Delay-Constrained Optimal Data Aggregation in Hierarchical Wireless Sensor Networks

Abstract

A lot of realistic applications with wireless sensor networks adopt hierarchical architecture in which sensor nodes are grouped into clusters, with each cluster relying on a gateway node for local data aggregation and long-distance radio transmission. Compared to normal sensor nodes, the gateway nodes, also called application nodes (ANs), are equipped with relatively powerful transceivers and have more energy. Nevertheless, since an AN is the main gateway for sensor nodes within its clusters, its energy may be depleted more quickly than normal sensor nodes. As such, it is important to find methods to save energy for ANs. This paper presents a Delay-Constrained Optimal Data Aggregation (DeCODA) framework that considers the unique feature of traffic patterns and information processing at ANs for energy saving. Mathematical models and analytical results are provided, and simulation studies are performed to verify the effectiveness of the DeCODA framework.

Appendix

In this appendix, we use the same method as in [14] to derive the energy function in this paper. A similar function was provided in [9] without proof.

It is commonly known that for an AWGN channel with average signal power constraint S and noise power constraint N, the maximum capacity that an optimal coding scheme can achieve is given by

$$C = \frac{1}{2} \log(1+S/N) \text{ bits/transmission}.$$

(24)

If we assume a sub-optimal code with rate Rate = ϕC where ϕ ≈ 1, from Eq. 24, it is easy to get

$$S =N(2^{2\phi Rate} -1).$$

(25)

Consider a channel with the maximum transmission speed of 1 Mbps and with Rate = 6 [9]. Assume that the transmission duration of a 128 bits packet is τ since the actual transmission speed may be smaller than the full speed to save energy [9]. The relationship of actual $\hat{Rate}$ and τ can be expressed as follows,

$$\hat{Rate} = \frac{0.000128*6}{\tau}.$$

(26)

Assuming a noise level of 1, the energy per bit is $w = S/\hat{Rate}$, and the energy per packet is given by

$$w(\tau) = 128* \frac{\tau}{0.000768}\big(2^\frac{0.001536}{\tau} -1\big),$$

(27)

where 128 is the packet size in bits.

Using the same method, if we assume the packet size is 10 Kb and the maximum transmission speed is 1 Mbps as in [9], we can obtain an energy function that is the same as Equation (15) in [9]. Note that the power level is a relative value normalized by the noise level, which is 1 in this case. Assuming a different noise level may change the required power level and thus the energy consumption to achieve the same bit error rate, but all conclusions in this paper still hold since the shape of the energy function remains the same.