BEACHES: Beamspace Channel Estimation for Multi-Antenna mmWave Systems and Beyond

Alexandra Gallyas-Sanhueza; Christoph Studer; Ramina Ghods; Seyed Hadi Mirfarshbafan

REVIEW 3 major objections 4 minor 23 references

BEACHES: Beamspace Channel Estimation for Multi-Antenna mmWave Systems and Beyond

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read BEACHES shows that mmWave channel estimation can be reduced to soft-thresholding a DFT beamspace vector, with a SURE-based threshold that is provably MSE-optimal as the antenna count grows.

desk verdict A genuinely useful O(B log B) SURE-tuned beamspace denoiser with a real proof gap: the advertised large-antenna optimality is not established as written. read the letter →

arxiv 1908.02884 v1 pith:P6A4EHQX submitted 2019-08-08 eess.SP cs.ITmath.IT

Ramina Ghods , Alexandra Gallyas-Sanhueza , Seyed Hadi Mirfarshbafan , Christoph Studer This is my paper · ORCID

classification eess.SPcs.ITmath.IT

keywords beamspacechannelestimationmassiveMIMOmmWavecommunicationsterahertzStein'sunbiasedriskestimatorsoft-thresholdingsparselow-complexitysignalprocessing

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 proposes BEACHES, a channel-estimation method for millimeter-wave (mmWave) and terahertz multi-antenna uplinks that treats the problem as denoising in the beamspace domain. Because high-frequency channels are a small superposition of directional paths, their DFT (beamspace) representation is approximately sparse, so a soft-thresholding step can suppress noise. The paper's central move is to set the threshold automatically with Stein's unbiased risk estimate (SURE), and it proves that in the limit of infinitely many antennas the SURE curve coincides with the true mean-square error, so the threshold that minimizes SURE is the MSE-optimal threshold. In simulations for line-of-sight and non-line-of-sight 60 GHz channels with 256 antennas, BEACHES matches the bit-error rate of atomic norm minimization and Newtonized orthogonal matching pursuit while running orders of magnitude faster. The upshot is that the expensive off-grid machinery may be unnecessary for practical mmWave channel denoising.

What carries the argument

The load-bearing object is Stein's unbiased risk estimator for complex soft-thresholding, specialized to the beamspace channel model. For a weakly differentiable estimator $\mu(\hat{\mathbf y})$ of a vector observed in complex Gaussian noise, SURE (5) is an unbiased estimate of MSE; for $\mu=\eta(\cdot,\tau)$ it reduces to expression (6), a piecewise quadratic function of $\tau$ with jumps at the observed magnitudes $|\hat y_b|$. BEACHES sorts the $|\hat y_b|$ so the pieces are intervals between consecutive sorted magnitudes, evaluates the quadratic minimizer in each interval in constant time using running sums, and picks the $\tau$ with smallest SURE. This reduces the parameter-selection problem to an $O(B\log B)$ sweep, consisting of an FFT, a sort, and an inverse FFT, which is what makes the method cheap enough for practical hardware.

What would settle it

Generate beamspace channels from the model with a small number of paths at finite array sizes such as $B=64$ and $B=256$, add noise at SNRs from -10 to 15 dB, and compare the $\tau$ that minimizes SURE (6) with the $\tau$ that minimizes the true MSE; a systematic gap between the two minimizers, or a loss of BER parity with ANM and NOMP when the beamspace entries are strongly correlated, would show that the large-antenna optimality claim does not transfer to finite arrays.

Watch

Extended reading notes

Core claim

BEACHES estimates the uplink channel vector by taking the DFT of the noisy antenna-domain observation, applying the complex soft-thresholding operator $\eta(\hat{\mathbf y},\tau)$ entry by entry, and transforming back. The parameter $\tau$ is chosen by a sweep over the sorted magnitudes of the beamspace vector that minimizes the SURE expression (6), which depends only on the observations, the noise variance $E_0$, and $\tau$. Theorem 2 states that $\lim_{B\to\infty}\mathrm{SURE}_\tau = \mathrm{MSE}$, so in the large-antenna regime minimizing SURE provably minimizes the channel-estimation MSE. The paper's simulations show that this simple procedure delivers uncoded bit-error rates on par with the off-grid methods ANM and NOMP, and 2-3 dB better than maximum-likelihood estimation at a bit-error rate of $10^{-2}$, while the runtime is lower by factors of about 120-1500 versus NOMP and 29,000-58,000 versus ANM.

