Sparse Array Sensor Selection in ISAC with Identifiability Guarantees

Piya Pal; Robin Rajam\"aki

REVIEW 1 major objections 5 minor 25 references

Sparse Array Sensor Selection in ISAC with Identifiability Guarantees

T0 review · 1 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A uniform linear transmit array can support a sensor-selection ISAC codebook whose size matches the unconstrained binomial count, while a nonredundant array supports exactly one codeword, so redundancy is necessary for index-modulation…

desk verdict The counting results are correct, but the ULA codebook claim in the abstract and conclusions overreaches: the Nt≤Nr+1 condition is essential and omitting it gives wrong codebook sizes. read the letter →

arxiv 2412.21002 v1 pith:6PWPYZAA submitted 2024-12-30 eess.SP

Robin Rajamäki , Piya Pal This is my paper · ORCID

classification eess.SP

keywords integratedsensingandcommunicationssensorselectionindexmodulationsparsearrayssumco-arrayidentifiabilityuniformlineararraycodebookdesign

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how many different subsets of transmit sensors can double as information-bearing codewords in an integrated sensing and communications (ISAC) system without sacrificing the radar's ability to identify the maximum number of targets its array geometry allows. The answer is fully characterized at two geometric extremes. For a uniform linear array (ULA) whose receive array is large enough relative to the transmit array, every codeword that contains the two end sensors preserves the contiguous sum co-array, so the optimal codebook has exactly $\binom{N_t-2}{Q-2}$ entries, comparable to the unconstrained sensor-selection codebook $\binom{N_t}{Q}$. For a nonredundant array, which has the largest sum co-array and therefore the best identifiability, the only admissible codeword is the full transmit array, so no communication is possible through sensor selection alone. The paper concludes that array redundancy is necessary for this form of index-modulation communication, and it provides general upper and lower bounds on the codebook size for intermediate geometries.

What carries the argument

The load-bearing object is the sum co-array condition $S+D_r=D_t+D_r=U_{N_\Sigma}$ from Eq. (5): a rank-$|S|$ sensor-selection waveform achieves maximal identifiability of $N_\Sigma/2$ targets exactly when the selected subarray's sum set with the fixed receive array is contiguous and equals the full sum co-array, a fact the paper takes from a cited companion result. The counting proof then pivots on Lemma 1, which shows the two outermost transmit sensors must belong to every admissible subarray, giving the upper bound $\binom{N_t-2}{Q-2}$. For the ULA, including both end sensors is also sufficient under $N_t\le N_r+1$, so the upper bound is tight; for a nonredundant array, strict size counting forces $Q=N_t$ and leaves a single codeword. A constructive lower bound is obtained by embedding a dilated ULA of $L=N_\Sigma/N_r$ sensors in every codeword, yielding $\binom{N_t-L}{Q-L}$ guaranteed codewords.

What would settle it

Brute-force enumeration settles the counting claim: for a ULA with small $N_t$ and $N_r$, list every $Q$-sensor subarray, compute $S+D_r$, and count how many equal $U_{N_t+N_r-1}$; Proposition 1 predicts exactly $\binom{N_t-2}{Q-2}$ such subarrays whenever $N_t\le N_r+1$, and any mismatch would disprove it. For the nonredundant case, the same enumeration should show that no proper subset of the transmit array satisfies $S+D_r=D_t+D_r$, leaving only the full array.

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Extended reading notes

Core claim

The central claim is Proposition 1: when the sum co-array has the ULA size $N_\Sigma=N_t+N_r-1$ and $N_t\le N_r+1$, any $Q$-sensor transmit subarray that includes the two extreme sensors has the same contiguous sum set as the full transmit-receive pair, and the identifiability-maximizing codebook therefore has exactly $\binom{N_t-2}{Q-2}$ codewords. At the opposite extreme, a nonredundant array with $N_\Sigma=N_tN_r$ forces $Q=N_t$, and exactly one codeword (all transmit sensors active) is admissible. These two results bracket the trade-off: redundancy in the array geometry buys sensor-selection communication capability, while a large sum co-array buys target identifiability but consumes the degrees of freedom needed to encode information.

