On Range Sidelobe Reduction for Dual-functional Radar-Communication Waveforms

Athina Petropulu; Christos Masouros; Fan Liu; Tharmalingam Ratnarajah

REVIEW 3 major objections 5 minor 10 references

On Range Sidelobe Reduction for Dual-functional Radar-Communication Waveforms

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A MIMO DFRC waveform can be jointly optimized for radar and communication, cutting range sidelobes by up to 17 dB while improving achievable sum-rate.

desk verdict A useful sidelobe-control extension of the authors' prior DFRC design, but the printed equations do not actually implement the stated objective and need correction before the results can be trusted. read the letter →

arxiv 1908.04650 v1 pith:2RXNPEU4 submitted 2019-08-13 eess.SP

Fan Liu , Christos Masouros , Tharmalingam Ratnarajah , Athina Petropulu This is my paper · ORCID

classification eess.SP

keywords dual-functionradar-communicationwaveformdesignrangesidelobereductionintegratedlevelmanifoldoptimizationobliquemulti-userinterferenceMIMOradar

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 is trying to establish that a MIMO dual-function radar-communication (DFRC) waveform can control its range sidelobes, the time-domain clutter that appears in nearby range bins, without giving up much communication performance. The authors add the integrated sidelobe level (ISL) to a weighted objective that penalizes multi-user interference and deviation from a reference radar waveform, and they solve the resulting nonconvex problem with a first-order Riemannian conjugate gradient method on the complex oblique manifold of matrices satisfying per-antenna power constraints. With the weights $\rho_1=\rho_3=0.15$ and $\rho_2=0.7$, the reported simulations show a 12 dB sidelobe reduction for an omni-directional design and a 17 dB reduction for a directional design, together with an improved achievable sum-rate over the closed-form baseline that only matches the radar beampattern.

What carries the argument

The carrying object is the complex oblique manifold $\mathcal{M}=\{X\in\mathbb{C}^{N\times L}:\operatorname{diag}(XX^H)=\frac{LP_T}{N}\mathbf{1}_N\}$, the set of waveforms that respect the per-antenna power budget. On this manifold the paper runs a Riemannian conjugate gradient (RCG) algorithm: the Euclidean gradient is projected onto the tangent space, combined with the previous descent direction using a Polak-Ribiere coefficient, and brought back to the manifold by the retraction $R_X(Z)=\beta\,\operatorname{ddiag}((X+Z)(X+Z)^H)^{-1/2}(X+Z)$ with $\beta=\sqrt{LP_T/N}$. This machinery keeps every iterate feasible while descending, and the per-iteration complexity is dominated by the gradient computation, stated as $O(N^2PL-N^2P^2/2)$.

What would settle it

Re-run the algorithm from many random initializations under the paper's settings ($N=16$, $K=4$, $L=100$, $P=8$, $\rho_1=\rho_3=0.15$, $\rho_2=0.7$) and record the converged objective and range-sidelobe level; if the outcomes spread widely or the gradient norm does not fall below $10^{-6}$ within the reported tens of iterations, the claimed 12/17 dB reductions are initialization-dependent rather than a stable property of the design. A second check is to vary the weights and channel realizations and see whether convergence and the sidelobe gain survive.

Watch

Extended reading notes

Core claim

The central claim is that range-sidelobe suppression can be folded directly into the DFRC waveform optimization without requiring the waveform covariance to equal a fixed radar covariance. The paper minimizes $F(X)=\rho_1\|HX-S\|_F^2+\rho_2\sum_{p=-P,p\neq 0}^{P}\|XJ_pX^H\|_F^2+\rho_3\|X-X_0\|_F^2$ subject to $\operatorname{diag}(XX^H)=\frac{LP_T}{N}\mathbf{1}_N$, where the first term is multi-user interference, the second is the integrated sidelobe level, and the third keeps the waveform close to a radar-friendly reference. Because the feasible set is a complex oblique manifold, the algorithm projects the Euclidean gradient onto the tangent space, forms a conjugate descent direction via the Polak-Ribiere coefficient, and retracts back to the manifold. The reported result is that this relaxed, weighted design beats the closed-form beampattern-constrained design in both communication sum-rate and range sidelobe level, at the cost of a small mismatch in the spatial beampattern.

