Pulse Signal Advantages for 6G MANET

Ad hoc RF network communications pose major technical challenges, especially for highly mobile users. These challenges will only grow with sixth-generation (6G) elevated carrier frequencies and bandwidths. The “users” of a mobile ad hoc network (MANET) might be human, or simply machine platforms (such as drones, autonomous vehicles, satellites, and even projectiles).

Future 6G resources (e.g., high carrier frequencies, wider signal bandwidths, and miniaturized antenna arrays) might enable MANETs of unique capabilities. But common network constructs such as centralized base stations are inconsistent with the nature of the MANET. This discussion advances the use of pulse waveforms to overcome basic obstacles in the realization of 6G-based MANETs.

MANET Challenges

Ad hoc networks may require spontaneous user access without centralized scheduling or control activities. In addition, future 6G networks may require operation with minimal latency. These requirements may be contrary to traditional paradigms of network coordination through a base station or centralized access point.

Certain latencies are inherent in the operation of 4G and 5G networks. This may include procedures of resource allocation and beam management, requiring tens of milliseconds of overhead. By contrast, some 6G networks might require a reduction of latency from orders of milliseconds to microseconds.

In addition to operational impediments, current 5G networks embrace waveform techniques which may be problematic for certain 6G MANETs. This includes orthogonal frequency-division multiple access (OFDMA). In particular, OFDMA can require precise signal synchronization between a base station (or access point) and multiple users. Downlink synchronization is simplified by transmission from a single point (the base station), but the uplink can require the base station to synchronize multiple distributed users. The uplink challenge will only be exacerbated by wide-bandwidth 6G signals and highly mobile users.

Pulse Structure

The use of pulse signals may resolve many operational and physical issues in future 6G MANETs. In particular, short pulses might mitigate basic physical challenges to the use of OFDM in MANETs. In this discussion, a communications pulse may have a complex internal structure, as opposed to being a simple burst of energy or “UWB pulse”. In particular, the “pulse” as discussed herein may consist of a set of modulated sub-carriers. Processes of quadrature amplitude modulation (QAM) and OFDM signal generation might produce these sub-carriers.

The Discrete Fourier Transform (DFT) is central to both the OFDM pulse and OFDMA “symbols”. Sub-carrier generation using these techniques may be presented in terms of the Inverse DFT (IDFT) as given below;

where;

f(n) is the output of the IDFT (sampled time domain representation of pulse or symbol)

F(j) is the input sequence to the IDFT (amplitudes and phases of the sub-carriers)

W = e^(2πi)/N 

N is the transform size (typically an integral power of 2)

n is an index on the IDFT outputs (0 ≤ n < N)

j is an index on the IDFT inputs (0 ≤ j < N)

In mathematical terms, the complex exponential W^jn above defines a set of orthogonal “basis functions” for the IDFT (or DFT). In the language of OFDM or OFDMA symbol generation, these basis functions are the sub-carriers (sine and cosine functions). Further, in either OFDM or OFDMA, each sub-carrier may be modulated (adjusted) in amplitude and phase according to a complex value F(j), as part of the QAM “mapping process”.

The transform length “N” is a key parameter in comparing a narrow OFDM symbol (pulse) to a broad OFDMA symbol. The parameter N defines the number of sub-carriers. It also defines the width of the symbol in terms of discrete signal samples, where the symbol might be perceived as the “output” of the IDFT (neglecting any symbol extension by a “cyclic prefix”). As discussed below, an OFDM pulse signal of small N may have several advantages over an OFDM signal (or symbol) having a much larger value of N.

Short Pulse Physical Advantages

Reduced Doppler Spreading

“Doppler spreading” can be a fundamental problem in high-frequency MANETs. It is rooted in the physics of RF signal transmission. It can cause undesired frequency shifts of the “sub-carriers” of wide 5G OFDM “symbol” waveforms. The effect is exacerbated by both higher operating frequencies and high relative velocities of users. As such, it can be of even greater concern for 6G networks.

However, Doppler effects can be mitigated by the use of narrow pulses, as opposed to wide “time domain” symbols of 5G waveforms. Specifically, for the same channel bandwidth and carrier frequency, a short OFDM pulse yields a wider frequency spacing of sub-carriers, resulting in proportionally smaller effects due to Doppler spreading. This is qualitatively seen in the sub-carrier spacing and “bandwidths” of Figure 1. The Figure compares the wide sub-carrier spacing of a narrow pulse, as compared to the closer sub-carrier spacing of a broad pulse (or 5G symbol). In the Figure, N=64 for the narrow pulse versus N=1024 for the broad pulse with the same channel bandwidth (ω_C) for both cases.