Load-bearing premise

The identifiability guarantee rests on the cited theorem from [20] that a rank-$|S|$ sensor-selection waveform achieves maximal identifiability if and only if its sum set with the receive array equals the full contiguous sum co-array; if that equivalence requires conditions beyond contiguity and full column rank, then the label 'identifiability-maximizing' attached to the counted codebooks would need qualification.

Editorial extensions

If this is right

Uniform linear arrays become the natural geometry for sensor-selection ISAC: they attain the upper bound $\binom{N_t-2}{Q-2}$, matching the unconstrained codebook size up to the two fixed edge sensors, while still guaranteeing identifiability of $N_\Sigma/2$ targets.
Nonredundant arrays, despite their superior identifiability, cannot support spatial-modulation communication: with exactly one admissible codeword, no bits are carried by sensor selection alone.
The upper bound applies to every admissible geometry, so at least two transmit sensors (the extremes) are always dedicated to the sensing constraint and are not free to carry communication information.
The constructive lower bound shows that for integer $L=N_\Sigma/N_r$, a codebook of size at least $\binom{N_t-L}{Q-L}$ is always achievable, so the guaranteed codebook shrinks as the desired number of identifiable targets grows.
For a ULA the codebook size is maximized by choosing $Q\approx N_t/2$, so the number of bits per symbol grows linearly with the number of transmit antennas, as in unconstrained spatial modulation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the Eq. (5) equivalence holds for all contiguous sum co-arrays, the edge-sensor upper bound implies that no array geometry can exceed $\binom{N_t-2}{Q-2}$ identifiability-maximizing codewords, making array redundancy a quantitative communications resource rather than only a sensing design choice.
The exact optimal codebook size for intermediate redundancy, $N_t+N_r-1<N_\Sigma<N_tN_r$, remains open; a natural conjecture consistent with the bounds is that $|C^\star|$ interpolates between $\binom{N_t-2}{Q-2}$ and 1 as the optimal geometry shifts from ULA-like to nested configurations.
Requiring every codeword individually to achieve maximal identifiability is a strong constraint; permitting a small identifiability loss for some codewords, or combining several subarrays over successive symbols for sensing, could plausibly support much larger constellations.
A small MIMO testbed comparing bit-error rate and target localization for a ULA versus a nonredundant array at equal RF-chain count would provide a direct empirical check of the predicted large difference in achievable constellation size.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Rajamäki and Pal give the first exact codebook-size formulas for sensor-selection ISAC under an identifiability constraint: for ULA with Nt≤Nr+1, |C*| = C(Nt-2, Q-2), and for nonredundant arrays, |C*|=1. The optimization problem is new, and the proofs are clean. Lemma 1 is a neat necessity argument (edge sensors must be included), and Proposition 1's ULA sufficiency is exactly explained by the overlap condition. Proposition 2's nested construction is a good lower-bound trick. I checked the counting; it holds.

The soft spot is the abstract and conclusions, not the formal statements. Proposition 1 is conditional on Nt≤Nr+1, and that condition is doing real work. The abstract says a ULA 'only requires including two specific sensors' and achieves a codebook 'comparable to the unconstrained case' with no qualification. That's false when the Tx array is longer than the Rx array. Example: Dt=U5, Dr=U2, Q=3. The two edge sensors are 0 and 4. Among the three subsets containing both, only {0,2,4} gives S+Dr=U6; {0,1,4} gives {0,1,2,4,5} and {0,3,4} gives {0,1,3,4,5}. So |C*|=1, not C(3,1)=3. The paper's own Proposition 1 technically avoids this, but a reader using the abstract on Nt>Nr+1 configurations will get non-guaranteed codewords. This must be fixed before publication, either by adding the condition to the headline claims or by repositioning the ULA result as 'when the Tx array is no longer than the Rx array.'

Other weaknesses are minor. The paper is narrow—noiseless identifiability, 1D collinear arrays, equal-sized subarrays, no rate analysis—but it is upfront about that. The dependency on the cited equivalence from [20] is external but reasonable; it's consistent with the contiguous-sum-set literature. The concavity remark in Section 4.4 is loose but not load-bearing.

Who is this for? People working on sparse-array ISAC and index modulation will find the characterization useful, even if the regime is restrictive. The formal results deserve a serious referee. I would accept for review and ask for the condition fix; I'd also ask the authors to state explicitly that [20]'s theorem is assumed, or to sketch its proof.

