Performance bounds and cutoff rates of quantum limited OOK with optical amplification

The bit error probability (BER) and the generalized cutoff rate (GCR) of optically amplified, direct-detection on-off keying (OOK) signaling are addressed utilizing the classical theory of Fredholm integral equations. The approach accounts for the impact of optical bandlimiting and upper bounds on the BER are found via Chernoff techniques, which address the resultant intersymbol interference (ISI) incurred by the linear pulse distortion. Simple rigorous upper bounds on the BER are derived in terms of basic system parameters relaxing the need for solving Fredholm related equations. Random coding is used to obtain the GCR of this channel. The theory is demonstrated for the Lorentzian and finite-duration bandpass optical filters and the optical bandwidth which optimally balances the ISI versus the amplified spontaneous emission noise is found