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Sensing With Communication Signals: From Information Theory to Signal Processing

Fan Liu, Ya-Feng Liu, Yuanhao Cui, Christos Masouros, Jie Xu, Tony Xiao Han, Stefano Buzzi, Yonina C. Eldar, Shi Jin

arXiv:2502.10819v1cs.ITmath.IT

TL;DR

Communication-centric ISAC research has largely left the sensing effects of practical channel coding unexplored. This tutorial reviews theory and signal-processing approaches for random communication signals and identifies design objectives for sensing and communication across waveform and MIMO systems.

  • Problem

    Although channel coding is critical to communication systems, its impact on sensing with random ISAC signals remains largely unexplored, despite the goal of balanced sensing and communication performance.

    Source: 4) Sensing with Channel-Coded Signals · p. 21

  • Method

    The tutorial reviews ISAC’s information-theoretic foundations, analyzes random-signal ACF statistics, and surveys design approaches for modulation, constellations, pulse shaping, and MIMO precoding.

    Source: 3) Signal Processing for Sensing · p. 11, §VII · p. 22

  • Results

    The tutorial identifies improving sensing without sacrificing communication, or establishing a scalable S&C tradeoff, as design objectives for communication-centric ISAC.

    Source: §VII · p. 22

  • Takeaways & Limitations

    The tutorial aims to guide development of ISAC air-interface technologies compatible with current cellular networks.

    Source: §VII · p. 22

    The sensing impact of channel coding remains largely unexplored in the studies reviewed.

    Source: 4) Sensing with Channel-Coded Signals · p. 21

Abstract

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The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multi-input multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals.

I. INTRODUCTION … II. DETERMINISTIC-RANDOM TRADEOFF IN ISAC SYSTEMS: AN INFORMATION-THEORETIC PERSPECTIVE

The tutorial examines ISAC using random communication payloads for sensing and communication, motivating signal processing tailored to their deterministic-random tradeoff (DRT) and surveying its theory and methods.

1) Sensing-Centric Design:

  • Sensing-centric designs embed communication bits in radar waveforms, but their reliance on slow-time coding typically limits data rates to the pulse repetition frequency –.Information may be carried through chirp amplitude, phase, frequency, or rate, or through MIMO spatial techniques such as sidelobe control and index modulation.Source: 1) Sensing-Centric Design · p. 2

2) Communication-Centric Design:

  • Communication-centric designs reuse formats such as OFDM, OTFS, and AFDM, but generic communication signals can yield degraded, difficult-to-tune sensing performance –.OTFS operates in the delay-Doppler domain, while AFDM was proposed to improve S&C, especially in high-mobility scenarios.Source: 2) Communication-Centric Design · p. 2

3) Joint Design:

  • Joint design formulates S&C waveform selection as multi-objective optimization, offering flexibility at considerably higher complexity than the other approaches –.Examples include minimizing communication interference subject to radar beampattern constraints, or minimizing sensing CRB subject to communication SINR or rate requirements.Source: 3) Joint Design · p. 2
  • Communication-centric ISAC is presented as practical for 5G-A and 6G because it is low-cost and compatible with cellular infrastructure, alongside ongoing 3GPP, ETSI, and IEEE sensing efforts –[46].The introduction highlights positioning work in Rel-18, ISAC use cases and service requirements toward Rel-19, and anticipated air-interface study in Rel-20 toward Rel-21 specifications.Source: 3) Joint Design · p. 2

B. Sensing With Random Communication Signals

  • Over 85% of resources are data payloads, while PHY reference signals occupy up to 10%-15%, motivating payload reuse to improve range-Doppler resolution and target detection and estimation.Relying on pilots alone can require sensing samples across multiple frames, increasing complexity and latency.Source: B. Sensing With Random Communication… · pp. 2–3
  • Random payloads improve communication rate but can degrade sensing because communication favors randomness while radar requires deterministic signals with favorable ambiguity properties –.The tutorial describes the resulting DRT as a challenge for characterizing the S&C Pareto boundary and notes that evaluates communication- and sensing-optimal points in a point-to-point vector Gaussian ISAC channel.Source: B. Sensing With Random Communication… · p. 3

