1 ALOHA for Wireless Sensor Networks with Random Frequency Offsets Kirtan N. Modi, Satya Ponnaluri, Stephen G. Wilson, and Ma¨ ıt´ e Brandt-Pearce † Abstract — The impact of random frequency offsets on low-end sensor networks is considered. Results indicate that opening up receiver bandwidth not only helps improve throughput as measured in bits per second but can also result in improved bandwidth efficiency as measured in bits/sec/Hz. Implementing such a system will not only drive down node costs but also increase their operational lifetime. ALOHA based random access for a wireless sensor network with K nodes transmitting to a central base station is considered. Most literature on ALOHA is based on the assumption of perfect frequency syn- chronization among nodes [1]. The impact of ran- dom frequency offsets between the different trans- mitting nodes and the base station receiver which may occur either naturally, when low-end oscillators are used, or due to relative mobility, is considered in this paper. A system consisting of dumb nodes such that the transmitted carrier frequency of each node has a Gaussian distributed error (of variance σ 2 f ) with respect to the nominal carrier frequency at the centralized receiver is assumed. Let the transmit bandwidth employed by each node be R b . Unlike conventional systems which employ a narrow-band receiver of bandwidth R b , this paper proposes the use of a wide-band receiver operating with a band- width of 4σ f + R b about the carrier frequency. Al- though this may increase the receiver complexity, it results in reduced node complexity thereby trans- lating in cost savings when designing mote type de- vices. The objective of this paper is to compare the achievable throughput in bits/sec as well as the achievable bandwidth efficiency in bits/sec/Hz of such a system as compared with that of conventional systems employing narrow-band receivers and more complex (hence expensive) and relatively less mobile nodes. Related work in the context of multichannel ALOHA can be found in [2]. Fig. 1 shows the achievable throughput while Fig. 2 shows the achievable bandwidth efficiency for a system with a load of 0.1 packets/slot/node for dif- ferent number of nodes and for varying values of the receiver bandwidth which can be measured as the ra- tio σ f /R b . As expected, for any number of nodes the throughput increases with increasing receiver band- width. Although it is not clear if bandwidth effi- † Charles L. Brown Department of Electrical and Com- puter Engineering, University of Virginia, Charlottesville, VA 22903. This work was supported by a grant from MITRE Corp. Contact: knm3v@virginia.edu 0 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 2.5 3 x 10 4 K Throughput in bits/sec Aloha with Narrow Band Receiver Aloha with WideBand Receiver σ f /R b = 4 σ f /R b = 1 Fig. 1. Figure shows achievable throughput in bits/sec for different receive bandwidths, measured in terms of σ f /R b , as the number of nodes vary. 0 10 20 30 40 50 60 70 80 90 100 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 K Bandwidth Efficiency in bits/sec/Hz Aloha with Narrow Band Receiver Aloha with WideBand Receiver σ f /R b = 1/40 σ f /R b = 4 Fig. 2. Figure shows achievable bandwidth efficiency in bits/sec/Hz for different receive bandwidths, measured in terms of σ f /R b , as the number of nodes vary. ciency is an important measure for comparing sen- sor network systems, results indicate that the pro- posed approach may result in improved bandwidth efficiency as the total system load (corresponding to the number of nodes) increases further the wide band receiver based system design proposed. References [1] J.G. Proakis, Digital Communications, 3rd ed., New York, NY: McGraw-Hill, 1995. [2] S. Crozier and P. Webster, “Performance of 2-dimensional sloppy-slotted aloha random access signaling,” in Intl. Conf. on Wireless Comm. (ICWC), Vancouver, BC, Canada, June 1992, IEEE, pp. 383–386.