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Pulse-position modulation

Pulse-position modulation (PPM) is an analog or modulation technique in which the temporal position of a within a fixed-duration frame varies proportionally to the instantaneous of the modulating signal, while the 's and width remain constant. This method encodes information by shifting the 's occurrence relative to a reference timing, often using a per symbol slot to represent multiple bits in implementations, such as M-ary signaling where one of 2^M possible positions conveys the data. Proposed by J. R. Pierce at the in the mid-20th century for atmospheric laser communication systems, PPM offers high power efficiency, particularly in optical channels, by minimizing average transmitted power compared to formats like binary (BPSK) or quadrature (QPSK) at low signal-to-noise ratios (SNR < 6.5 dB). In PPM systems, the modulating signal is sampled and compared against a reference to generate pulses whose positions encode the amplitude levels; for instance, in analog PPM derived from (PWM), a monostable multivibrator triggers on the trailing edge of the PWM pulse to produce the position-shifted output. Demodulation typically involves synchronization to recover the timing reference, followed by pulse detection and conversion back to the original signal, often through intermediate PWM reconstruction. Key characteristics include constant power consumption due to fixed pulse amplitude and duration, robust anti-interference performance from the position-based encoding, and the incorporation of guard times or dead times in practical implementations to account for jitter or laser constraints. The power spectral density of PPM signals features both discrete lines and a continuous component, influenced by factors like slot occupancy and random timing variations, making it suitable for bandwidth-constrained environments. PPM finds prominent applications in optical communications, where its efficiency supports deep-space links and free-space laser systems with Q-switched lasers, as well as in radar for random pulse positioning to enhance detection. Despite advantages like low average optical power requirements and simplicity in pulse generation, PPM demands precise transmitter-receiver synchronization, which can complicate implementation in noisy or asynchronous channels.

Fundamentals

Definition and Principles

Pulse-position modulation (PPM) is a modulation technique that encodes information in the temporal position of pulses within fixed time intervals, while keeping the pulse amplitude and duration constant. In this scheme, the relative position of a single pulse per symbol period conveys the message, distinguishing it from other pulse modulation methods that vary amplitude or width. PPM can operate in analog form, where the instantaneous amplitude of the modulating signal determines continuous pulse shifts, or in digital form, where discrete positions represent symbols. The core principle of PPM lies in its reliance on precise timing to transmit data, offering robustness against amplitude noise compared to pulse-amplitude modulation (PAM), as the pulse shape remains invariant and only its occurrence time varies. Unlike pulse-width modulation (PWM), which adjusts pulse duration, PPM focuses exclusively on position, enabling efficient use of bandwidth in power-limited channels. The symbol duration, denoted as T, defines the fixed interval containing the pulse, sampled at a rate sufficient to capture the message bandwidth per the Nyquist theorem. In digital M-ary PPM, each symbol encodes \log_2 M bits by selecting one of M possible discrete positions for the pulse within the symbol period T, achieving a bit rate of (\log_2 M) / T bits per second. The pulse for the k-th symbol (where k = 0, 1, \dots, M - 1) is positioned at time t_k = k \cdot \frac{T}{M}, dividing the symbol into equal timeslots of duration T / M. This structure supports high data rates in applications such as optical systems, where PPM's timing precision enhances efficiency.

Signal Representation

Pulse-position modulation (PPM) signals consist of a periodic train of short pulses with constant amplitude and fixed duration, where the timing of each pulse's leading edge varies within a defined symbol period T to convey information. The pulse position is shifted relative to a reference time, typically the start of the symbol interval, with the shift determined by the modulating signal. For binary PPM, two possible positions are used—such as early or late within T—to represent a single bit, resulting in a waveform where pulses alternate between these offsets across successive symbols. In quaternary PPM (4-ary), four discrete positions divide the symbol period into slots, enabling two bits per symbol; the waveform shows pulses appearing in one of the four slots per T, creating a pattern of variable inter-pulse intervals that embed the data. The mathematical form of a PPM signal can be expressed as
s(t) = \sum_{n=-\infty}^{\infty} A \, p(t - nT - \tau_n) ,
where A denotes the fixed pulse amplitude, p(t) is the baseband pulse shape (commonly a rectangular function of width W \ll T), n indexes the symbols, and \tau_n is the time offset for the n-th symbol selected from M discrete values in [0, T) for M-ary PPM. This summation models the transmitted waveform as a sequence of isolated, position-shifted pulses, with information encoded solely in the offsets \tau_n. The bandwidth B required for an M-ary PPM signal (with M positions encoding \log_2 M bits per symbol) is approximately
B \approx \frac{M}{2T} ,
derived from the need to resolve the time slots in the receiver, where finer slot resolution for larger M demands greater bandwidth; this linear growth with M underscores PPM's trade-off between power efficiency and spectral occupancy.