Referee Report

1 major / 5 minor

Summary. The paper studies transmit sensor selection for integrated sensing and communications (ISAC) in a monostatic MIMO system. Each codeword corresponds to a Q-element subset S of the transmit array D_t, and the authors require that each S achieves the maximum number of identifiable targets, which they translate (via a cited equivalence) into the sum-set condition S + D_r = D_t + D_r = U_{N_Σ}. The central contribution is a set of bounds on the number of such subsets. Lemma 1 gives an upper bound of C(N_t-2, Q-2) by showing that the two extreme transmit sensors must be included. Proposition 1 gives exact values for two canonical geometries: for a ULA (with the additional condition N_t ≤ N_r + 1) the bound is tight, yielding a codebook of size C(N_t-2, Q-2); for a nonredundant array the only admissible codeword is the full transmit array. Proposition 2 provides a constructive lower bound of C(N_t-L, Q-L) when L = N_Σ/N_r is an integer. The authors conclude that redundancy is necessary for sensor-selection communication and that the ULA supports a large codebook.

Significance. If the results hold, this is a useful first analytical step toward understanding the trade-off between sensing identifiability and communication codebook size in ISAC. The problem formulation is novel, and the counting arguments in Lemma 1 and Propositions 1 and 2 are clean and, within their stated hypotheses, correct. The explicit characterization for the ULA and nonredundant arrays is a concrete contribution that can guide array geometry selection in practice. The paper also honestly identifies its scope: the bounds leave an 'uncertainty region' for intermediate values of N_Σ, and the tightness of the ULA result is conditional on N_t ≤ N_r + 1.

major comments (1)

[2.2] The paper's central identifiability guarantee — that a sensor-selection waveform achieves maximal identifiability if and only if S + D_r = D_t + D_r = U_{N_Σ} — is imported from an unpublished arXiv preprint [20]. Since the title and the entire problem formulation rest on this equivalence, the authors should either provide a proof (or at least a precise statement of the theorem with all necessary conditions on U, D_t, D_r) or clearly present it as an assumption. As written, a reader cannot verify the sensing interpretation that motivates the codebook definition, especially because the equivalence is 'if and only if' and the paper's counting results alone do not establish any sensing property.

minor comments (5)

[Section 4.3 (Proof of Proposition 2)] There are a few typos in the proof: 'the sum set is S + D_t = U_{N_Σ}' should be 'S + D_r = U_{N_Σ}', and the chain 'U_L = D_t + D_r ⊇ S + D_r ⊇ D_1 + D_r = U_L' should use U_{N_Σ} (or U_{N_r L}) on both ends, since D_1 + D_r = U_{N_r L} = U_{N_Σ}.
[Figure 2 caption and surrounding text] The caption of Fig. 2 says the examples illustrate 'Proposition 2,' but the text in Section 4.2 refers to 'this fact, revealed by the proof of Proposition 1, is illustrated in Fig. 2a.' Please align the citation so the reader knows which proposition each subfigure is demonstrating.
[Section 4 (admissibility discussion)] The sentence 'Any positive tuple (Q, N_t, N_r, N_Σ) is admissible ... if (6) and (8) are satisfied' is stated without proof. For non-integer N_Σ/N_r the paper does not provide a construction, and the claim that such tuples are always realizable by some (D_t, D_r) is not obvious. Please add a reference or a brief construction for general N_Σ.
[Section 4.4] The maximizer of C(N_t-2, Q-2) is written as Q = ⌊N_t/2 − 1⌉ + 2, but this notation is ambiguous; the standard statement is that the maximum is attained at Q = floor((N_t-2)/2) + 2 or Q = ceil((N_t-2)/2) + 2. Please state it clearly.
[Section 2.2 and Eq. (6)] In the sentence following Eq. (6), 'Tx subarray S ⊆ D_r' should be 'S ⊆ D_t', since S is a subset of the transmit array. Also, in the introduction, 'identiﬁablity' is misspelled.