C. Organization of This Paper

  • The tutorial reviews DRT through capacity-distortion theory and Gaussian-channel CRB-rate regions, then treats random-signal ACF statistics as a multi-target ranging metric,, [58].It covers closed-form expected squared ACF under arbitrary modulation and constellation mappings with Nyquist pulse shaping, separating the pulse-filter-determined squared mean from data-randomness variance.Source: C. Organization of This Paper · p. 3, §II · p. 4
  • The tutorial surveys modulation, constellation, pulse-shaping, and MIMO precoding designs, reporting that OFDM has the lowest average ranging sidelobe among orthogonal linear modulations for i.i.d. QAM/PSK [58]–.It also reviews probabilistic constellation shaping to increase communication rate while reducing OFDM sidelobes, Nyquist pulse designs that reshape ACF, data-dependent and data-independent MIMO precoding, and open research challenges.Source: C. Organization of This Paper · pp. 3–4

A. System Model … 2) S&C Performance Evaluation:

The section models a point-to-point ISAC system in which one signal serves communication and sensing, then uses capacity-distortion theory to evaluate their tradeoff under sensing and resource constraints.

A. System Model

  • A unified ISAC signal serves a communication receiver and a dedicated sensing receiver, which may be collocated with the transmitter or linked to it in a cooperative bistatic setup.The sensing receiver knows the transmitted signal, whereas the communication receiver does not because the signal carries user information.Source: A. System Model · p. 4, Figure 1 · p. 4
  • Estimation performance is quantified by MSE, while detection performance uses detection and false-alarm probabilities; under fixed false-alarm probability, minimizing average Hamming distortion maximizes detection probability.Both task types can be represented by bounded-distance distortion measures.Source: A. System Model · pp. 4–5

B. Capacity-Distortion Theory

  • Capacity-distortion theory extends rate-distortion analysis to characterize achievable communication-sensing boundaries across channel models and sensing tasks.It abstracts sensing through a generic distortion measure rather than specifying an estimation or detection task.Source: A. System Model · p. 5, 1) Information-Theoretic Model for… · p. 5

1) Information-Theoretic Model for Monostatic ISAC:

  • The monostatic model treats ISAC as a memoryless state-dependent delayed-feedback channel, with the target parameter as state, communication output y, and target-return feedback z [55], –.The state may represent delay, Doppler, angle, or target presence.Source: 1) Information-Theoretic Model for… · p. 5
  • Its coding scheme maps messages and past feedback to transmitted signals, while decoding uses communication outputs and sensing state and estimation uses transmitted signals and returned feedback [55].The target state is modeled as i.i.d. across time slots.Source: 1) Information-Theoretic Model for… · p. 5

2) S&C Performance Evaluation:

  • Sensing performance uses average per-block distortion, and the memoryless channel permits an optimal single-letter estimator minimizing expected posterior distortion.Distortion can represent Euclidean estimation error or Hamming detection error; the resulting estimation error is the sensing cost for a given signal.Source: 2) S&C Performance Evaluation · p. 5
  • The framework measures communication by average message error probability and constrains signal resource cost, defining achievable rate-distortion-cost tuples under a resource budget.The C-D tradeoff describes the achievable communication rate for a given distortion and budget.Source: 2) S&C Performance Evaluation · pp. 5–6
  • The operational C-D tradeoff is equivalent to an information-theoretic optimization maximizing conditional mutual information over signal distributions subject to distortion and resource constraints; it can be solved iteratively using Blahut-Arimoto, [68],.The objective is I(x; y|h), the mutual information between input and communication output conditioned on the channel state.Source: 2) S&C Performance Evaluation · p. 6

3) Example: · C. CRB-Rate Region for Vector Gaussian ISAC Channels · 1) Generic Framework:

A scalar Gaussian example illustrates the communication–sensing tradeoff through changing input distributions, while a vector Gaussian framework defines a CRB–rate region for random MIMO ISAC signals. The framework models communication rate and sensing cost jointly, with practical characterization focused on extreme points and a time-sharing inner bound.