Load-bearing premise

Everything rests on the iterative algorithm actually finding a low-enough local minimum of the nonconvex objective in tens of iterations; the paper states that strict convergence analysis remains open, so a stall in a poor local valley would undo the claimed sidelobe and rate gains.

Editorial extensions

If this is right

Should the claim hold, DFRC base stations can produce a single waveform that serves downlink users and suppresses range sidelobes at the same time, with the reported 12 dB omni-directional and 17 dB directional sidelobe reductions.
The weighted objective relaxes the rigid covariance equality of the closed-form design, so the radar beampattern is only approximately matched; the authors argue this mismatch is acceptable given the improved sum-rate.
The per-antenna power constraint is maintained exactly at every iteration, so the resulting waveform is directly transmittable with the intended power distribution.
Because the per-iteration cost is a matrix gradient computation, the design is computationally light enough to permit re-optimization as the communication channel changes, assuming the observed convergence behavior persists.

Reading between the lines

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

Beyond the paper, the same manifold formulation is a natural template for adding other radar constraints, such as Doppler sidelobe levels or peak-to-average-power ratio, by changing the objective or the retraction while keeping the per-antenna power constraint built in.
Beyond the paper, initializing at the closed-form solution (10) instead of a random point may improve convergence stability and give a more direct comparison, since that solution is the reference the relaxation is built around.
Beyond the paper, the reported 12/17 dB gains are tied to one weight setting and simulation choice; a deployment-oriented test would vary antenna counts, user numbers, block lengths, and weights to see whether the sidelobe reductions persist and whether a principled weight-selection rule emerges.

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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

Colleague—

The paper proposes adding range-sidelobe energy to the authors' earlier closed-form DFRC design and solving the new nonconvex problem with a Riemannian conjugate gradient method on the complex oblique manifold. That is a sensible and relevant extension: sidelobe control is a real missing piece in DFRC waveform design, and the manifold geometry is the right tool for the per-antenna power constraint. The numerical section shows big sidelobe reductions and sum-rate gains over the closed-form baseline.

The trouble is that the printed math does not support the algorithm as stated. Equation (13) claims ρ1PMUI + ρ2PISL = ‖AX−B‖²_F with A and B as in (14). Direct expansion gives ρ1‖HX−S‖²_F + ρ2‖X−X0‖²_F, i.e. ρ1PMUI + ρ2PSIM, not ρ2PISL. So problem (15), which is derived from (13), is not a recast of (12): the ISL weight in (12) is ρ2, while in (15) the ISL term carries ρ3, and the similarity weight is swapped. Section V then says ρ1=ρ3=0.15 and ρ2=0.7, so the reported 12–17 dB sidelobe reductions are not tied to one well-defined objective. Add to this that the gradient printed in (17) omits the ρ3 prefactor on the quartic ISL term. If Algorithm 1 literally uses (17), the descent direction does not reflect the sidelobe weight, and the numerical sidelobe suppression has no explanation in the printed algorithm. The authors also acknowledge that strict convergence for RCG remains open, so the near-optimality claim rests only on empirical behavior.

Let me be careful: these look like fixable typos, not a fundamentally wrong approach. The intended objective—weighted MUI plus ISL plus similarity—is coherent, and the manifold machinery is standard. But as printed, a reader cannot reproduce the results. The comparison baseline is the authors' own earlier design, which is acceptable for a follow-up but means the gains are not independently benchmarked.

