Capacity investigation of on-off keying in noncoherent channel settings at low SNR

On–off keying (OOK) has repossessed much new research interest to realize green communication for establishing autonomous sensor networks. To realize ultra-low power wireless design, we investigate the minimum energy per bit required for reliable communication of using OOK in a noncoherent channel setting where envelope detection is applied at the receiver. By defining different OOK channels with average transit power constraints, the achievability of the Shannon limit for both cases of using soft and hard decisions at the channel output is evaluated based on the analysis of the capacity per unit-cost at low signal-to-noise ratio. We demonstrate that in phase fading using hard decisions cannot destroy the capacity only if extremely asymmetric OOK inputs are used with a properly chosen threshold. The corresponding pulse-position modulation scheme is explicitly studied and demonstrated to be a Shannon-type solution. Moreover, we also consider a slow Rayleigh fading scenario where the transmitter and receiver have no access to channel realizations. Throughput per unit-cost results are developed to explore the tradeoff between power efficiency and channel quality for noncoherent OOK using soft and hard decisions. Copyright © 2015 John Wiley & Sons, Ltd. *Correspondence P. Zhang, Eindhoven University of Technology, Den Dolech 2, 5612AZ Eindhoven, The Netherlands. E-mail: [email protected] Received 28 June 2014; Revised 24 November 2014; Accepted 12 December 2014