Load-bearing premise

The proof that SURE converges to the MSE treats the beamspace channel entries as independent and identically distributed draws from a fixed sparse distribution, even though the model represents them as a DFT of a few sinusoidal paths, which makes the entries correlated; the paper does not verify that the convergence theorem's conditions hold for this correlated model.

Editorial extensions

If this is right

If the asymptotic SURE-MSE equivalence holds at operating array sizes, BEACHES removes the need for manual threshold tuning in beamspace denoising, since the data alone determine $\tau$.
Off-the-grid methods such as ANM and NOMP are not needed for competitive bit-error rate in the simulated LoS and non-LoS 60 GHz scenarios, so mmWave channel estimation can be implemented with FFT, sorting, and scalar operations.
The computational savings grow with scenario difficulty: the paper reports speedups up to 1,500x over NOMP and 58,000x over ANM in the non-LoS case.
Because the SURE expression only needs the noise variance $E_0$ and the beamspace observation magnitudes, the method adapts automatically to changing propagation conditions and numbers of paths.
The same SURE-based thresholding logic can apply to any approximately sparse beamspace vector, making the approach a candidate for terahertz and other high-dimensional array systems.

Reading between the lines

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

The same SURE-sweep idea transfers to other element-wise denoisers, such as hard thresholding or nonnegative shrinkage, where closed-form SURE expressions exist; those variants would inherit the same $O(B\log B)$ tuning cost.
One could test BEACHES as a front-end for hybrid or low-resolution-ADC architectures, where the paper's assumption of all-digital antennas and unquantized observations would need modification.
Because the algorithm only uses sorted magnitudes of the beamspace coefficients, it may be robust to phase errors or to channels with many weak paths where sparsity is less pronounced, though the paper does not explore this.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

Here's my take on BEACHES. The real contribution is the simple O(B log B) exact search over soft-threshold parameters: the authors derive a complex-domain SURE for the soft-thresholding operator, then sort the magnitudes of the beamspace observations and evaluate the SURE quadratic on each interval in linear time. That is a new, clean, and practical result. For a mmWave channel estimator, it gives a parameter-free denoiser that seems to match ANM and NOMP in the simulations at orders-of-magnitude lower complexity. That is worth something.

The theory is where I part ways. Theorem 1 (unbiased SURE in the complex domain) is a standard integration-by-parts argument and appears correct. Theorem 2, which claims SURE converges to MSE as B approaches infinity, is not proven as written. The proof invokes [20, Thm. III.15-16], a CAMP state-evolution result for sequences with i.i.d. entries, and applies it to the beamspace entries of a superposition of L sinusoids. Those entries are not i.i.d. (their magnitudes range from O(sqrt(B)) down to O(1/sqrt(B))), and no limiting distribution H is defined or verified. The derivative term in SURE is also discontinuous at |y_b| = tau, so it is not pseudo-Lipschitz; the paper says it is bounded, which is true away from the threshold but not in a neighborhood of it. Even if pointwise convergence were repaired, that alone would not justify the argmin claim: the algorithm selects tau by minimizing SURE, and the paper does not prove uniform convergence or argmin consistency. So the headline claim that BEACHES 'provably minimizes MSE in the large-antenna limit' is not established.

The saving grace is that the algorithm itself does not depend on the theorem. The efficient threshold search is an exact minimization of the SURE expression, and Theorem 1 already gives that SURE is unbiased for any fixed B. The practical value stands on those two legs plus the simulations. The simulations look plausible, though they lack error bars and code/data; that is a minor issue for a methods paper, not a fatal one. The boundary handling in Algorithm 1 is also under-specified (the footnote acknowledges the issue but the pseudocode does not implement the epsilon perturbation). Citations to the SURE and CAMP literature are appropriate.

Who should read this? Anyone building a low-complexity mmWave channel estimator or looking for a baseline to compare against. It deserves a serious referee, but I would ask the authors to fix or soften the asymptotic claim, either by adding a proper state-evolution argument for the beamspace model or by stating SURE minimization as a design heuristic. This is not a takedown; it is a useful algorithm with an overreaching proof.

