M.Sc Thesis

M.Sc StudentHaddad Bassel
SubjectThroughput Efficient Modulation Schemes for Bandwidth-
Limited Optical Systems
DepartmentDepartment of Electrical and Computer Engineering
Supervisor DR. Shraga Bross


Optical direct detection systems have long been considered for deep-space communication. For moderate data rates and where good performance for low-power consumption is paramount; pulse-position modulation (PPM) was shown to be a suitable modulation scheme. When higher data rates are considered PPM seems to exhibit inherent throughput limitation since the only way throughput can increase is by reducing the pulsewidth. This is unacceptable when the transmitter is subject to stringent bandwidth constraint. In order to improve the transmission efficiency under a given bandwidth constraint, several alternative techniques have been suggested such as multipulse or combinatorial PPM (MPPM). This modulation scheme is a generalization of PPM that allows more than one pulse per symbol interval.

The capacity of the direct-detection photon channel under peak and average power constraints was derived by Kabanov, Davis and Wyner. The error exponent and construction of specific codes achieving capacity were also reported by Wyner, and in particular it was shown that binary signaling is capacity achieving. It should be emphasized that in all of the above studies no bandwidth constraints were imposed.

In this thesis we consider a three-level amplitude modulated multipulse PPM for use in bandwidth limited optical systems. Shamai demonstrated that when the direct detection photon channel is subject to bandwidth constraint, capacity is no longer achieved by binary distribution.

Three-level amplitude modulated PPM is an extension of MPPM which allows two pulse levels per each ``active" signaling slot. In particular, we consider the optimum receiver for this Three-level MPPM code and investigate its capacity, cutoff rate and error probability in the quantum-limited regime. For the case where background dark current is present, the cutoff rate and error probability are considered.

This facilitates the evaluation of the bandwidth efficiency of the proposed modulation as compared to regular multipulse PPM, which delivers the same throughput and detection quality under the same average-power constraint.

Performance analysis demonstrated that, as compared to the reference MPPM scheme, 3L-MPPM achieves higher spectral efficiency. Moreover, in the quantum-limited case, 3L-MPPM attains similar or higher capacity and cutoff rate as compared to MPPM. In the presence of background noise, 3L-MPPM advantage over MPPM is pronounced further, particularly for low-to-moderate signal to noise ratios (SNRs).

This improvement is due to the flexibility that 3L-MPPM has in choosing the optimal ratio between the two pulse levels subject to the same average power constraint.