Who is this for? Researchers working on dual-functional radar-communication waveform design. The idea is worth engaging with, but only after the authors correct the equations and, ideally, release code and data. I'd send it to peer review: a serious referee can verify the corrections and the numerics. Desk rejection would throw out a useful contribution to a busy subfield on the basis of repairable errors.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a waveform design for MIMO dual-functional radar-communication (DFRC) systems that jointly minimizes multiuser interference (MUI), integrated sidelobe level (ISL), and a similarity penalty with respect to a reference waveform, subject to a per-antenna power constraint. The optimization problem is non-convex, and the authors develop a Riemannian conjugate gradient (RCG) method on the complex oblique manifold. Numerical simulations for N=16, K=4, L=100 report 12 dB and 17 dB range-sidelobe reductions in omni-directional and directional designs, respectively, together with improved sum-rate over the closed-form baseline of [4]. The core idea is plausible and relevant, but the printed formulation contains algebraic inconsistencies that affect the exact algorithm as described.

Significance. If the formulation and algorithm were corrected, the contribution would be significant for DFRC waveform design: it is one of the first attempts to control range sidelobes explicitly in a joint radar-communication waveform, and the manifold-based approach offers a computationally efficient first-order descent method with per-antenna power control. The numerical study is reasonably comprehensive for the system size considered. However, the load-bearing derivations in Section IV are not correct as printed, so the reported gains cannot be attributed to Algorithm 1 as written. The strengths are the clear system model, the explicit integrated-sidelobe metric, and the use of the oblique manifold to handle the per-antenna constraint; the weakness is the inconsistency among equations (12), (13), (15), and (17).

major comments (3)

[Section IV, Eq. (13)] The identity ρ1PMUI + ρ2PISL = ‖AX−B‖_F^2 with A=[√ρ1 H; √ρ2 I_N] and B=[√ρ1 S; √ρ2 X0] is false; direct expansion gives ρ1‖HX−S‖_F^2 + ρ2‖X−X0‖_F^2 = ρ1PMUI + ρ2PSIM. Consequently, problem (15), which is derived from this identity, is not a recasting of (12): the weights of the ISL and similarity terms are swapped between the two formulations. Since Section V sets ρ1=ρ3=0.15 and ρ2=0.7, the reported 12–17 dB sidelobe reductions are not tied to a single well-defined objective; the paper must be corrected so that (12), (13), and (15) refer to the same weighted problem.
[Section IV, Eq. (17)] The Euclidean gradient printed for the objective in (15) omits the factor ρ3 multiplying the quartic ISL term. The correct gradient is 2 A^H(AX−B) + 2ρ3 Σ_{p≠0}(XJp X^H X Jp^H + X Jp^H X^H X Jp). As printed, the gradient has no dependence on the ISL weight, so Algorithm 1, if implemented literally with (17), would not account for the sidelobe term; the documented sidelobe suppression therefore has no explanation in the printed algorithm. The authors should either state that the numerical results were obtained with a corrected gradient (and provide it) or revise the algorithm description.
[Algorithm 1 and Remark, Section IV] The algorithm input specifies ρ_i for all i, but the construction of A and B in (14) uses only ρ1 and ρ2, and the gradient (17) does not use ρ3 at all; the role of ρ3 in the iteration is therefore undefined. The Remark's admission that strict convergence analysis remains open is a useful limitation, but it does not resolve the inconsistency between the stated problem (12) and the problem actually implemented by the algorithm.

minor comments (5)

[Section IV, Eq. (20)] The term PXk(F(Xk−1)) is not well-defined because F(Xk−1) is a scalar; the standard Polak-Ribière formula on a manifold involves the projected previous gradient (or descent direction), for instance PXk(grad F(Xk−1)) or PXk(Πk−1), depending on convention.
[Section V] The sentence 'by solving (12) under only a small weighting factor ρ3 = 0.15' appears to treat ρ3 as the ISL weight, whereas in (12) ρ3 multiplies the similarity term PSIM; this sentence should be reworded after the weight notation is fixed.
[Algorithm 1 input] The list of inputs should be aligned with the corrected notation, making explicit which weights enter the quadratic part and which enter the quartic part of the objective.
[Section V, numerical results] The number of Monte-Carlo trials used for the sum-rate curves is not reported, and no error bars are shown; adding this information would improve reproducibility.
[Throughout] Minor typographical issues: 'interets' in the Introduction should be 'interests', and the phrase 'remains open problem' in the Remark should be 'remains an open problem'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the derivation is self-contained, with algebraic inconsistencies in Eqs. (13)/(17) that are correctness issues rather than circularity.

