# Ultra-Wideband Analog Radio-over-Fiber Communication System Employing Pulse-Position Modulation
## 2 The Use of PPM  
In this paper, TR-PPM is employed, where data are encoded by allocating pulses of duration \(\tau\) (s) into time bins of duration \(\Delta\) (s). Each of \(M=2^{b}\) positions (time bins) represents a different symbol described by a predefined number of bits \(b\). An additional reference pulse at the beginning of each frame helps to calculate the value of the received symbols. The first time bin starts after \(\text{M}\cdot\Delta+T_{\text{g}}\) seconds from the reference pulse, where guard time, denoted as \(T_{\rm g}\) (s), is introduced to ensure a safe interval between the pulses. This interval compensates for the hardware's inherent dead time, encompassing signal propagation delays and the duration required for processing. An example of a TR-PPM frame, which provides reference and symbol pulses with \(M=4\) positions, is shown in Figure 2.  
The allocation of data symbols into the time between short pulses, measured in picoseconds (ps), significantly enhances energy efficiency per symbol. The root mean square (RMS) of the signal is defined as \(u_{\rm RMS}=\sqrt{\int_{0}^{T/2}u(t)^{2}\,dt}\), where duration \(T_{1/2}=M\cdot\Delta+T_{\rm g}\) and \(T=2\cdot T_{1/2}\) represent frame duration consisting of two halves of a TR-PPM symbol duration \(T_{1/2}\), (s). The decrease in signal RMS \(u_{\rm RMS}\), achieved by using pulses with minimal pulse duration \(\tau\), enables an increase in transmission distance while maintaining the same mean power consumption compared to conventional modulation schemes like OOK. By decreasing the time bins' width \(\Delta\), more data in PPM can be allocated, increasing data transmission speed. It is worth noticing that although in some PPM applications, a simplified scheme with \(\Delta=\tau\) is used, the information is carried solely by the timing of the pulses' rising edges. Hence, the pulse width \(\Delta\) is not critical from an information-carrying perspective. However, pulse width affects both the link's energy efficiency and the signal's frequency bandwidth. Consequently, the narrower pulses create more energy-efficient transmission, whereas longer pulses require smaller bandwidth and are easier to detect. In the latter case, the pulse width shouldn't exceed guard time \(T_{g}\) to avoid overlapping the pulses.  
As PPM encodes data in the time domain, precise time-to-digital conversion is essential for its demodulation. Ideally, each pulse has equal and constant amplitude and steep rising edge, allowing for pulse detection with a constant threshold that triggers precisely on one of the pulse's edges. As demodulation is performed by TDC, the precision of TDC significantly influences the speed of PPM communication. To avoid symbol errors, the time interval \(\Delta\) must be adjusted according to the TDC precision, ensuring that the measured time does not drift into adjacent pulse time bins.  
Pulse threshold detection with precise time recording is what the Eventech Stream Time Tagger (ESTT) 7 Series event timer [35] provides. This event timer was used as TDC for PPM demodulation in previous papers [36; 37], and it was also chosen as a TDC for PPM demodulation in this research. ESTT's time precision is around \(1.5\,\mathrm{ps}\) with a dead time of \(40\,\mathrm{ns}\), which must be defined as the guard-time \(T_{\rm g}\) in PPM.  
Recently, a space-rated version of the ESTT-Eventech Space Ready Timing Module (ESRTM) was developed and is available for use in space applications where precise time measurement is needed [38]. ESRTM enables the implementation of a PPM receiver for Earth orbit and deep space satellites without the need to develop a dedicated system. ESRTM was launched with the European Space Agency's Hera mission [39] on 7 October 2024.  
Figure 2: Example structure of one TR-PPM frame with \(M=4\).