3) Example:

  • The scalar example assumes a real Gaussian channel, power budget B = 10, and perfect feedback, and is explicitly a toy model rather than a realistic ISAC transmission scenario.The communication receiver recovers x, while the sensing receiver estimates h from the echo using an MMSE estimator.Source: 3) Example · p. 6
  • Along the scalar C-D boundary, the optimal input distribution changes smoothly from Gaussian at the communication-optimal point to BPSK at the sensing-optimal point, reducing signal randomness.The plotted boundary and Pareto-optimal distributions are for the real-valued scalar Gaussian channel with B = 10.Source: 3) Example · p. 6, Figure 3 · p. 6

1) Generic Framework:

  • The vector Gaussian model uses a random dual-functional waveform X over N slots, with sensing and communication channels that can be correlated and a sensing parameter vector η with prior Pη.The parameter vector may include target delay, Doppler, and angle; X is known to the sensing receiver but unknown to the communication receiver.Source: 1) Generic Framework · pp. 6–7
  • The vector channel model applies to monostatic and cooperative bi-static ISAC, with an Nt-antenna transmitter communicating to an Nc-antenna receiver while a separate Ns-antenna receiver senses targets.The transmitter emits X over N consecutive time slots.Source: 1) Generic Framework · pp. 6–7
  • Communication rate is characterized by I(X; Y|Hc), while sensing uses the Miller–Chang bound, averaging the CRB over random but known X as a sensing cost.The Bayesian MCB lower-bounds MSE for weakly unbiased estimates; its Bayesian Fisher information is affine in the sample covariance RX, and the bound may be attained by MAP estimation at high SNR.Source: 1) Generic Framework · p. 7
  • Varying α from 0 to 1 traces the CRB-rate Pareto boundary under the average transmit-power budget PT, defining the achievable CRB-rate region.Figure 4 illustrates the tradeoff for a P2P monostatic ISAC system.Source: 1) Generic Framework · p. 7, Figure 4 · p. 7
  • Because the full boundary is computationally challenging to obtain over infinite-dimensional PX, the communication- and sensing-optimal distributions PCS and PSC are emphasized; their connecting line gives a time-sharing inner bound.This inner bound is part of the CRB-rate region characterization.Source: 1) Generic Framework · p. 7

2) S&C Performance at PCS: · 3) S&C Performance at PSC:

At PCS, Gaussian signaling maximizes communication rate while sensing CRB is bounded; at PSC, deterministic sample covariance supports sensing, but communication-rate characterization is harder.

2) S&C Performance at PCS:

  • At PCS, the rate-maximizing Gaussian input uses a covariance aligned with Hc’s right singular vectors and water-filling eigenvalue allocation.The signal structure uses an information-bearing random matrix with i.i.d. CN(0, 1) entries.Source: 2) S&C Performance at PCS · p. 7
  • The resulting achievable communication rate at PCS is given by the Shannon capacity formula.Source: 2) S&C Performance at PCS · p. 7
  • Unlike rate, which depends on statistical covariance, the PCS sensing CRB depends on sample covariance RX, whose complex Wishart distribution makes its nonlinear expectation unlikely to have a closed form.The CRB lower and upper bounds become identical as N →∞.Source: 2) S&C Performance at PCS · p. 7

3) S&C Performance at PSC:

  • At PSC, evaluation is harder because neither the optimal ISAC signal distribution nor the achievable communication rate is explicitly determined.Source: 3) S&C Performance at PSC · p. 7
  • At PSC, Jensen’s inequality characterizes the CRB, and its optimal covariance is attained by deterministic CRB minimization subject to a transmit-power constraint.Source: 3) S&C Performance at PSC · p. 8
  • At PSC, equality holds when RX is deterministic, yielding an ISAC structure whose semi-unitary, data-bearing Q carries the constrained communication degrees of freedom.Q belongs to a Stiefel manifold.Source: 3) S&C Performance at PSC · p. 8
  • At PSC, an explicit communication-rate form is challenging, but gives a high-SNR asymptotic rate achieved by uniformly distributed Q over the Stiefel manifold.The offset c0 is irrelevant to SNR and approaches zero as N →∞.Source: 3) S&C Performance at PSC · p. 8

4) DRT in Vector Gaussian ISAC Channels: … 2) Modulation Basis:

The paper connects the vector-Gaussian deterministic-random tradeoff (DRT) to communication-centric signal processing: random data signals support communication and sensing, but their randomness creates design tradeoffs. It introduces a single-antenna signal model and reviews its constellation and modulation-basis choices.