Operation

Encoding

Pulse-position modulation (PPM) encoding transforms input data into a signal where information is conveyed by the temporal position of fixed-width, fixed-amplitude pulses within predefined time slots. In digital implementations, the process begins by grouping serial input message bits into M-bit symbols, where each symbol corresponds to log₂(2^M) bits of information. Each M-bit symbol is then mapped to a unique pulse position index k, ranging from 0 to 2^M - 1, determining the slot in which a single pulse is transmitted during the symbol period T. This mapping ensures that multiple bits are encoded per pulse, improving bandwidth efficiency in applications like optical communications. The step-by-step encoding proceeds as follows: First, the input bits are serialized and buffered into M-bit symbols using a symbol encoder or shift register. Next, a lookup table or combinatorial logic assigns the position index k to each symbol—for instance, in quaternary PPM (M=2), the bits 00 map to k=0, 01 to k=1, 10 to k=2, and 11 to k=3. A clock signal divides the symbol period T into 2^M equal slots of duration Δt = T / 2^M. The pulse generator, often a monostable multivibrator, is triggered at the symbol start, and a variable delay—implemented via a digital counter, delay line, or phase shifter—positions the pulse's leading edge at time k * Δt relative to the symbol onset. The multivibrator ensures a constant pulse width τ, typically much smaller than Δt, after which the system resets for the next symbol. Precise clock synchronization is essential to maintain slot alignment during this process. A common block diagram for PPM encoding includes key components such as a bit-to-symbol mapper, clock generator for symbol and slot timing, delay control logic (e.g., a counter that loads k and counts clock pulses to initiate the pulse), and the monostable multivibrator for pulse shaping. In scenarios deriving PPM from pulse-width modulation (PWM), a monostable multivibrator is triggered on the trailing edge of the PWM pulse to produce a fixed-width pulse whose position corresponds to the PWM width, which is proportional to the signal amplitude. The clock provides uniform symbol timing, ensuring non-overlapping frames. In binary PPM (M=1), encoding simplifies to assigning bit 0 to an early pulse position (e.g., first slot) and bit 1 to a late position (e.g., second slot), often using a simple toggle or counter to select between two delay values within a doubled slot duration. This approach, common in , uses a lookup table or direct logic to set the delay, with the multivibrator producing the pulse at the selected time.

Decoding

Decoding in (PPM) involves extracting the symbol information from the received signal by determining the precise timing of the pulse within each predefined symbol period, assuming synchronization has been established. The receiver typically starts a timer or counter at the onset of the symbol interval and measures the pulse arrival time \tau, which is then mapped to the corresponding symbol index k using the relation k = \round\left(\frac{\tau \cdot 2^M}{T}\right), where T is the symbol period duration and M is the number of bits per symbol, effectively dividing the period into $2^M discrete slots for threshold-based decision making. This process quantizes the pulse position into one of the possible slots, with decisions made by comparing \tau against slot boundaries to identify the transmitted symbol. A typical PPM receiver block diagram includes a pulse detector to sense the incoming pulse, a time-to-amplitude converter (TAC) or equivalent timing circuit to measure arrival time, and a comparator or quantizer to map the measured time to a discrete symbol index. The pulse detector, often an avalanche photodiode (APD) or photomultiplier tube (PMT) in optical systems, amplifies the weak signal to trigger the timing measurement. The TAC generates a linear ramp voltage that starts charging upon symbol initiation and stops upon pulse detection, producing an output voltage proportional to \tau. This voltage is then digitized or compared against reference levels corresponding to slot midpoints for symbol selection. In digital implementations, a high-speed counter increments at a clock rate finer than the slot resolution (e.g., sub-nanosecond ticks) until the pulse edge is detected, yielding a count value that is scaled to determine k. In analog decoding approaches, a ramp generator—often configured as an integrator with a constant current source charging a capacitor—produces the time-proportional voltage until the pulse arrives, after which a sample-and-hold circuit captures the level for comparison against a bank of thresholds representing slot positions. This method converts the temporal information directly into an electrical amplitude for straightforward quantization, commonly using an analog-to-digital converter (ADC) to resolve the position into $2^M levels. Error sources in this stage include timing jitter, arising from noise in the pulse detector (e.g., shot noise in optical receivers) or variations in the ramp linearity, which can shift the measured \tau and lead to incorrect slot decisions, particularly in low-signal environments. Jitter is exacerbated by factors such as thermal noise in the integrator circuitry or pointing inaccuracies in the receiver optics, potentially increasing the symbol error rate by displacing the pulse into an adjacent slot.