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: the ULA and nonredundant-array codebook counts follow from the definitions and elementary counting; the only self-citation dependency is the cited identifiability equivalence from [20], which is not used to prove itself.

full rationale

The central counting results are self-contained. Proposition 1 is derived directly from the definition Cc(Q,Dt,Dr) = {S subset of Dt : |S| = Q, S + Dr = Dt + Dr} and elementary set-sum arithmetic: for Dt = UNt and Dr = UNr with Nt <= Nr + 1, any S containing the two edge sensors {0, Nt - 1} satisfies S + Dr = U_{Nt+Nr-1}, while Lemma 1 shows both edge sensors are necessary. This yields |C*| = C(Nt-2, Q-2) by construction, not by importing a conclusion. The nonredundant-array result is equally direct: NΣ = NtNr forces Q = Nt from the bound Q >= NΣ/Nr, leaving only S = Dt. The lower bound in Proposition 2 is also constructive and proved by explicit set inclusion, so no fitted parameter is later renamed as a prediction. The only external ingredient is the identifiability-to-contiguity equivalence in Eq. (5), cited to the authors' prior work [20]; the codebook-size theorems do not depend on the proof of that equivalence, so this is a normal citation rather than a circular reduction. A separate, non-circular concern is that the abstract and conclusions state the ULA codebook result without the Nt <= Nr + 1 condition from Proposition 1, which overstates the range of validity for transmit arrays longer than the receive array; this is a qualification issue, not circularity. Overall, no significant circularity is present, and the minor self-citation dependency warrants a low score of 2.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted to data; all quantities (Q, Nt, Nr, NΣ, L) are problem parameters or derived from them. The paper imports domain assumptions from array processing and from the authors' prior identifiability work, and introduces no new physical entities.

assumptions (4)

domain assumption Up to K ≤ |Dt+Dr|/2 targets can be uniquely identified from the noiseless measurement model with a contiguous sum co-array and a full-column-rank waveform.
Invoked in Section 2.2 to justify using NΣ/2 as the identifiability KPI; cited to [18, Ch.1] as prior art.
domain assumption For a contiguous sum co-array, a sensor-selection waveform of rank |S| achieves maximal identifiability if and only if S+Dr = Dt+Dr = U_NΣ.
This is the bridge between the codebook definition (Eq. 5) and the sensing guarantee; cited to [20] and not re-derived in this paper.
domain assumption The waveform matrix U is fixed, full column rank, and known to the user equipment.
Stated in Section 2.1; needed for rank(S)=|S| and for the [20] equivalence to apply.
domain assumption Sensor positions are one-dimensional, collinear, and normalized to an integer half-wavelength grid.
Standard array-processing model used throughout; enables the contiguous U_NΣ notation and the extreme-sum arguments in Lemma 1.

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Cite this review

Pith. "Pith review of Sparse Array Sensor Selection in ISAC with Identifiability Guarantees." pith.science (2026). https://pith.science/paper/6PWPYZAA

@misc{pith2026241221002,
  author       = {Pith},
  title        = {Pith review of: Sparse Array Sensor Selection in ISAC with Identifiability Guarantees},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6PWPYZAA}},
  note         = {Machine review of arXiv:2412.21002}
}

read the original abstract

This paper investigates array geometry and waveform design for integrated sensing and communications (ISAC) employing sensor selection. We consider ISAC via index modulation, where various subsets of transmit (Tx) sensors are used for both communications and monostatic active sensing. The set of Tx subarrays make up a codebook, whose cardinality we maximize (for communications) subject to guaranteeing a desired target identifiability (for sensing). To characterize the size of this novel optimal codebook, we derive first upper and lower bounds, which are tight in case of the canonical uniform linear array (ULA) and any nonredundant array. We show that the ULA achieves a large codebook - comparable to the size of the conventional unconstrained case - as satisfying the identifiability constraint only requires including two specific sensors in each Tx subarray (codeword). In contrast, nonredundant arrays, which have the largest identifiability for a given number of physical sensors, only have a single admissible codeword, rendering them ineffectual for communications via sensor selection alone. The results serve as a step towards an analytical understanding of the limits of sensor selection in ISAC and the fundamental trade-offs therein.