Figure 1: Sub-Carrier “Bandwidths” – Relation to N

As seen, frequency domain displacement of sub-carriers for N=64 can be less significant than the same displacement for N=1024 in Figure 1. Therefore, Doppler spreading has less effect on the demodulation of the narrow pulses. In fact, the effect can be relatively negligible for certain 6G carrier frequencies. An example is given below, where the Doppler shift of an RF carrier signal between two MANET users may be expressed as;

Where;

Δf = Doppler shift of RF carrier as seen by a receiver

v   = relative velocity between the two network users

f_C = frequency of the carrier signal

c   = speed of light

For a scenario where the relative velocity is 60 miles per hour (mph) with a carrier frequency of 20 Ghz, the Doppler shift of the carrier is then;

Assuming a pulse bandwidth of 256MHz and for N=64, the sub-carriers of Figure 1 might then be spaced at;

Accordingly, the Doppler shift of 2KHz is much less than 1% of the 4MHz sub-carrier spacing, suggesting a very minor effect on sub-carrier demodulation for the given example (although higher frequency sub-carriers can experience slightly larger effects than those of lower frequency).  This also suggests distinct pulse advantages for higher velocity users in both land-based and airborne MANETs.

Control of Peak-to-Average-Power-Ratio (PAPR)

Large “peak-to-average-power-ratio” (PAPR) is an inherent issue of 4G and 5G systems having very wide OFDM symbols. It is characterized by large peaks in symbol power levels due to the superposition of many sub-carriers.

Elevated PAPR levels are sometimes addressed by “clipping” of time-domain signals' peaks that exceed certain levels. This approach, however, can inject noise across a multiplicity of sub-carriers. Therefore, signal quality is degraded at the receiver side.

In certain other 4G and 5G designs, PAPR levels in long symbols are suppressed by scrambling the order of the F(j) input sequence to the IDFT. This is an iterative process by which F(j) might be re-ordered several times, with the resulting PAPR tested with each new order. The process might continue until an acceptable PAPR level is found. However, for the long symbols of 4G and 5G systems, the approach can be time-consuming and computationally intensive.

By contrast, an advantage of a narrow pulse (as compared to a wide OFDM symbol) is naturally lower PAPR levels. This is due to fewer subcarriers in the OFDM pulse, as well as its shorter length in the time domain. This advantage can either simplify power amplifier design, and/or increase the propagation range of the pulse signals (by increasing the average transmitted power of the pulse signals).

Rapid User Detection and Localization

An aspect of modern network operations is “beam management”. An integral part of conventional beam management is “spatial searching”. This is a cooperative procedure that may take place between a base station and a user. The procedure might add tens of milliseconds of latency in establishing a connection. The pulse signal approach can reduce such latency by means of RF direction-finding methods.

In the 6G MANET, it is desired that users establish communications independently (i.e., without centralized control) and with minimal latency or delay. To do so, a network must separate user signals in either space, time, or frequency (or by codes) and must establish spontaneous user connectivity without a central arbiter. Pulse waveforms may address these requirements. For example, various “direction finding” mechanisms exist to detect and establish the source of pulse signals. These may operate on a “mono-pulse” basis, to allow very rapid determination of the angle of arrival (AOA) and time of arrival (TOA) of a pulse. Direction finding systems might be based on either “amplitude comparison” or “phase comparison”, with amplitude comparison often easier to implement.

Figure 2: Direction Finding by Amplitude Comparison

Amplitude comparison techniques are distinctly different from beamforming. They rely on comparing the incident power received in overlapping, identical antenna patterns as shown in Figure 2. This is an inherently “monopulse” technique capable of extremely rapid response, given sufficient SNR. Amplitude comparison may support low-latency signal acquisition and avoid long “spatial searching” procedures.

Amplitude comparison employs broad, overlapping antenna gain patterns to intercept a sender’s signal. These patterns provide wide-angle spatial coverage. As seen in Figure 2, a signal from a network transmitter “intersects” a receiver’s antenna patterns at points A′ and B′.  The AOA of the signal may then be measured by comparing the signal power levels inferred at points A′ and B′. Different techniques exist for making this comparison, which can depend on antenna gain patterns. One technique which may be used when the patterns are “sine” shaped is given as follows;

where B_P and A_P are the detected power from the antenna patterns. The accuracy of this direction finding process is naturally enhanced by higher SNR levels.