Implementation Aspects

Synchronization

Synchronization in pulse-position modulation (PPM) is critical because the information is conveyed exclusively through the precise timing of pulses within predefined time slots, necessitating accurate alignment of transmitter and receiver clocks to recover symbol and slot boundaries. Without proper timing recovery, errors in pulse position detection can lead to incorrect symbol interpretation. Key challenges include clock drift, which introduces gradual offsets due to differences in oscillator frequencies between transmitter and receiver, and additive noise, which perturbs pulse arrival times and exacerbates timing uncertainty. To address these issues, initial synchronization is typically established using pilot tones—periodic reference pulses inserted into the signal stream—or preambles composed of known symbol patterns that allow the receiver to estimate and correct initial timing offsets. For continuous operation, self-synchronization techniques leverage the leading or trailing edges of received pulses to dynamically adjust the local clock, commonly implemented with phase-locked loops (PLLs) that lock onto the average pulse timing or delay-locked loops (DLLs) that minimize delays between reference and feedback signals. In differential PPM schemes, synchronization demands are mitigated by encoding each pulse position relative to the preceding pulse, thereby eliminating the need for an absolute time reference and improving robustness to drift. In optical PPM systems, synchronization is often facilitated by incorporating periodic unmodulated slots or inter-symbol guard times, which provide empty intervals free of pulses to enable cleaner clock recovery without interference from data symbols. A fundamental requirement for reliable decoding is that the synchronization error Δτ must be less than half the slot duration, expressed as Δτ < T / (2^{M+1}), where T is the symbol duration and M is the number of information bits per symbol (corresponding to 2^M slots per symbol). This bound ensures that pulse positions can be unambiguously distinguished, preventing overlap or misassignment between adjacent slots.

Multipath Interference Sensitivity

Pulse-position modulation (PPM) is particularly vulnerable to multipath interference, where signals arriving via multiple propagation paths with varying delays cause pulse smearing or multiple pulse arrivals within the symbol duration T, resulting in position ambiguity at the receiver. This effect is exacerbated in frequency-selective fading channels, where the multipath delay spread exceeds a fraction of T, leading to greater distortion compared to flat fading scenarios, in which the delay spread is negligible relative to T. The primary consequence of multipath in PPM is an elevated bit error rate (BER) due to inter-symbol interference (ISI), as delayed echoes from preceding pulses overlap with the current symbol, corrupting position detection. In Rayleigh fading channels, PPM exhibits higher BER degradation than on-off keying (OOK) without equalization; for instance, multiple-PPM schemes suffer a performance loss of several dB relative to OOK under similar multipath conditions. To mitigate these effects, rake receivers can combine energy from multiple multipath components in PPM-based ultra-wideband systems, improving BER by capturing delayed arrivals through selective finger allocation. Guard intervals between symbols, as implemented in standards like for time-hopping PPM, extend the symbol period to exceed the maximum delay spread, reducing ISI from echoes. Hybrid approaches combining PPM with spread-spectrum techniques, such as direct-sequence or time-hopping codes, further resolve multipath by providing rake-compatible resolution of individual paths, though specific optimizations remain an area of active research. Compared to M-FSK, PPM shows greater sensitivity to multipath dispersion in such environments.

Performance

Advantages and Disadvantages

Pulse-position modulation (PPM) exhibits high power efficiency owing to its constant pulse amplitude, which maintains a fixed transmitter power output regardless of the modulating signal, minimizing power variations and enabling effective use in power-constrained systems such as optical communications. This constant amplitude also provides robustness against amplitude noise, as the information is encoded solely in the pulse timing rather than its strength, allowing reliable transmission in environments with fluctuating signal levels. Additionally, PPM supports non-coherent detection, particularly beneficial in optical links where phase synchronization is challenging, thereby simplifying receiver implementation compared to coherent schemes. Despite these strengths, PPM demands significantly larger bandwidth than other pulse modulations, scaling approximately with the modulation order —for M-ary PPM, the bandwidth is roughly M/(2T) times wider than that of binary modulation, where T is the symbol duration, due to the need for multiple time slots per symbol. This bandwidth expansion arises from dividing each symbol into M distinct positions, limiting spectral efficiency to about log₂(M)/M bits per hertz for large M. Furthermore, PPM incurs high implementation complexity, especially in synchronization and decoding, as precise timing recovery is essential to distinguish pulse positions accurately. It is also highly sensitive to timing jitter, which can shift pulse positions and increase error rates, particularly in high-order schemes. Overall, PPM presents a classic power-bandwidth trade-off: it achieves lower power consumption than (PWM) by avoiding variable pulse durations, but at the cost of greater bandwidth usage, making it preferable in scenarios prioritizing energy efficiency over spectral occupancy.