Referee Report

3 major / 4 minor

Summary. The paper proposes BEACHES, a beamspace channel estimation method for massive MIMO mmWave/THz uplink systems. The channel vector is modeled as a superposition of L complex sinusoids in the antenna domain; after taking a DFT, the paper denoises the beamspace vector by complex soft-thresholding with threshold τ. To avoid manual tuning, BEACHES computes Stein's unbiased risk estimate (SURE) for the soft-thresholding estimator and selects τ by minimizing the SURE expression over intervals defined by the sorted magnitudes of the noisy beamspace observations. Theorem 1 proves the standard SURE identity in the complex domain, and Theorem 2 claims that SURE converges to MSE as B→∞, so the chosen threshold minimizes MSE in the large-antenna limit. Simulations with a QuaDRiGa 60 GHz model for LoS and non-LoS channels show BER comparable to ANM and NOMP at orders-of-magnitude lower runtime.

Significance. If Theorem 2 were rigorously established, the paper would provide a practical, low-complexity denoiser with automatic parameter selection for a relevant wireless setting; the runtime comparison in Table I and the BER results in Fig. 2 are concrete and favorable. The derivation of Theorem 1 in Appendix A is a correct application of Stein's identity, and the algorithmic idea of minimizing SURE over sorted intervals is clean and computationally attractive. The weakness is that the central asymptotic optimality claim rests on an unproved application of a CAMP state-evolution theorem to correlated beamspace entries, so the paper's headline theoretical guarantee is not currently supported as written.

major comments (3)

[Appendix B, Eq. (14)] The proof of Theorem 2 applies [20, Thm. III.15 and III.16], a state-evolution result for complex approximate message passing, to the beamspace entries ```\hat h_b```. Those theorems require the entries of the observed vector to be independent (or to satisfy a specific exchangeability/state-evolution condition) and the empirical distribution of the true entries to converge to a fixed random variable H. Under the channel model (1), ```\hat h = F h``` is the DFT of a superposition of L complex sinusoids: the entries are correlated, and their magnitudes range from O(√B) down to O(1/√B) depending on whether a path is on the DFT grid. No limiting distribution H is defined for this model and none of the theorem's conditions are verified. Therefore Eq. (14) is not justified, and the convergence claim (7) is not established by the manuscript's argument.
[Appendix B, Eq. (16)] The transition to Eq. (16) treats the sum of the derivative terms ```\partial[\eta_R]_b/\partial[\hat y_R]_b + \partial[\eta_I]_b/\partial[\hat y_I]_b``` as a pseudo-Lipschitz function and applies (14). These derivative terms are not pseudo-Lipschitz: they are discontinuous at |```\hat y_b| = \tau```, and SURE is undefined at those points, as the paper itself states after Eq. (6). The proof neither checks the pseudo-Lipschitz condition nor explains how the measure-zero discontinuity is handled in the limit interchange. This is a second unverified condition in the proof of Theorem 2.
[Theorem 2 and Section III-C] Even if the pointwise limit ```\lim_{B→∞} SURE_\tau = MSE``` held for each fixed ```\tau```, the paper's advertised conclusion that BEACHES 'provably minimizes the MSE in the large-antenna limit' would not follow. The algorithm selects ```\tau^*``` by minimizing the empirical SURE function over the intervals defined by the sorted magnitudes ```|\hat y_b|``` (Section III-C and Algorithm 1). The paper does not prove uniform convergence of ```SURE_\tau``` to MSE or an argmin-consistency result, so convergence of the selected threshold to the MSE-minimizing threshold is not established. The central theoretical claim therefore needs an additional, nontrivial argument or a revised, weaker statement.

minor comments (4)

[Algorithm 1, line 4] The update ```V = \sum_{k=1}^{B}(|\hat y^s_k|)^{-1}``` is undefined if any sorted magnitude is zero. For Gaussian noise this has probability zero, but the pseudocode should state the convention (e.g., omit zero entries or replace them by a small positive value).
[Algorithm 1, lines 5–7 and footnote 2] The pseudocode evaluates SURE_```\tau``` at the interval boundaries ```\hat y^s_{k-1}``` and ```\hat y^s_k```, where the SURE expression is undefined, while the text says the values should be computed arbitrarily close to these boundaries. This inconsistency should be resolved either by defining the one-sided limits in Eq. (8) or by rewriting the loop to evaluate the limits explicitly.
[Appendix B, Eq. (15)] The expression ```E_{\hat y}[ B^{-1}\|\eta(\hat y,\tau)-\hat y\|^2 ]``` uses the symbol ```\hat y``` for both the random vector and the fixed vector inside the norm; this is confusing and should be rewritten with a generic random vector such as ```\tilde y```.
[Appendix B, after Eq. (14)] The phrase 'H is a random variable with the sparse distribution of the channel vector in the beamspace domain' is not a definition. The distribution of ```\hat h_b``` depends on B through the DFT of L sinusoids; without an explicit asymptotic model for L and the angles ```\Omega_\ell```, the statement is not precise.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: BEACHES' SURE-based threshold selection is self-contained; the technical gap in Theorem 2 is a correctness concern, not a circular one.

