Abstract
Indoor diffuse optical intensity channels are bandwidth constrained due to the multiple reflected paths be- tween the transmitter and the receiver which cause consider- able inter-symbol interference (ISI). The transmitted signal amplitude is inherently non-negative, being a light intensity signal. All optical intensity root Nyquist pulses are time- limited to a single symbol interval which eliminates the pos- sibility of finding bandlimited root Nyquist pulses. However, potential exists to design bandwidth efficient pulses. This pa- per investigates the modified hermite polynomial functions and prolate spheroidal wave functions as candidate wave- forms for designing spectrally efficient optical pulses. These functions yield orthogonal pulses which have constant pulse duration irrespective of the order of the function, making them ideal for designing an ISI free pulse. Simulation re- sults comparing the two pulses and challenges pertaining to their design and implementation are discussed.
Highlights
The capacity of Radio Frequency (RF) systems is limited due to scarcity and cost of licensing
The root Nyquist pulse is required to be of small duration so that the number of interfering neighbors is small
While comparing the frequency domain plots obtained it was observed that the band occupied by the Modified Hermite Polynomial Function (MHPF) pulse is 1.3 times the band occupied by Prolate Spheroidal Wave Functions (PSWF) pulse which is roughly equal to π/2 (Fig. 10)
Summary
The capacity of Radio Frequency (RF) systems is limited due to scarcity and cost of licensing. Steve Hranilovic [1] proved that all optical intensity root Nyquist pulses must be time limited to a single symbol interval. From studies on pulse shaping techniques for time limited systems [13, 14, 15] Prolate Spheroidal Wave Functions (PSWF) and Modified Hermite Polynomial Function (MHPF) have emerged as potential pulse shaping functions as they provide the optimal spectral concentration Individual discussion on these two contender pulses is widely available but no comparison between the two has been drawn. The problem was reduced to solving the linear objective function This design can be extended to the optical domain by introducing an additional constraint of optical signal remaining non-negative.
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