Constant Modulus Waveforms for IoT-Centric Integrated Sensing and Communications

Integrated sensing and communications (ISAC) is considered a key enabler to support application scenarios such as the Internet-of-Things (IoT) in which both communications and sensing play significant roles. Multi-carrier waveforms, such as orthogonal frequency division multiplexing (OFDM), have been considered as good candidates for ISAC due to their high communications data rate and good time bandwidth property for sensing. Nevertheless, their high peak-to-average-power-ratio (PAPR) values lead to either performance degradation or an increase in system complexity. This can make OFDM unsuitable for IoT applications with insufficient resources in terms of power, system complexity, hardware size or cost. This article provides IoT-centric constant modulus waveform designs that leverage the advantage of unit PAPR and thus are more suitable in resource-limited scenarios. More specifically, several single-carrier frequency and/or phase-modulated waveforms are considered. A comprehensive discussion on their radar sensing and communications performance is conducted based on performance metrics, including the radar ambiguity function, the bandwidth property, the data rate, and the communications receiver complexity.

💡 Research Summary

The paper addresses the design of waveforms for Integrated Sensing and Communications (ISAC) that are tailored to the stringent power, cost, and complexity constraints of massive Internet‑of‑Things (IoT) deployments. While multicarrier schemes such as Orthogonal Frequency‑Division Multiplexing (OFDM) have been popular for ISAC because they provide high data rates and large occupied bandwidths—both advantageous for radar range resolution—their high peak‑to‑average‑power‑ratio (PAPR) creates two major problems in low‑power IoT devices. First, a high PAPR forces power amplifiers to operate with a large back‑off from saturation, reducing power‑efficiency and shortening battery life. Second, the nonlinear distortion introduced by operating amplifiers in the nonlinear region degrades both the transmitted spectrum (causing out‑of‑band leakage) and the received signal quality (increasing error‑vector magnitude and bit‑error‑rate). The authors argue that these drawbacks make OFDM unsuitable for many IoT scenarios such as Bluetooth Low Energy (BLE), LoRa, and emerging “Internet‑of‑Radars” (IoR) where devices must run for years on a small battery and keep hardware simple.

To overcome this, the authors propose a family of constant‑modulus (CM) waveforms that inherently have a unit PAPR (0 dB). All the proposed schemes are single‑carrier in the sense that each time slot contains only one active subcarrier, which can be interpreted as a special case of OFDM‑Index Modulation (OFDM‑IM). By modulating only the frequency, the phase, or both, the transmitted envelope remains constant while still embedding information. The paper categorises the CM designs into two broad groups:

1. Fixed‑frequency patterns (stepped‑frequency waveforms).
   Linear Stepped Frequency (LSF) sweeps through a predetermined set of frequencies in a linear order, providing a large overall bandwidth and thus high mean‑square‑bandwidth (MSW) for radar range resolution. However, LSF’s ambiguity function (AF) exhibits strong diagonal ridges, leading to a high peak‑sidelobe level (PSL) and poorer global detection performance.
   Costas‑coded stepped frequency applies a carefully designed permutation (Costas code) to the frequency sequence. This dramatically suppresses AF sidelobes, yielding a low PSL while preserving the large bandwidth. The trade‑off is increased receiver complexity because the frequency order must be decoded, typically requiring O(N log N) operations.

2. Frequency‑and‑phase modulation hybrids.
   Schemes such as binary phase‑shift keying (BPSK) combined with frequency‑shift keying (FSK), pure phase‑modulation (PSK), or continuous‑wave FMCW‑like chirps are examined. These designs keep the transmitter extremely simple—often implementable with a basic direct‑digital‑synthesis (DDS) block—and the receiver can be realized with linear‑complexity correlators. Their radar performance is modest: MSW is lower than stepped‑frequency schemes, leading to coarser range resolution, but the AF typically has a low PSL because the waveform is deterministic and narrowband. Communication‑wise, the data rate is limited by the modulation order (e.g., 1–2 bits per sub‑pulse) but is sufficient for low‑throughput IoT links.

The authors introduce a performance evaluation framework that balances radar and communication metrics:

Radar metrics – mean‑square bandwidth (local delay resolution), ambiguity‑function PSL (global detection accuracy), and Doppler resolution (determined by pulse duration, assumed equal across schemes).
Communication metrics – maximum achievable bits per sub‑pulse under an ideal channel (reflecting modulation order), and per‑sub‑pulse receiver computational complexity (expressed as O(·) normalized by the number of sub‑pulses).

Through extensive numerical simulations, the paper demonstrates that:

• Costas‑coded stepped‑frequency achieves the best radar performance (high MSW, low PSL) but incurs the highest receiver complexity.
• Linear stepped‑frequency offers a large bandwidth but suffers from high PSL, making it less attractive when false‑alarm suppression is critical.
• Phase‑only schemes (BPSK/FSK, PSK) provide the lowest complexity and are ideal for ultra‑low‑power devices, yet their radar range resolution is limited.
• FMCW‑like chirps strike a middle ground: they retain constant envelope, have moderate MSW, and can be processed with simple matched filters.

The paper then maps each waveform class to representative IoT use‑cases:

• Ultra‑low‑power sensor networks (BLE, LoRa) – favor simple phase‑modulated single‑carrier CM waveforms because battery life and hardware cost dominate.
• High‑precision ranging applications (UWB‑based indoor positioning, IoR) – benefit from Costas‑coded stepped‑frequency or FMCW‑type CM waveforms, which deliver fine range resolution while keeping the transmitter efficient.
• Smart wearables and wireless radar sensor networks – may adopt hybrid frequency‑phase schemes that balance modest data rates with acceptable radar performance.

The authors stress that the “single‑carrier, constant‑modulus” design principle enables ISAC systems to meet the dual goals of energy efficiency and hardware simplicity without sacrificing essential radar capabilities. They also outline future research directions: extending CM designs to multiple‑input multiple‑output (MIMO) configurations, developing adaptive scheduling algorithms that dynamically select frequency/phase patterns based on instantaneous channel or sensing requirements, and building hardware prototypes to validate the theoretical PAPR and non‑linearity advantages in real RF front‑ends.

In summary, the paper makes a compelling case that, for the massive, power‑constrained IoT ecosystem envisioned for 6G, constant‑modulus single‑carrier waveforms are a pragmatic and technically sound alternative to traditional OFDM‑based ISAC solutions, offering a tunable trade‑off between radar resolution, communication throughput, and implementation complexity.