full rationale

The paper's central chain—defining the radar and communication metrics in Eqs. (3), (7), and (11), forming the weighted objective (12), and then applying an oblique-manifold RCG algorithm to the feasible set—is self-contained. The reference waveform X0 and the benchmark (9) are taken from the authors' prior work [4], but that is a published closed-form solution with an independent derivation, not a privately asserted premise that guarantees the conclusion. The proposed objective and its numerical evaluation do not define the reported sidelobe reduction in terms of the input waveform or the benchmark; the sidelobe reduction is an optimized quantity measured by an independent figure of merit. The Remark after Algorithm 1 explicitly states that strict convergence analysis of RCG remains an open problem, which is a stated limitation about iteration guarantees, not a circular reliance on the target result. Separately, Eqs. (13) and (17) contain algebraic inconsistencies: Eq. (13) equates a ρ2-weighted integrated-sidelobe term with a ρ2-weighted similarity term ||X−X0||^2_F, and Eq. (17) omits the ρ3 prefactor on the quartic ISL gradient. These are correctness concerns about whether Algorithm 1 as printed minimizes the claimed objective (12), but they do not make any predicted quantity equivalent to an input by construction, and therefore they do not amount to circularity under the rubric used here.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central result rests on the hand-chosen weighting factors, the accepted radar and communication models, the prior closed-form design from the authors' own work, and the unproven convergence of the RCG algorithm. No new physical entities are introduced.

free parameters (1)

Weighting factors ρ1, ρ2, ρ3 = ρ1 = 0.15, ρ2 = 0.7, ρ3 = 0.15 (simulation settings; notation inconsistent between (12) and (15))
The balance among MUI, range-sidelobe, and similarity is chosen by hand in Section V; the reported gains depend on this choice.

assumptions (4)

domain assumption The radar model (4)-(7) with point scatterers and the integrated sidelobe power PISL as defined is an adequate measure of radar range-sidelobe performance.
The objective and the simulation validation both rely on this metric; the paper does not justify it against other radar performance measures.
domain assumption The communication channel H is perfectly known at the BS, and minimizing the MUI energy PMUI in (3) is a valid surrogate for maximizing achievable sum-rate.
Used in equations (1)-(3) and later in the objective; channel estimation error is not considered.
standard math The closed-form solution (10) to problem (9) from [4] is correct and produces a valid reference waveform X0.
The similarity term PSIM and the baseline both depend on this cited result, which the paper adopts without proof.
ad hoc to paper The Riemannian Conjugate Gradient algorithm on the complex oblique manifold converges to a useful near-optimal stationary point within tens of iterations.
The paper states strict convergence analysis remains open; the numerical claims assume the algorithm works as intended.

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Cite this review

Pith. "Pith review of On Range Sidelobe Reduction for Dual-functional Radar-Communication Waveforms." pith.science (2026). https://pith.science/paper/2RXNPEU4

@misc{pith2026190804650,
  author       = {Pith},
  title        = {Pith review of: On Range Sidelobe Reduction for Dual-functional Radar-Communication Waveforms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2RXNPEU4}},
  note         = {Machine review of arXiv:1908.04650}
}

read the original abstract

In this paper, we propose a novel waveform design for multi-input multi-output (MIMO) dual-functional radar-communication systems by taking the range sidelobe control into consideration. In particular, we focus on optimizing the weighted summation of communication and radar metrics under per-antenna power budget. While the formulated optimization problem is non-convex, we develop a first-order descent algorithm by exploiting the manifold structure of its feasible region, which finds a near-optimal solution within a low computational overhead. Numerical results show that the proposed waveform design outperforms the conventional techniques by improving the communication rate while reducing the range sidelobe level.