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Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

[20]

Spatial modulation for generalized MIMO: Challenges, opportunities, and implementation,

M. Di Renzo, H. Haas, A. Ghrayeb, S. Sugiura, and L. Hanzo, “Spatial modulation for generalized MIMO: Challenges, opportunities, and implementation,” Pro- ceedings of the IEEE , vol. 102, no. 1, pp. 56–103, 2014

work page 2014
[1]

INTRODUCTION ISAC is envisioned to be a core technology of 6G and be- yond wireless systems [1]. In multiple-input multiple out- put (MIMO) ISAC, two key resources shared by the sensing and communications functionalities are the transmit wave- form and sensor array geometry, which impact, e.g., link re- liability, throughput, and spatial resolution. Joint...

work page
[2]

codebook

SIGNAL MODEL AND BACKGROUND Consider a narrowband MIMO ISAC system, where a base station (BS) with collocated Tx and Rx arrays simultaneousl y senses the environment and communicates with a single M - antenna user equipment (UE). Crucially, the BS uses the same Tx array geometry Dt and spatio-temporal waveform matrix S ∈ CT ×Nt for both (active) sensing a...

work page
[3]

First, we deﬁne the set of Q-sensor Tx subarrays whose sum sets equal that of a given physical Tx-Rx array pair (Dt,Dr): Cc(Q,Dt,Dr) ≜ {S ⊆ Dt : |S| = Q, S + Dr = Dt + Dr}

IDENTIFIABILITY -MAXIMIZING CODEBOOK: OPTIMAL TX SENSOR SELECTION FOR ISAC We propose constraining the sum set of all codewords in the ISAC codebook to guarantee maximum identiﬁability. First, we deﬁne the set of Q-sensor Tx subarrays whose sum sets equal that of a given physical Tx-Rx array pair (Dt,Dr): Cc(Q,Dt,Dr) ≜ {S ⊆ Dt : |S| = Q, S + Dr = Dt + Dr}...

work page
[4]

Note that the range of values that such Q and NΣ can take depends on (free) parameters Nt, Nr ∈ N+

BOUNDS ON SIZE OF OPTIMAL CODEBOOK: PRELIMINARY INSIGHTS INTO ISAC TRADE-OFF We start by specifying for which tuples (Q, Nt, Nr, NΣ ) set C⋆ is nonempty. Note that the range of values that such Q and NΣ can take depends on (free) parameters Nt, Nr ∈ N+. Firstly, the number of sum co-array elements can be shown to satisfy NΣ ∈ [Nt + Nr − 1, NtNr], where th...

work page
[5]

Such waveforms ﬁnd applications in resource-efﬁcien t MIMO ISAC systems, where, for instance, the transmitter has a limited number of RF chains due to power or cost constraints

CONCLUSIONS This paper presented ﬁrst results on transmit-sensor-sele ction- based ISAC waveform design with identiﬁability guaran- tees. Such waveforms ﬁnd applications in resource-efﬁcien t MIMO ISAC systems, where, for instance, the transmitter has a limited number of RF chains due to power or cost constraints. We formulated a novel codebook optimizati...

work page
[6]

F. Liu, C. Masouros, and Y . C. Eldar, Integrated Sensing and Communications. Springer Singapore, 2023

work page 2023
[7]

Joint radar-communication strategies for autonomous vehicles: Combining two key automotive technologies,

D. Ma, N. Shlezinger, T. Huang, Y . Liu, and Y . C. Eldar, “Joint radar-communication strategies for autonomous vehicles: Combining two key automotive technologies,” IEEE Signal Processing Magazine , vol. 37, no. 4, pp. 85–97, 2020

work page 2020

Show all 25 references

[8]

Cognitive antenn a selection for automotive radar using Bobrovsky-Zakai bound,

J. Tabrikian, O. Isaacs, and I. Bilik, “Cognitive antenn a selection for automotive radar using Bobrovsky-Zakai bound,” IEEE Journal of Selected T opics in Signal Pro- cessing, vol. 15, no. 4, pp. 892–903, 2021

2021
[9]

Hybrid MIMO ar- chitectures for millimeter wave communications: Phase shifters or switches?

