Range Dependence of an Optical Pulse Position Modulation Link in the Presence of Background Noise

Introduction We analyze the information efficiency of a deep-space optical communication link with background noise employing the pulse position modulation (PPM) format and a direct-detection receiver based on Geiger-mode... [ view full abstract ]

Introduction

We analyze the information efficiency of a deep-space optical communication link with background noise employing the pulse position modulation (PPM) format and a direct-detection receiver based on Geiger-mode photon counting.

Methods

The PPM format uses M equiprobable symbols defined by the location of a single light pulse in a frame of M otherwise empty bins. The information rate is quantified using Shannon mutual information, and is optimized with respect to the PPM order M. The photon information efficiency (PIE) is given by the ratio of mutual information and the received average number of photons per time bin. We compare PIE of various decoding strategies which differ by the class of output events processed to retrieve information, ranging from the case when only events with one (K=1) photocount in a single PPM frame are used (simple decoding) to all combinations of up to K=M photocounts (complete decoding). We use numerical approach to identify the optimal operating regime and derive easily computable formulas in the limit of vanishing average detected signal power.

Results

In Fig. 1 we present contour plots of PIE as a function of the PPM order M and the received signal power n_a for a fixed noise power n_b = 10^(-3). The dashed curves indicate optimal PPM order M* as a function of n_a. Decoding restricted to single-photocount events (a) is compared to the complete decoding scenario (b). The qualitative difference between these two cases is clearly seen in Fig. 2(a) which presents performance of PPM with optimal order M* for complete (solid curves) and simple decoding (dashed curves) for several values of the background noise strength n_b. The arrows indicate the asymptotic values derived analytically. It is clear that to attain a non-zero asymptotic value of PIE one must use complete decoding, otherwise PIE tends to zero with n_a -> 0. Achieving such performance requires infrequent strong pulses as seen in Fig.2(b) which means that received energy is compressed in single time bin.

Discussion

Attainable system performance dramatically depends on the adopted decoding strategy. The scaling of the received mean photon number with covered distance r is quadratic r^(-2). Complete decoding scenario allows to achieve r^(-2) scaling of the information rate with the distance in comparison to r^(-4) for other strategies. The optimal operating regime requires a careful adjustment of the PPM order to the system characteristics, growing as r^2 with the covered distance.