Communications in the observation limited regime

Abstract

We consider the design of communications systems when the principal cost is observing the channel, as opposed to transmit energy per bit or spectral efficiency. This is motivated by energy constrained communications devices where sampling the signal, rather than transmitting or processing it, dominates energy consumption. We show that sequentially observing samples with the maximum a posteriori entropy can reduce observation costs by close to an order of magnitude using a (24,12) Golay code. This is the highest performance reported over the binary input AWGN channel, with or without feedback, for this blocklength. Sampling signal energy, rather than amplitude, lowers circuit complexity and power dissipation significantly, but makes synchronization harder. We show that while the distance function of this non-linear coding problem is intractable in general, it is Euclidean at vanishing SNRs, and root Euclidean at large SNRs. We present sequences that maximize the error exponent at low SNRs under the peak power constraint, and under all SNRs under an average power constraint. Some of our new sequences are an order of magnitude shorter than those used by the 802.15.4a standard.

(cont.) In joint work with P. Mercier and D. Daly, we demonstrate the first energy sampling wireless modem capable of synchronizing to within a ns, while sampling energy at only 32 Msamples per second, and using no high speed clocks. We show that traditional, minimum distance classifiers may be highly sensitive to parameter estimation errors, and propose robust, computationally efficient alternatives. We challenge the prevailing notion that energy samplers must accurately shift phase to synchronize with high precision.