R. M´ endez-Rial, C. Rusu, N. Gonz´ alez-Prelcic, A. Alkhateeb, and R. W . Heath, “Hybrid MIMO ar- chitectures for millimeter wave communications: Phase shifters or switches?” IEEE Access, vol. 4, pp. 247–267, 2016

2016
[10]

Antenna se- lection strategy for transmit beamforming-based joint radar-communication system,

A. Ahmed, S. Zhang, and Y . D. Zhang, “Antenna se- lection strategy for transmit beamforming-based joint radar-communication system,” Digital Signal Process- ing, vol. 105, p. 102768, 2020

2020
[11]

Joint antenna selection and transmit beamforming for dual-function radar-communication systems,

F. Wang, A. L. Swindlehurst, and H. Li, “Joint antenna selection and transmit beamforming for dual-function radar-communication systems,” in IEEE Radar Confer- ence (RadarConf), 2023, pp. 1–6

2023
[12]

A bandwidth efﬁcient dual- function radar communication system based on a MIMO radar using OFDM waveforms,

Z. Xu and A. Petropulu, “A bandwidth efﬁcient dual- function radar communication system based on a MIMO radar using OFDM waveforms,” IEEE Transactions on Signal Processing, vol. 71, pp. 401–416, 2023

2023
[13]

Sparse array and pre- coding design for integrated sensing and communication systems,

R. P . Sankar and S. P . Chepuri, “Sparse array and pre- coding design for integrated sensing and communication systems,” in IEEE 13rd Sensor Array and Multichannel Signal Processing W orkshop (SAM), 2024, pp. 1–5

2024
[14]

Receiver antenna allocation for joint sensing and communica- tions,

I. V an Der Werf, G. Leus, and S. P . Chepuri, “Receiver antenna allocation for joint sensing and communica- tions,” in IEEE 13th Sensor Array and Multichannel Sig- nal Processing W orkshop (SAM), 2024, pp. 1–5

2024
[15]

Signaling strategies for dual-function radar communi- cations: an overview,

A. Hassanien, M. G. Amin, Y . D. Zhang, and F. Ahmad, “Signaling strategies for dual-function radar communi- cations: an overview,” IEEE Aerospace and Electronic Systems Magazine, vol. 31, no. 10, pp. 36–45, 2016

2016
[16]

Dual- function MIMO radar communications system design via sparse array optimization,

X. Wang, A. Hassanien, and M. G. Amin, “Dual- function MIMO radar communications system design via sparse array optimization,” IEEE Transactions on Aerospace and Electronic Systems , vol. 55, no. 3, pp. 1213–1226, 2019

2019
[17]

Spatial modulation for joint radar-communications systems: Design, analysis, and hardware prototype,

D. Ma, N. Shlezinger, T. Huang, Y . Shavit, M. Namer, Y . Liu, and Y . C. Eldar, “Spatial modulation for joint radar-communications systems: Design, analysis, and hardware prototype,” IEEE Transactions on V ehicular T echnology, vol. 70, no. 3, pp. 2283–2298, 2021

2021
[18]

Hybrid index modulation for dual-functional radar communica- tions systems,

J. Xu, X. Wang, E. Aboutanios, and G. Cui, “Hybrid index modulation for dual-functional radar communica- tions systems,” IEEE Transactions on V ehicular T ech- nology, vol. 72, no. 3, pp. 3186–3200, 2023

2023
[19]

Index modulation for integrated sensing and communi- cations: A signal processing perspective,

A. M. Elbir, A. Celik, A. M. Eltawil, and M. G. Amin, “Index modulation for integrated sensing and communi- cations: A signal processing perspective,” IEEE Signal Processing Magazine, vol. 41, no. 5, pp. 44–55, 2024

2024
[21]

Super-resolution with sparse arrays: A non-asymptotic analysis of spatio-temporal trade-offs,

P . Sarangi, M. C. H¨ uc¨ umeno˘ glu, R. Rajam¨ aki, and P . Pal, “Super-resolution with sparse arrays: A non-asymptotic analysis of spatio-temporal trade-offs,” IEEE Transactions on Signal Proc., pp. 1–14, 2023

2023
[22]

M. G. Amin, Ed., Sparse Arrays for Radar , Sonar , and Communications. Wiley-IEEE, 2024

2024
[23]

Li and P

J. Li and P . Stoica, MIMO radar signal processing . John Wiley & Sons, 2009

2009
[24]