4) DRT in Vector Gaussian ISAC Channels:

  • Shifting from communication-optimal i.i.d. Gaussian D to sensing-optimal semi-unitary Q reduces signal randomness, while greater randomness can cost communication rate and worsen sensing CRB.At the sensing-optimal point, deterministic sample covariance achieves the minimum CRB; a Gaussian-distributed signal can inflate it by a factor greater than 1. For N → ∞, deterministic RX makes Gaussian signaling optimal for both functions, but this is only an upper bound for finite L.Source: 4) DRT in Vector Gaussian ISAC Channels · p. 8

D. From DRT Theory to Random ISAC Signal Processing

  • Because data-carrying signals are random, their echo fluctuations can impair target detection and estimation, motivating sensing metrics and processing tailored to random ISAC signals.The overview covers modulation, constellation mapping, pulse-shaping filters, and MIMO precoders, while leaving source and channel coding, sampling, and quantization as future directions.Source: D. From DRT Theory to Random ISAC… · p. 8

III. COMMUNICATION-CENTRIC ISAC TRANSMISSION

  • In the single-antenna P2P model, the transmitter sends random data payloads to a communication receiver while a sensing receiver uses their echoes to estimate multiple target delays.The communication receiver does not know the information symbols, whereas the sensing receiver knows them; the two receivers detect symbols amid multipath and extract target ranges, respectively.Source: §III · p. 8, Figure 5 · p. 9

A. Communication-Centric ISAC Signal Model

  • The baseband model forms N discrete-time samples x from N independently drawn constellation symbols s using an N-dimensional unitary modulation basis U.The signal model is presented as a practical realization of the paper’s information-theoretic model.Source: A. Communication-Centric ISAC Signal… · p. 9

1) Constellation:

  • The constellation is assumed rotationally invariant, zero-mean, zero-pseudovariance, and unit-power; common PSK, QAM, and APSK meet these conditions, while BPSK and 8-QAM are exceptions.Probabilistic constellation shaping is allowed, so constellation points need not be transmitted uniformly.Source: 1) Constellation · p. 9

2) Modulation Basis:

  • The unitary modulation basis U can represent SC, OFDM, CDMA, affine-Fourier, or OTFS signaling, with symbols mapped to their respective time, frequency, code, affine-Fourier, or delay-Doppler domains.The examples include Walsh codes for CDMA2000, an IDAFT basis with tunable parameters c1 and c2, and two-dimensional OTFS.Source: 2) Modulation Basis · p. 9
  • A cyclic prefix longer than the maximum target or communication-path delay is assumed to facilitate efficient frequency-domain signal processing.Source: 2) Modulation Basis · p. 9

3) Pulse Shaping Filter: … 2) Signal Processing for Communication:

The section describes Nyquist pulse shaping for limiting bandwidth and avoiding inter-symbol interference, then outlines communication and sensing channel models and their receiver processing. It also identifies channel overlap as a source of a subspace tradeoff.

3) Pulse Shaping Filter:

  • A band-limited Nyquist pulse limits signaling bandwidth while ensuring zero inter-symbol interference, with one-sided bandwidth B and roll-off factor α.Source: 3) Pulse Shaping Filter · p. 9
  • The Nyquist zero-ISI condition has an equivalent folded-spectrum criterion; g(f) is the pulse autocorrelation’s Fourier transform and the pulse’s squared frequency spectrum.Source: 3) Pulse Shaping Filter · p. 10

B. Signal Processing for Communication and Sensing

1) Receive Signal Model:

  • The communication receiver detects information symbols using an estimate of its channel, while the sensing receiver detects targets and extracts their delays using prior knowledge of the transmitted signal.Source: 1) Receive Signal Model · p. 10

2) Signal Processing for Communication:

N Diag (FNhc) FNF H … 1) Discretization of the ACF:

DFT processing turns the communication link into parallel AWGN channels, while sensing uses matched filtering and the statistical behavior of the random signal’s ACF to guide performance analysis. The section also develops a discretized ACF representation that retains pulse-shaping effects.

