Design and Performance Analysis of an Index Time-Frequency Modulation Scheme for Optical Communications

Abstract

In this article, we propose an index modulation system suitable for optical communications, based on jointly driving the time and frequency of the signal: an index-time frequency hopping (I-TFH) system. We analyze its performance from the point of view of its efficiency in power and spectrum, and its behavior in terms of error probability for the nonturbulent free-space optical (FSO) channel. We compare I-TFH with already proposed index modulated systems of the same nature, but where the amplitude or the number of transmitters are driven instead of the signal frequency. We derive and compare approximations for the average symbol and bit error probabilities of all these systems. The simulation results show that said approximations are tight enough for a wide range of signal-tonoise ratios and system parameters. Moreover, I-TFH shows to be better performing in BER and/or power efficiency than the comparative alternatives, and may offer interesting properties in a variety of contexts.

A Spatial Time-Frequency Hopping Index Modulated Scheme in Turbulence-free Optical Wireless Communication Channels

“…In this Section we present simulation results for the BER and SER, along the calculated values for P b and P e using the previously developed formulas 3 . For comparison, we offer results for SMPPM [37] and I-TFH [36], as limit cases where either the FSK symbol part or the OSSK symbol part have been removed. Notice that the authors of [37] only analyzed the average symbol error probability P e of SMPPM.…”

“…As a way to extend the possiblities of the SMPPM symbol, and make it carry additional information, instead of just sending rectangular optical pulses within each of the w signal slots, another kind of modulated symbol may be sent by driving other properties of the signal. Similar ideas have already been exploited, for example by using PPM and jointly driving the phase or polarization of the optical signal [25], or by using MPPM and jointly driving the frequency of the light intensity fluctuations during the nonzero transmitted optical pulses [36].…”

“…To demodulate the FSK symbol part, we consider a detection process like the one described in [36], where the standard non-coherent FSK receiver is applied over the w MPPM signal slots identified during the previous phase. The FSK detector calculates, for the hypothetical k−th signal slot and i = 0, · · · , M F − 1,…”

“…where we have taken into account that the proportion of erroneous bits for an FSK symbol error is estimated as 2 n F −1 /(2 n F − 1) [46], and the conditional symbol error probability can be approximated by (36). Notice that the average number of erroneous bits given are quantities that depend on the specific OSSK pattern, and are conditional measurements to be later jointly averaged following (43).…”

“…Quite recently, other hybrid modulation schemes have emerged in the context of Visible Light Communications (VLC), where frequency-and time-domain, or frequency-and intensity-domain joint strategies are exploited, see [34] and [35], respectively. Moreover, an IM system based on MPPM, where an FSK symbol is sent during the active slots, instead of just sending a constant amplitude rectangular pulse shape unable to carry any additional information, was proposed for OWC IM/DD communications in [36]. This system jointly drives the time and the frequency axis, and therefore constitutes an index-time frequency hopping (I-TFH) modulation.…”