full rationale

The derivation chain is not circular. The threshold τ is selected by minimizing the SURE expression (6), which is computed from the noisy beamspace observation ŷ and the known noise variance E0, not from the true channel vector h or from the MSE metric being reported. Theorem 1 establishes E[SURE] = MSE via a standard integration-by-parts argument (Appendix A), and Theorem 2 is an asymptotic claim about SURE converging to MSE for the soft-thresholding estimator. Even if the proof of Theorem 2 relies on CAMP convergence results [20, Thm. III.15 & III.16] whose i.i.d. and pseudo-Lipschitz conditions may not hold for correlated DFT beamspace entries, this is a mathematical validity issue, not circularity: the cited results are external, parameter-free statements and are not assumed to contain the paper's conclusion. The self-citations in the paper ([6], [9]) are contextual references to prior work on low-resolution ADCs and ANM-based mmWave channel estimation and are not load-bearing for the SURE derivation. No fitted input is renamed as a prediction, no uniqueness theorem is imported from the authors' own prior work, and no ansatz is smuggled in via self-citation. The paper's central algorithmic contribution—adaptive soft-thresholding with SURE-based parameter selection—is a self-contained application of standard SURE theory, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

BEACHES introduces no tuned constants; E0 and the DFT are standard system inputs. The main auxiliary assumption is the applicability of an i.i.d. convergence theorem to a correlated sparse channel model, which is not verified.

assumptions (3)

domain assumption The mmWave channel is a superposition of L complex sinusoids as in Eq. (1), giving sparse beamspace structure.
This is the standard directional channel model (cited [17]); BEACHES's denoising performance and the convergence argument both depend on this sparsity.
domain assumption The channel estimation error e is complex Gaussian with known variance E0.
Algorithm 1 takes E0 as an input and the SURE formula (6) requires it; if E0 is unknown or misspecified, the threshold choice is no longer MSE-optimal.
ad hoc to paper The pseudo-Lipschitz convergence theorem [20, Thm. III.15 and III.16] applies to the beamspace entries h_hat_b under model (1).
The theorem is stated for i.i.d. sequences, but h_hat = Fh for a superposition of L sinusoids gives correlated entries; the paper does not verify the condition.

how reviews work

0 comments

Cite this review

Pith. "Pith review of BEACHES: Beamspace Channel Estimation for Multi-Antenna mmWave Systems and Beyond." pith.science (2026). https://pith.science/paper/P6A4EHQX

@misc{pith2026190802884,
  author       = {Pith},
  title        = {Pith review of: BEACHES: Beamspace Channel Estimation for Multi-Antenna mmWave Systems and Beyond},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P6A4EHQX}},
  note         = {Machine review of arXiv:1908.02884}
}

read the original abstract

Massive multi-antenna millimeter wave (mmWave) and terahertz wireless systems promise high-bandwidth communication to multiple user equipments in the same time-frequency resource. The high path loss of wave propagation at such frequencies and the fine-grained nature of beamforming with massive antenna arrays necessitates accurate channel estimation to fully exploit the advantages of such systems. In this paper, we propose BEAmspace CHannel EStimation (BEACHES), a low-complexity channel estimation algorithm for multi-antenna mmWave systems and beyond. BEACHES leverages the fact that wave propagation at high frequencies is directional, which enables us to denoise the (approximately) sparse channel state information in the beamspace domain. To avoid tedious parameter selection, BEACHES includes a computationally-efficient tuning stage that provably minimizes the mean-square error of the channel estimate in the large-antenna limit. To demonstrate the efficacy of BEACHES, we provide simulation results for line-of-sight (LoS) and non-LoS mmWave channel models.

Figures

Figures reproduced from arXiv: 1908.02884 by the authors.

**Figure 1.** Massive MU-MIMO mmWave uplink system: U UEs transmit pilots over a mmWave/THz wireless channel, which are used to estimate the channel vectors associated to each UE at the B-antenna basestation. avoid this basis mismatch problem. These methods, however, exhibit excessively high complexity, which renders the design of corresponding hardware designs challenging. A. Contributions We propose a new channel estimation alg… view at source ↗

**Figure 2.** Uncoded bit error-rate (BER) of various channel denoising methods [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

Massive MIMO for next generation wireless systems,

E. G. Larsson, O. Edfors, F. Tufvesson, and T. L. Marzetta, “Massive MIMO for next generation wireless systems,” IEEE Communications Magazine, vol. 52, no. 2, pp. 186–195, Feb. 2014

work page 2014
[2]

Millimeter wave mobile communications for 5G cellular: It will work!