N Diag (FNhc) FNF H

  • Applying a DFT diagonalizes the circulant channel and removes ISI, yielding N parallel AWGN channels for communication processing.The diagonalization uses the circulant matrix’s DFT property.Source: N Diag (FNhc) FNF H · p. 10
  • OFDM reduces symbol-detection complexity by diagonalizing multipath channels, while SC, CDMA, AFDM, and OTFS can meet requirements such as reliable communication in high-mobility channels.Source: N Diag (FNhc) FNF H · p. 10

3) Signal Processing for Sensing:

  • For sensing, the matched filter uses the transmitted baseband signal rather than the pulse-shaping filter, and its output contains the signal ACF.The section uses basic matched-filter ranging to isolate the impact of random data, leaving advanced algorithms such as compressive sensing for future work.Source: 3) Signal Processing for Sensing · p. 11
  • Targets are detected as peaks in the squared matched-filter output, with thresholding such as CFAR; high peaks at target delays and low sidelobes aid detection and estimation.The passage illustrates three targets at 10 m, 20 m, and 25 m under SNR = 0 dB.Source: 3) Signal Processing for Sensing · p. 11, Figure 6 · p. 11
  • Coherent integration averages the output noise and suppresses sidelobes across independent realizations, making sensing performance depend on the integrated ACF’s geometry.The method transmits M i.i.d. symbol sequences and assumes target parameters remain constant across the M slots.Source: 3) Signal Processing for Sensing · p. 11

C. Characterization of the ISAC ACF

  • Because communication-symbol randomness makes the ACF a random function, the analysis focuses on its expected squared magnitude to characterize sensing performance and inform signal design.The section reviews efforts to derive closed-form expressions for this expectation for generic communication signals.Source: 3) Signal Processing for Sensing · p. 11

1) Discretization of the ACF:

  • The ACF discretization uses a temporal grid with L > 1 to capture pulse-shaping effects; setting L = 1 simplifies the signal to x = Us but neglects pulse-shaping contributions to ACF mainlobes and sidelobes.The passage attributes the discrete signal model’s cyclic convolution to the cyclic prefix.Source: 1) Discretization of the ACF · p. 11
  • The sampled pulse is energy-normalized, and digital upsampling and interpolation form a higher-resolution signal before transmission and ACF computation.The discrete ACF is expressed using periodic time-shift matrices, whose periodicity follows from the cyclic prefix.Source: 1) Discretization of the ACF · p. 12

2) The “Iceberg in the Sea” Structure of the ACF:

The average squared ACF has an “iceberg” component that sets its overall shape and a “sea-level” variance component driven largely by communication-symbol randomness. Modulation basis, constellation, and pulse shaping all influence its shape.

2) The “Iceberg in the Sea” Structure of the ACF:

3) Example: … 2) Ranging-Optimal Modulation for Super-Gaussian Constellations:

For random ISAC signals, waveform design reshapes the average squared ACF to reduce ranging sidelobes, with the optimal modulation basis depending on constellation kurtosis. The section illustrates how coherent integration lowers sidelobes and shows that OFDM is ranging-optimal for sub-Gaussian constellations, whereas SC is optimal for super-Gaussian constellations.

3) Example:

  • Increasing coherent integrations from M = 1 to 100 and 1000 reduces the ACF sidelobe “sea level” by 20 dB and 30 dB, respectively.In the example, the random OFDM signal’s ACF aligns closely with the pulse ACF near the mainlobe, while sidelobes beyond it are dominated by the “sea level” component.Source: 3) Example · pp. 12–13

IV. WAVEFORM DESIGN FOR RANDOM ISAC SIGNALS

  • The design objective is to minimize the average peak-to-sidelobe level ratio of R_k for multi-target range estimation in the matched-filter framework.Doppler and angle estimation with random signals are left for future research.Source: §IV · p. 13
  • For sufficiently large M, constellation kurtosis has negligible effect on the average mainlobe level, so design can focus on minimizing the average sidelobe level.The mainlobe level is determined solely by constellation kurtosis; at large M it approaches the approximately constant value N^2.Source: §IV · p. 13

A. Modulation Basis Design

  • The optimal modulation basis depends on whether the constellation is sub-Gaussian (κ < 2) or super-Gaussian (κ > 2); for standard complex Gaussian symbols (κ = 2), the average sidelobe level is basis-independent.Common QAM and PSK constellations are sub-Gaussian, while examples of super-Gaussian constellations include index modulation and APSK with exponentially growing radii.Source: A. Modulation Basis Design · p. 13