Detection Methods

Non-coherent detection represents a primary strategy for PPM receivers, relying on energy measurements within predefined time slots without the need for a phase reference. The receiver integrates the signal energy over each slot and identifies the slot exhibiting the peak energy as the pulse location, enabling straightforward implementation via envelope detectors or integrate-and-dump circuits. This approach is particularly advantageous in , where direct detection occurs through photon counting at the receiver or by detecting threshold crossings in the signal envelope, facilitating robust performance in intensity-modulated channels. For , the symbol error rate under non-coherent detection is approximated at high SNR as P_s \approx \frac{M-1}{2} \exp\left( -\frac{E_b \log_2 M}{2 N_0} \right), where M denotes the modulation order, E_b the energy per bit, and N_0 the noise power spectral density. Coherent detection, in contrast, employs phase-synchronized correlation between the received waveform and replica templates for each possible pulse position, leveraging a local oscillator aligned with the carrier phase to maximize signal-to-noise ratio. This technique demands precise carrier recovery mechanisms, such as phase-locked loops, introducing significant synchronization overhead that renders it less prevalent in PPM implementations compared to non-coherent alternatives. While coherent methods can yield superior sensitivity in ideal conditions, their complexity often limits adoption in practical systems prioritizing simplicity. In RF contexts, non-coherent PPM detection circumvents the requirement for phase-locked loops, distinguishing it from coherent M-ary frequency shift keying implementations and thereby streamlining hardware demands. Hybrid detection schemes, integrating non-coherent energy assessment with partial phase information, have emerged to mitigate degradation in fading channels, enhancing reliability without full synchronization costs.

Comparisons

Versus Pulse Width and Amplitude Modulation

Pulse-position modulation (PPM) differs from (PWM) primarily in how information is encoded: PPM varies the position of a fixed-width, fixed-amplitude pulse within a time slot, whereas PWM varies the width of a pulse while keeping its amplitude constant. This results in PPM maintaining constant pulse power and energy per symbol, making it more suitable for power-limited systems such as , where average transmit power is constrained. In contrast, PWM's varying pulse width leads to fluctuating power levels, reducing its efficiency in such scenarios. However, PPM demands precise timing synchronization for decoding, rendering it more sensitive to compared to PWM, which measures pulse duration and is thus more tolerant of small positional shifts. Regarding noise performance, PPM exhibits superior immunity to since pulse height remains fixed, while PWM, though less affected by amplitude variations than amplitude-based schemes, can still suffer if noise alters the perceived width. When compared to pulse-amplitude modulation (PAM), PPM avoids variations in pulse amplitude altogether, encoding information solely through timing, which provides strong immunity to low-frequency amplitude noise and channel fading effects common in wireless or optical links. PAM, by contrast, directly modulates pulse height proportional to the signal, making it highly susceptible to additive noise that corrupts amplitude levels, often requiring additional error correction. PPM also ensures fixed energy per symbol due to its constant pulse parameters, enhancing power efficiency over PAM's variable energy consumption tied to signal amplitude. Despite these benefits, PPM's reliance on accurate position detection increases its bandwidth needs relative to PAM, which can operate with simpler amplitude-based decoding but at the cost of poorer noise resilience. In terms of overall metrics, PPM demonstrates the highest power efficiency (constant transmit power), followed by PWM (moderate, width-dependent), and PAM (lowest, amplitude-dependent); for noise performance, PPM excels against amplitude disturbances but is most vulnerable to timing errors, PWM offers balanced resistance, and PAM fares worst overall.