In an RF network where users are equipped with amplitude comparison systems, a given user (sender) might emit one or more wide-bandwidth pulse(s) which may be detected by other users (receivers). The relative AOA and TOA of the sender might then be localized on the basis of one or more pulses. Further, the sender might be identified by a code embedded into the wide-bandwidth emitted pulse. A receiver might then “lock on” and track future pulses from a sender, when said pulses might be transmitted at regular intervals. Also, once a signal lock has been achieved, RF beamforming might be employed to form a more focused antenna pattern between the sending and receiving network users. Thus, a pulse train signal from the sender might be separated from that of other network users by space (AOA), time (TOA), and code parameters.

Signal Data Capacity

Within the MANET or other networks, users might be separated by either time, frequency, physical space, or codes, or some combination thereof. By wide-bandwidth pulses, users might occupy the same spectral space (channel) while being separated in time. With beamforming, network users might also be separated in physical space.

In most modern RF networks, users are typically not separated by time (or pulses), but instead by frequency multiplexing. This is the concept behind OFDMA systems, which divide available channel bandwidth into sub-bands, where each sub-band consists of a multiplicity of sub-carriers. Each network user might then occupy a given sub-band. This band-limited approach (as with other forms of frequency multiplexing) typically results in a continuous time domain signal.

It is then instructive to compare the information capacities of a narrow-band continuous signal and a wide-bandwidth pulse. This might be performed using Shannon’s law for maximum data rates of a signal, which can be stated as:

where;

C(bps) = a maximum data rate of “C” bits per second

ω = bandwidth of the transmission channel in Hz,

SNR_C = a linear ratio of signal power to noise power, for Gaussian noise of a constant power spectral density (psd) across the channel.

Then the maximum data which can be transmitted by a pulse width of “T” seconds is T•C (the product of time and data rate). Similarly, for a continuous signal which is longer than the pulse by a factor of “M”, the maximum amount of data which may be transmitted is (M•T•C).  The example below compares such a continuous signal and pulse, where the pulse has a channel bandwidth of ω, and the continuous signal of a user occupies a channel sub-band of (ω/M) Hz (as might be the case in OFDMA).

For the same signal power, the SNR of the continuous signal might exceed that of the pulse by a factor of M (as the continuous signal power is “squeezed” into a narrower bandwidth, wherein substantial noise is essentially filtered out). It can then be shown by Shannon’s law that the deliverable data for the continuous signal may be expressed as;

whereas the data which might be delivered by the pulse is;

As seen above, the data delivered by the continuous signal (D₁) exceeds that of the pulse, but not by a factor of M. Instead, D₁ has a logarithmic dependency upon M. Figure 3 illustrates this result by plotting the ratio D₁/ D₂  for various SNR levels.

Figure 3: Ratio of Data Capacities

To exemplify for SNR_C=1 (a relatively low SNR), from the expressions above, the ratio D₁/ D₂  is calculated as;

Therefore, the ratio (D₁/ D₂) does not have a linear relationship to the factor M. In particular, the ratio increases with larger M but at a decreasing rate. This is illustrated in Figure 3 for the given example (where SNR_C=1) and for greater SNRs. By the nature of Shannon’s law, the example is an “idealized” comparison, not including potential effects such as multi-path fading, narrow-band interference, and other signal distortions.

From the above example, the ratio D₁/ D₂ shows an advantage of a continuous signal versus the pulse. But as seen in Figure 3, this ratio exhibits little improvement for large M. (The ratio may be referenced as D_R below).

Optimization of Energy Resources

In modern personal communication devices, displays are major consumers of power, followed by RF circuitry and processors (neglecting speakers). But some MANET users, as in the Internet-of-Things (IoT), may have no displays and yet still be limited in energy resources. This issue might be alleviated by the use of OFDM pulse signals.

In a continuous signal network where users are separated in frequency, RF circuits might be active during transmission (and reception) for significant periods of time. But in a system of pulses, RF circuits might be rendered dormant in time intervals between pulses to conserve energy. This difference leads to a trade-off between “spectral efficiency” versus “energy efficiency”, as may be illustrated in Figure 4.