1) Ranging-Optimal Modulation for Sub-Gaussian Constellations:

  • For sub-Gaussian constellations, OFDM, up to subcarrier permutation and phase shifts, achieves the lowest average ranging sidelobe at every lag.The result follows from minimizing squared-spectrum fluctuations; the optimal basis can have unit-modulus entries, and the proof uses Schur-convexity and majorization.Source: 1) Ranging-Optimal Modulation for… · p. 14, Figure 9 · p. 14

2) Ranging-Optimal Modulation for Super-Gaussian Constellations:

  • For super-Gaussian constellations, SC, up to time-symbol permutation and phase shifts, achieves the lowest average ranging sidelobe at every lag.The optimum corresponds to a uniform bi-stochastic matrix.Source: 2) Ranging-Optimal Modulation for… · p. 14

3) Example: … 1) Generic Pulse Shaping Design:

The section explains how modulation, constellation shaping, and pulse design manage ranging sidelobes and communication performance in random ISAC signals. It relates these design choices to frequency-domain kurtosis and illustrates their sensing–communication tradeoffs.

3) Example:

  • With 16-QAM, OFDM yields 5 dB lower average squared ACF sidelobes at every lag than SC and CDMA2000; M=100 integration reduces sea-level sidelobes by 20 dB.The example uses N=128 i.i.d. symbols, L=10 oversampling, and an RRC pulse with α=0.35.Source: 3) Example · p. 14

4) Discussion on Optimality of OFDM/SC:

  • Random payload fluctuations cause frequency-domain squared-spectrum variability and ACF sidelobes; minimizing frequency-domain kurtosis therefore reduces average ranging sidelobes.For sub-Gaussian symbols, OFDM retains their kurtosis and is optimal; for super-Gaussian symbols, SC maximizes the rotation and is optimal.Source: 4) Discussion on Optimality of OFDM/SC · pp. 14–15

B. Constellation Design

  • For a fixed modulation format and pulse filter, PSK minimizes kurtosis and sidelobes but may provide lower rates than same-order QAM; PCS and GCS reshape constellation statistics,.PCS changes symbol probabilities, whereas GCS directly optimizes symbol amplitudes and phases.Source: B. Constellation Design · p. 15

1) Probabilistic Constellation Shaping for ISAC:

  • PCS maximizes communication MI subject to a kurtosis bound; for OFDM with QAM, the resulting convex program is solved by modified Blahut–Arimoto with global convergence.The formulation imposes normalized-power and rotational-symmetry constraints; the kurtosis bound controls average ranging sidelobes.Source: 1) Probabilistic Constellation Shaping… · p. 15

2) Example:

  • Adjusting PCS kurtosis threshold c0 provides a scalable S&C tradeoff and significantly outperforms time-sharing uniform 64-QAM and 64-PSK.The example relates lower sidelobes to improved weak-target detection amid strong clutter, alongside achievable communication rate.Source: 2) Example · p. 16, Figure 10 · p. 16

C. Pulse Shaping Design

  • For a given constellation and modulation basis, average squared ACF sidelobe power is convex in the squared pulse spectrum g, enabling minimization within region KSL.Source: C. Pulse Shaping Design · p. 16

1) Generic Pulse Shaping Design:

  • Generic pulse design enforces Nyquist and monotonic roll-off constraints plus normalized power, forming a linearly constrained convex Pareto problem that preserves communication performance.The Nyquist property eliminates ISI; the roll-off factor α determines which entries of g are fixed at 0 or 1.Source: 1) Generic Pulse Shaping Design · p. 16

2) Iceberg Shaping: … A. Signal Model and Ergodic LMMSE

With coherent integration, iceberg shaping reduces ranging error and helps reveal a weak target by suppressing pulse sidelobes in the region of interest. The discussion then introduces random-signal MIMO precoding and an ergodic LMMSE criterion that accounts for signal randomness.

