheduling policy with average delay no greater than D. If the traffic arrives at an average rate of Ā bits per second, then for a stable system, the long-term average energy per bit is given by P*(D)/Ā, i.e., P*(D) also reflects the minimum energy per bit needed for a given average delay. For any system where the channel and arrival processes are not both constant, P* (D), will be a strictly decreasing and convex function of D. In [2], the behavior of P*(D) was characterized in the asymptotic regime of large delays (low power). In this regime, it was shown that P*(D) approaches a limiting value of V(Ā) at rate of ⊖(1/D²). This rate can be achieved with a sequence of buffer threshold policies whose only dependence on the buffer occupancy is via a simple threshold rule. Moreover, this weak dependence on the buffer occupancy is required for a sequence of policies to be order optimal (i.e., have the optimal convergence rate). More recently, the asymptotic behavior of of P*(D) in the asymptotic regime of small delays (high power) has been characterized [5]. In this regime, the optimal power/delay trade-off behaves quite differently from the large delay regime. In particular, the convergence rate is shown to depend strongly on the behavior of the fading distribution near zero. We focus on two broad classes of channels: one class ("type A channels") that requires infinite power to minimize the queueing delay, and one class ("type B channels") for which the queueing delay can be minimized with finite power. These classes include most common fading models, such as Rayleigh, Ricean and Nagakami fading. For type B channels, P*(1) - P*(D) = ⊖((D - 1) ^γ/γ-1) as D -→ 1, where γ is a parameter that depends on the fading distribution. For type A channels, P*(D) = ⊖(In(-/D-1) as D → 1. In both cases the optimal rate is achieved by a sequence of channel threshold policies which only depend on the channel gain through a simple threshold rule. Extensions of these result to networks of multiple users will also be touched on if time is available.