Versus M-ary Frequency Shift Keying

In additive white Gaussian noise (AWGN) channels, pulse-position modulation (PPM) and M-ary frequency shift keying (M-FSK) achieve comparable bit error rate (BER) performance for the same bit energy to noise power spectral density ratio (E_b/N_0), as both schemes can be treated as noncoherent M-ary orthogonal signaling. The symbol error probability P_s for noncoherent detection is expressed as P_s = 1 - \left(1 - \exp\left(-\frac{E_s}{2N_0}\right)\right)^{M-1}, where E_s = M E_b is the symbol energy and M is the modulation order; the approximate BER is then P_b \approx P_s / \log_2 M. PPM often enables simpler noncoherent receiver structures compared to coherent alternatives, enhancing practicality in bandwidth-constrained systems. In flat fading channels, such as , both PPM and M-FSK exhibit similar BER performance with a diversity order of 1, since the fading multiplier affects all orthogonal signals uniformly without introducing intersymbol interference (ISI). The average BER for noncoherent M-ary orthogonal signaling over Rayleigh fading follows a closed-form expression involving the moment-generating function, yielding P_b \approx \frac{M-1}{2 \log_2 M} \left(1 + \frac{E_b}{N_0}\right)^{-1} at high SNR, confirming equivalent degradation for both modulations. However, PPM's short pulses make it less impacted by slow flat fading variations in low-multipath environments. In frequency-selective fading channels, PPM suffers greater BER degradation due to ISI from multipath delay spread, as echoes from prior symbols overlap with the current pulse position, requiring higher E_b/N_0 (e.g., up to several dB increase for delay spreads exceeding pulse duration) or equalization to maintain target BER. Simulations show PPM's uncoded BER rises rapidly with normalized delay spread \tau_d / T_s > 0.1, where T_s is symbol duration, without mitigation. Conversely, M-FSK leverages frequency diversity, as separated tones experience uncorrelated , yielding improved robustness; the diversity order d can reach M for widely spaced frequencies, reducing error floors in multipath. These differences drive key trade-offs: PPM is favored in optical communications with inherently low multipath and near-flat channels, minimizing sensitivity and enabling efficient power use for short-range links. M-FSK, however, excels in RF environments with pronounced multipath, exploiting for better reliability over longer distances or in urban settings. For diversity gain comparison, the asymptotic BER in selective approximates P_b \approx c (E_b/N_0)^{-d}, where d=1 for PPM (no inherent diversity) but d \geq 2 (up to M) for M-FSK with proper tone spacing, highlighting M-FSK's superior slope in log-log BER vs. SNR plots. PPM's noncoherent detection simplicity provides an edge in low-complexity scenarios, as detailed in detection methods.

Applications

Optical and RF Communications

Pulse-position modulation (PPM) finds significant application in optical communications, particularly in free-space and optic systems, where its high power efficiency stems from the use of non-coherent detection and the inherently low multipath interference in optical channels. This modulation scheme allows for effective transmission over long distances with minimal signal distortion, making it ideal for environments where coherent detection is challenging due to or alignment issues. In optics, PPM enhances utilization and sensitivity, offering improvements of several (e.g., up to 16 over PCM at 1 Gbit/s) compared to traditional schemes like in direct-detection receivers. NASA has employed PPM in deep-space optical links, including simulations and demonstrations for Mars missions, where it supports high-order modulation with M-ary values up to 256 to achieve robust data rates under constrained power budgets. For instance, 256-ary PPM combined with turbo coding enables near-capacity performance on Poisson channels typical of deep-space optical communication, transmitting multiple bits per pulse while maintaining low average power. This approach is particularly advantageous for interplanetary links, such as those between Earth and Mars orbiters, where photon-counting receivers detect the precise slot position of laser pulses. In (RF) communications, is utilized in (UWB) systems for short-range, high-data-rate applications, leveraging impulse radio techniques to achieve data rates exceeding 100 Mbps over distances up to several meters. The modulation's ability to encode information via timing provides resistance to multipath fading in indoor environments, supporting uses like wireless personal area networks. Its power efficiency—arising from concentrated energy in narrow s—makes suitable for power-constrained RF scenarios, such as communications, where average transmit power must be minimized to extend operational life. A specific implementation of PPM appears in the ISO/IEC 15693 standard for contactless smart cards operating at 13.56 MHz, where data frames consist of 9.44 μs time slots to encode information via pulse positioning. This vicinity card standard uses pulse-position modulation for the forward link, allowing reliable short-range identification with low power consumption. Overall, 's power efficiency contributes to its adoption in these domains, though detailed performance metrics are discussed in the broader performance section.