2) Iceberg Shaping:

  • For sufficiently large coherent integration M, iceberg shaping focuses on minimizing the pulse-shaping filter’s squared ACF sidelobes in the region of interest [58].The objective minimizes either their sum or their maximum, yielding a linearly constrained convex quadratic program solvable with off-the-shelf numerical tools.Source: 2) Iceberg Shaping · p. 16
  • After integrating M = 1000 matched-filter outputs, ranging RMSE falls by more than 78%, and iceberg shaping improves accuracy by an additional 50% over RRC.The comparison uses OFDM with 16-QAM and a two-target scenario; Fig. 11 shows the range-estimation performance and target profiles.Source: Figure 11 · p. 17, 2) Iceberg Shaping · p. 17
  • With M = 1000 coherent integrations, sea-level sidelobes fall by 30 dB, enabling detection of the weak target with the designed pulse, while RRC can mislocate it near 24.5 m.The stronger target is 43–46 dB above the weaker target, and the iceberg-shaped filter minimizes ranging sidelobes within [23.74 m, 31.24 m].Source: 2) Iceberg Shaping · p. 17, Figure 11 · p. 17

V. MIMO PRECODING WITH RANDOM ISAC SIGNALS

  • The paper extends single-antenna analysis to MIMO ISAC with dedicated precoders for random signaling, presenting algorithms for sensing-only and joint sensing-and-communication designs.The signal model and precoding algorithms are organized in Secs. V-A, V-B, and V-C, respectively.Source: §V · p. 17

3) Example:

  • A design example of ISAC is introduced, but the supplied passage gives no further details.Source: 3) Example · p. 17

A. Signal Model and Ergodic LMMSE

  • The MIMO model represents communication and sensing receptions as channel matrices multiplied by the ISAC signal matrix plus additive noise, with the target impulse response modeled as wide-sense stationary.The model treats the sensing channel matrix as the parameter to estimate and aligns with a MIMO-OFDM subcarrier model; sensing estimates are collected across subcarriers for delay and angle processing.Source: A. Signal Model and Ergodic LMMSE · pp. 17–18
  • The ISAC signal matrix is formed from an optimized precoding matrix and a data-payload matrix, and the design optimizes a sensing cost using statistical information about the payload.The LMMSE precoder is used as an example; its estimator and MSE lead to a precoding design subject to a transmit-power budget.Source: A. Signal Model and Ergodic LMMSE · p. 18
  • For random Gaussian ISAC signals, the sensing objective is random, so the ergodic LMMSE averages MSE over the signals, analogously to an ergodic communication rate.This contrasts with deterministic orthogonal radar training, for which the LMMSE design simplifies to a closed-form water-filling solution.Source: A. Signal Model and Ergodic LMMSE · p. 18

B. Sensing-Only Precoding Design · 1) Data-Dependent Precoding:

Sensing-only precoding under random signaling provides a benchmark for later ISAC precoding designs. The section presents data-dependent and data-independent schemes, then derives data-dependent precoding for monostatic sensing.

B. Sensing-Only Precoding Design

W fELMMSE(W )

  • Two schemes are presented for the sensing-only optimization problem: data-dependent precoding (DDP) and data-independent precoding (DIP).Source: W fELMMSE(W ) · p. 18
  • In monostatic mode, both the transmitter and sensing receiver know each Gaussian data realization, allowing the precoding matrix to depend on the realizations.Source: 1) Data-Dependent Precoding · p. 18

1) Data-Dependent Precoding:

2) Data-Independent Precoding: … 1) Data-Dependent Precoding:

The section presents data-independent and data-dependent precoding for random-signal sensing and ISAC, then compares sensing performance against conventional water-filling and describes the ISAC optimization framework.

2) Data-Independent Precoding:

  • DIP finds a realization-independent precoder offline using projected SGD, approximating the unavailable true gradient with mini-batch gradients and projecting updates onto the power-feasible ball.The method is presented as a tradeoff between estimation performance and computational complexity.Source: 2) Data-Independent Precoding · p. 19
  • Larger DIP mini-batches reduce gradient-estimation variance but require more local-gradient computations; infinite batches recover projected GD, while momentum can accelerate convergence.The stepsizes must satisfy convergence conditions,.Source: 2) Data-Independent Precoding · p. 19

3) Example:

  • Water-filling incurs a 3 dB performance loss and severe error floor versus DDP and DIP, while DDP generally achieves the lowest ELMMSE.The comparison averages 1,000 i.i.d. Gaussian signal realizations across two antenna and sample-size settings.Source: Figure 12 · p. 19, 3) Example · p. 19