Figures

Figures reproduced from arXiv: 1908.04650 by the authors.

**Figure 2.** Numerical results. (a) Average achievable sum-rate [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[4]

F. Liu , C. Masouros , A. Li , H. Sun , and L. Hanzo , `` MU-MIMO communications with MIMO radar: F rom co-existence to joint transmission,'' IEEE Trans. Wireless Commun., vol. 17, no. 4, pp. 2755--2770, Apr 2018

work page 2018
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A. Hassanien , M. G. Amin , Y. D. Zhang , and F. Ahmad , ``Dual-function radar-communications: Information embedding using sidelobe control and waveform diversity,'' IEEE Trans. Signal Process., vol. 64, no. 8, pp. 2168--2181, Apr 2016

work page 2016
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F. Liu , L. Zhou , C. Masouros , A. Li , W. Luo , and A. Petropulu , ``Toward dual-functional radar-communication systems: O ptimal waveform design,'' IEEE Trans. Signal Process., vol. 66, no. 16, pp. 4264--4279, Aug 2018

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G. Hua and S. S. Abeysekera , ``Receiver design for range and doppler sidelobe suppression using MIMO and phased-array radar,'' IEEE Trans. Signal Process., vol. 61, no. 6, pp. 1315--1326, Mar 2013

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [4]

F. Liu , C. Masouros , A. Li , H. Sun , and L. Hanzo , `` MU-MIMO communications with MIMO radar: F rom co-existence to joint transmission,'' IEEE Trans. Wireless Commun., vol. 17, no. 4, pp. 2755--2770, Apr 2018

work page 2018

[2] [1]

11em plus .33em minus .07em 4000 4000 100 4000 4000 500 `\.=1000 = #1 \@IEEEnotcompsoconly \@IEEEcompsoconly #1 * [1] 0pt [0pt][0pt] #1 * [1] 0pt [0pt][0pt] #1 * \| ** #1 \@IEEEauthorblockNstyle \@IEEEcompsocnotconfonly \@IEEEauthorblockAstyle \@IEEEcompsocnotconfonly \@IEEEcompsocconfonly \@IEEEauthordefaulttextstyle \@IEEEcompsocnotconfonly \@IEEEauthor...

work page

[3] [2]

Paul , A

B. Paul , A. R. Chiriyath , and D. W. Bliss , ``Survey of RF communications and sensing convergence research,'' IEEE Access, vol. 5, pp. 252--270, Dec 2017

work page 2017

[4] [3]

Hassanien , M

A. Hassanien , M. G. Amin , Y. D. Zhang , and F. Ahmad , ``Dual-function radar-communications: Information embedding using sidelobe control and waveform diversity,'' IEEE Trans. Signal Process., vol. 64, no. 8, pp. 2168--2181, Apr 2016

work page 2016

[5] [5]

F. Liu , L. Zhou , C. Masouros , A. Li , W. Luo , and A. Petropulu , ``Toward dual-functional radar-communication systems: O ptimal waveform design,'' IEEE Trans. Signal Process., vol. 66, no. 16, pp. 4264--4279, Aug 2018

work page 2018

[6] [6]

Li and P

J. Li and P. Stoica, MIMO radar signal processing . 1em plus 0.5em minus 0.4em Wiley Press, 2008

work page 2008

[7] [7]

S. K. Mohammed and E. G. Larsson , ``Per-antenna constant envelope precoding for large multi-user MIMO systems,'' IEEE Trans. Commun., vol. 61, no. 3, pp. 1059--1071, Mar 2013

work page 2013

[8] [8]

Hua and S

G. Hua and S. S. Abeysekera , ``Receiver design for range and doppler sidelobe suppression using MIMO and phased-array radar,'' IEEE Trans. Signal Process., vol. 61, no. 6, pp. 1315--1326, Mar 2013

work page 2013