Radio Control and RFID Systems

In radio control systems for remote-controlled models, pulse-position modulation (PPM) encodes control signals by varying the position of pulses within a fixed frame, allowing multiple channels to be multiplexed over a single carrier frequency. Traditional PPM operates in frequency bands such as 27 MHz, 72 MHz for aircraft, and 75 MHz for surface vehicles, where the transmitter sends analog PPM signals to the receiver, which decodes them into individual servo pulses. A typical PPM frame lasts 22.5 ms, beginning with a 0.3 ms synchronization low pulse followed by 1-2 ms high pulses for each channel, representing control positions from minimum to maximum. Up to 10 channels can be supported by allocating sequential time slots within the frame, enabling control of throttle, steering, and auxiliary functions in models like cars, boats, and aircraft. However, PPM's analog nature makes it susceptible to noise, jitter, and , which can corrupt pulse timing and cause erratic model behavior without built-in error detection. This vulnerability, particularly in crowded spectrum environments, has rendered traditional PPM outdated, prompting a shift to digital protocols like (PCM) and spread-spectrum systems at 2.4 GHz for improved reliability and . In (RFID) systems, PPM facilitates communication from passive tags to readers, particularly in high-frequency (HF) standards operating at 13.56 MHz. The ISO/IEC 15693 protocol employs subcarrier-based PPM for tag-to-reader transfer, using load modulation to encode bits by positioning pauses on a subcarrier of 423.75 kHz ( divided by 32). Each consists of slots of 9.44 μs, where the pause location within a longer period (e.g., 18.88 μs for 1/4 PPM or much longer for 1/256 PPM) represents values, achieving rates up to 26 kbps in high-speed mode. The EPCglobal Class 1 RFID air , operating at 13.56 MHz, uses load for tag-to-reader responses with encodings such as FM0, , or sub-carrier methods, supporting data rates from 53 kbit/s to 848 kbit/s depending on the mode and divide ratio. This enables reliable identification over distances up to 1 meter in environments like libraries and . The frame in these RFID implementations relies on predefined pulse patterns to align reader and tag timing, ensuring robust decoding amid potential multipath effects.

Historical Development

Early Concepts

The concept of pulse-position modulation (PPM) was first proposed by J. R. Pierce at the in the mid-20th century, specifically for atmospheric communication systems. This marked the formal introduction of PPM as a technique where the position of pulses encodes information, offering advantages in power efficiency for optical channels. In the early 1960s, PPM found early practical application in (RC) systems for . engineers Don Mathers and Doug Spreng developed PPM-based control systems, enabling precise servo operation through timed pulses, which became a standard in hobbyist RC until the digital era.

Modern Advancements

During the mid-20th century, PPM gained traction in space applications, particularly through 's exploration of systems. In 1968, researchers at the Electronics Research Center and the designed PPM-based optical systems using photon-counting detectors to enable efficient data transmission over long distances, leveraging narrow pulses for high sensitivity in direct detection scenarios. This work laid groundwork for PPM's role in deep-space links, where its proved advantageous amid the emerging laser technology of the era. By the 1970s, as laser developments advanced free-space optical communications, PPM was formalized as a key modulation scheme for handling atmospheric and interstellar challenges, with experiments demonstrating high data rates up to 10^7 bits/s using M-ary formats and subnanosecond pulses. In the late 20th and early 21st centuries, PPM integrated into standards for (UWB) and (RFID) systems, enhancing short-range, low-power wireless technologies. During the and 2000s, UWB impulse radio protocols adopted PPM variants, such as time-hopping PPM (TH-PPM), to mitigate interference and support precise ranging in applications like sensor networks; this culminated in the IEEE 802.15.4a standard (2007), which incorporated PPM-based modulation for low-rate, low-power personal area networks. Similarly, UWB RFID systems from the early 2000s utilized PPM for tag-reader communication, enabling high-speed inventory tracking with minimal power consumption due to PPM's ability to encode data via pulse timing. Concurrently, research advanced high-order (high-M) PPM for deep-space optical links, with a seminal 2007 study introducing iterative coded PPM schemes that improved error performance and throughput in photon-starved environments, achieving near-capacity efficiency for NASA's interplanetary missions. As of 2025, PPM continues to evolve in forms for next-generation optical systems, particularly in contexts, where it combines with techniques like differential (DPSK) to boost and resilience in satellite-to-ground links. For instance, PPM-DPSK modulation has been proposed for ground-to-GEO-to-LEO optical networks, offering up to 20% higher data rates under channels compared to standalone PPM. However, in traditional (RC) applications, PPM's use has declined since the 2000s, supplanted by digital serial protocols like SBUS and DSMX, which provide greater and noise immunity for modern multirotor and systems.