C. ISAC Precoding Design

  • With the communication channel perfectly known, the ISAC precoding problem minimizes ELMMSE subject to a communication-rate requirement and a power budget.The communication rate is that of the P2P Gaussian channel.Source: C. ISAC Precoding Design · p. 19

W fELMMSE(W )

1) Data-Dependent Precoding:

  • DDP rewrites the rate constraint using an auxiliary variable and applies penalty-based alternating optimization, solving the auxiliary-variable subproblem convexly and the precoder subproblem by projected gradient descent.The precoder is optimized for a given data realization.Source: 1) Data-Dependent Precoding · p. 20

2) Data-Independent Precoding: … VII. CONCLUSIONS

The tutorial reviews communication-centric ISAC with random data payloads, its information-theoretic foundations, signal models, ACF analysis, design methods, and MIMO precoding, then identifies open research directions.

2) Data-Independent Precoding:; 3) Example:

  • For N = 20, DIP improves communication rate by 3bps/Hz over the baseline at the same ELMMSE, while DDP reduces ELMMSE by more than 1.5 dB versus DIP while meeting the required rate.The data-independent precoding method uses an auxiliary variable and penalty for Ω = W W H, solves by AO, and applies projected SGD to the W subproblem.Source: 3) Example · p. 20, 2) Data-Independent Precoding · p. 20

1) 2D Ambiguity Function Characterization:

  • Because the ACF captures only the zero-Doppler slice of the AF, evaluating moving-target sensing calls for 2D AF analysis, whose statistics under arbitrary signaling remain challenging.The 2D AF captures delay and Doppler, unlike the ACF’s static or quasi-static multi-target ranging view.Source: 1) 2D Ambiguity Function… · p. 20

2) Mismatched Filtering and Sparse Recovery under Random ISAC Signaling:

  • Mismatched filtering could suppress payload-induced sidelobes beyond matched filtering, but reciprocal filtering risks SNR loss, and random-signal effects on sparse recovery need investigation.Reciprocal filtering can remove random-data sidelobes but amplifies noise; sparse methods such as matching pursuit may improve resolution by exploiting target sparsity.Source: 2) Mismatched Filtering and Sparse… · pp. 20–21

3) Adaptive Modulation:; 4) Sensing with Channel-Coded Signals:

  • Adaptive modulation and constructive-interference exploitation could recover rate losses from sensing-favorable low-variability signals, while channel coding’s sensing impact remains unexplored across practical code families.Future work includes co-designing adaptive modulation and ISAC-tailored constructive-interference approaches, and assessing and optimizing Turbo, LDPC, and Polar codes for balanced S&C.Source: 3) Adaptive Modulation · p. 21, 4) Sensing with Channel-Coded Signals · p. 21

1) Networked Sensing and ISAC with Communication Signals:

  • Networked ISAC must manage interference among distributed nodes, motivating research on synchronization, clustering and scheduling, collaborative precoding, and network-level resource allocation.Data-dependent and data-independent precoders may be jointly optimized across base stations, with distributed algorithms limiting signaling overhead.Source: 1) Networked Sensing and ISAC with… · p. 21

2) Secure ISAC with Communication Signals:

  • ISAC creates data-eavesdropping and sensing-privacy vulnerabilities, yet sensing privacy lacks an information-theoretic framework; PHY-security co-design remains largely unexplored.Potential directions include adapting constellation, pulse-shaping, and precoding designs and co-designing them with artificial noise, jamming, and cooperative security.Source: 2) Secure ISAC with Communication… · p. 21

3) Sensing and ISAC with Artificial Intelligence (AI):

  • AI research must address processing random-signal echoes and relating recognition metrics to signal design, while model-driven and data-driven methods and end-to-end learning offer opportunities.AI may model nonlinear links between sensing metrics and signal parameters and optimize functional blocks such as constellation input distributions.Source: 3) Sensing and ISAC with Artificial… · pp. 21–22

4) Integrated Sensing, Communication, and Powering (ISCAP) with Communication Signals:

  • ISCAP must jointly balance sensing, communication, and power transfer, since nonlinear energy harvesting favors high-PAPR waveforms; system-level analysis and design remain underdeveloped.Research directions include evaluating practical harvesting across OFDM, CDMA, and OTFS waveforms and extending data-dependent and data-independent precoding.Source: 4) Integrated Sensing, Communication,… · p. 22

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