Figure 4: Data Capacity and Energy Consumption Ratios

The lower trace of Figure 4 plots the ratio D_R. As previously seen (in Figure 3), this indicates a superior “spectral efficiency” for a continuous signal versus the pulse signal (where D_R has been defined as a ratio of data capacity, even though spectral efficiency can be an instantaneous measurement). The plot is for the channel SNR = 1.

The upper trace of Figure 4 (E_R) is a ratio comparing the energy consumption of a continuous signal emitter to a pulse signal emitter, where the pulse emitter may “shut down” between pulses. As in the prior example, pulses are of width “T” seconds separated by M•T seconds. Assuming constant energy consumption during transmission, the E_R trace reflects “M” times more energy consumption by the continuous signal relative to the pulse signal.

Accordingly, there can be a trade-off where the pulse signals have less spectral efficiency, but significantly better energy efficiency than the continuous signals. As stated above, the continuous signals might be separated in the frequency domain, whereas pulse signals might be separated in time (e.g., via different pulse rate intervals), space (via beamforming), and code domains.

Enhanced Baseband Processing

A distinct advantage of short OFDM pulses can be simplified baseband processing, especially for the IDFT. As described above, the IDFT (and DFT) are central to the formation (and analysis) of the sub-carriers in both OFDM and OFDMA. However, a long OFDMA symbol often involves the use of complicated Fast Fourier Transform (FFT) hardware or software. By contrast, the short pulse may be processed by more simplistic DFT structures. Further, these might be implemented by highly efficient in-memory computing (IMC) circuits.

Recent patent descriptions (US 12363640 and US 12477468) present architectures for 6G baseband processing with IMC circuitry. IMC can be utilized as a type of analog processing that mimics digital processing. Functional advantages of digital processing might then be achieved, but with greatly reduced size and power consumption. Further, IMC circuits may process much higher bandwidths than more complex digital circuits.

Mitigation of Squint

Beamforming may exist in many future 6G systems. There are two basic types of RF beamforming. These are phase-based and time-delay beamforming. Of the two, phase-based beamforming is the more flexible. Unfortunately, the use of wide-bandwidth signals with phase-based beamforming presents a fundamental problem known as “squint”. Accordingly, the problem might apply to the wide-bandwidth pulse signal.

The phenomenon of squint degrades the accuracy of phase-based RF beamformers and can worsen with elevated 6G carrier frequencies and operating bandwidths. This can lead to a conflict between wide-bandwidth pulse signals and beamforming. However, digital phase-based beamforming might mitigate the problem of squint.

Phase-based beamforming by digital means (as opposed to analog or hybrid) has great potential in terms of flexibility. But the digital approach is generally perceived as impractical due to complexity, cost and power consumption. This is especially true for dense arrays of antenna elements as may be found in future 6G systems.

However, recent patent literature describes in-memory computing (IMC) methods that mimic the flexibility of digital phase-based beamforming. Such description may be found in US 12363640 and US 12477468. Dense arrays of IMC structures might then mitigate squint by the formation of complex beam patterns. Such methods may be particularly well suited to pulse-based 6G MANET systems, enabling very rapid (e.g., sub-microsecond) switching of RF beams on a pulse-to-pulse basis.

Active Sensing

In addition to other advantages, pulse signals can be used to sense or even image an environment. The basic principles are very mature and are used in radar, medical ultrasound, and even the animal world. Therefore, pulse signals may enable dual-mode networks for sensing and communications. Each mode might require different pulse modulation techniques. The wide-bandwidth OFDM pulse as described herein has many advantages for communications. Alternatively, pulses for sensing might employ linear frequency modulation (FM) as in “chirp” signals.

Due to the propagation constraints of 6G waveforms, sensing capabilities would necessarily be limited in range. Such a capability would also add complexity to an RF front end. At the same time, the dual-mode is theoretically possible and would add a valuable dimension to 6G MANETs.

Conclusion

The realization of future 6G MANETs might be greatly influenced by the choice of waveforms. In particular, the deployment of OFDM pulse signals may alleviate basic physical issues and also circumvent complex procedures, protocols, and processing found in current systems.

Also, the pulse approach can be advantageous in terms of user “energy efficiency”. In the 6G pulse MANET users might be separated by different pulse-rate-intervals (PRIs) and I.D. codes embedded into pulses. This may be a significant advantage in energy efficiency, as compared to a MANET where users are separated by frequency multiplexing.