Importance of array redun- dancy pattern in active sensing,

R. Rajam¨ aki and P . Pal, “Importance of array redun- dancy pattern in active sensing,” in IEEE 9th Interna- tional W orkshop on Computational Advances in Multi- Sensor Adaptive Proc. (CAMSAP) , 2023, pp. 156–160

2023
[25]

Array-informed waveform design for ac- tive sensing: Diversity, redundancy, and iden- tiﬁability,

——, “Array-informed waveform design for ac- tive sensing: Diversity, redundancy, and iden- tiﬁability,” arXiv, 2023. [Online]. Available: https://arxiv.org/abs/2305.06478v1

2023 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [20]

Spatial modulation for generalized MIMO: Challenges, opportunities, and implementation,

M. Di Renzo, H. Haas, A. Ghrayeb, S. Sugiura, and L. Hanzo, “Spatial modulation for generalized MIMO: Challenges, opportunities, and implementation,” Pro- ceedings of the IEEE , vol. 102, no. 1, pp. 56–103, 2014

work page 2014

[2] [1]

INTRODUCTION ISAC is envisioned to be a core technology of 6G and be- yond wireless systems [1]. In multiple-input multiple out- put (MIMO) ISAC, two key resources shared by the sensing and communications functionalities are the transmit wave- form and sensor array geometry, which impact, e.g., link re- liability, throughput, and spatial resolution. Joint...

work page

[3] [2]

codebook

SIGNAL MODEL AND BACKGROUND Consider a narrowband MIMO ISAC system, where a base station (BS) with collocated Tx and Rx arrays simultaneousl y senses the environment and communicates with a single M - antenna user equipment (UE). Crucially, the BS uses the same Tx array geometry Dt and spatio-temporal waveform matrix S ∈ CT ×Nt for both (active) sensing a...

work page

[4] [3]

First, we deﬁne the set of Q-sensor Tx subarrays whose sum sets equal that of a given physical Tx-Rx array pair (Dt,Dr): Cc(Q,Dt,Dr) ≜ {S ⊆ Dt : |S| = Q, S + Dr = Dt + Dr}

IDENTIFIABILITY -MAXIMIZING CODEBOOK: OPTIMAL TX SENSOR SELECTION FOR ISAC We propose constraining the sum set of all codewords in the ISAC codebook to guarantee maximum identiﬁability. First, we deﬁne the set of Q-sensor Tx subarrays whose sum sets equal that of a given physical Tx-Rx array pair (Dt,Dr): Cc(Q,Dt,Dr) ≜ {S ⊆ Dt : |S| = Q, S + Dr = Dt + Dr}...

work page

[5] [4]

Note that the range of values that such Q and NΣ can take depends on (free) parameters Nt, Nr ∈ N+

BOUNDS ON SIZE OF OPTIMAL CODEBOOK: PRELIMINARY INSIGHTS INTO ISAC TRADE-OFF We start by specifying for which tuples (Q, Nt, Nr, NΣ ) set C⋆ is nonempty. Note that the range of values that such Q and NΣ can take depends on (free) parameters Nt, Nr ∈ N+. Firstly, the number of sum co-array elements can be shown to satisfy NΣ ∈ [Nt + Nr − 1, NtNr], where th...

work page

[6] [5]

Such waveforms ﬁnd applications in resource-efﬁcien t MIMO ISAC systems, where, for instance, the transmitter has a limited number of RF chains due to power or cost constraints

CONCLUSIONS This paper presented ﬁrst results on transmit-sensor-sele ction- based ISAC waveform design with identiﬁability guaran- tees. Such waveforms ﬁnd applications in resource-efﬁcien t MIMO ISAC systems, where, for instance, the transmitter has a limited number of RF chains due to power or cost constraints. We formulated a novel codebook optimizati...

work page

[7] [6]

F. Liu, C. Masouros, and Y . C. Eldar, Integrated Sensing and Communications. Springer Singapore, 2023

work page 2023

[8] [7]

Joint radar-communication strategies for autonomous vehicles: Combining two key automotive technologies,

D. Ma, N. Shlezinger, T. Huang, Y . Liu, and Y . C. Eldar, “Joint radar-communication strategies for autonomous vehicles: Combining two key automotive technologies,” IEEE Signal Processing Magazine , vol. 37, no. 4, pp. 85–97, 2020

work page 2020