T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y . Azar, K. Wang, G. N. Wong, J. K. Schulz, M. Samimi, and F. Gutierrez, “Millimeter wave mobile communications for 5G cellular: It will work!” IEEE Access , vol. 1, pp. 335–349, May 2013

work page 2013
[3]

Rappaport, R

T. Rappaport, R. Heath, R. Daniels, and J. Murdock, Millimeter Wave Wireless Communications. Prentice Hall, 2015

work page 2015
[4]

Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design,

T. S. Rappaport, G. R. MacCartney, M. K. Samimi, and S. Sun, “Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design,” IEEE Transactions on Communications , vol. 63, no. 9, pp. 3029–3056, Sep. 2015

work page 2015
[5]

Channel estimation for millimeter- wave massive MIMO with hybrid precoding over frequency-selective fading channels,

Z. Gao, C. Hu, L. Dai, and Z. Wang, “Channel estimation for millimeter- wave massive MIMO with hybrid precoding over frequency-selective fading channels,” IEEE Communications Letters , vol. 20, no. 6, pp. 1259–1262, Jun. 2016

work page 2016
[6]

Throughput analysis of massive MIMO uplink with low-resolution ADCs,

S. Jacobsson, G. Durisi, M. Coldrey, U. Gustavsson, and C. Studer, “Throughput analysis of massive MIMO uplink with low-resolution ADCs,” IEEE Transactions on Wireless Communications , vol. 16, no. 6, pp. 4038–4051, Jun. 2017

work page 2017
[7]

Channel estimation and hybrid precoding for millimeter wave cellular systems,

A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE Journal of Selected Topics in Signal Processing , vol. 8, no. 5, pp. 831–846, Oct. 2014

work page 2014
[8]

Channel estimation and precoder design for millimeter-wave communications: The sparse way,

P. Schniter and A. Sayeed, “Channel estimation and precoder design for millimeter-wave communications: The sparse way,” in Proceedings of the 48th Asilomar Conference on Signals, Systems and Computers , Nov. 2014, pp. 273–277

work page 2014

Show all 23 references

[9]

mmWave channel estimation via atomic norm minimization for multi-user hybrid precoding,

J. Deng, O. Tirkkonen, and C. Studer, “mmWave channel estimation via atomic norm minimization for multi-user hybrid precoding,” in Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), Apr. 2018, pp. 1–6

2018
[10]

Limited feedback hybrid precoding for multi-user millimeter wave systems,

A. Alkhateeb, G. Leus, and R. W. Heath, “Limited feedback hybrid precoding for multi-user millimeter wave systems,” IEEE Transactions on Wireless Communications , vol. 14, no. 11, pp. 6481–6494, Nov. 2015

2015
[11]

Channel estimation via orthogonal matching pursuit for hybrid MIMO systems in millimeter wave communications,

J. Lee, G. Gil, and Y . H. Lee, “Channel estimation via orthogonal matching pursuit for hybrid MIMO systems in millimeter wave communications,” IEEE Transactions on Communications , vol. 64, no. 6, pp. 2370–2386, Jun. 2016

2016
[12]

Beamspace MIMO for millimeter-wave communications: System architecture, modeling, analy- sis, and measurements,

J. Brady, N. Behdad, and A. M. Sayeed, “Beamspace MIMO for millimeter-wave communications: System architecture, modeling, analy- sis, and measurements,” IEEE Transactions on Antennas and Propaga- tion, vol. 61, no. 7, pp. 3814–3827, Jul. 2013

2013
[13]

Compressed sensing off the grid,

G. Tang, B. N. Bhaskar, P. Shah, and B. Recht, “Compressed sensing off the grid,” IEEE Transactions on Information Theory , vol. 59, no. 11, pp. 7465–7490, Nov. 2013

2013
[14]

Atomic norm denoising with applications to line spectral estimation,

B. N. Bhaskar, G. Tang, and B. Recht, “Atomic norm denoising with applications to line spectral estimation,” IEEE Transactions on Signal Processing, vol. 61, no. 23, pp. 5987–5999, Dec. 2013

2013
[15]

Newtonized orthog- onal matching pursuit: Frequency estimation over the continuum,

B. Mamandipoor, D. Ramasamy, and U. Madhow, “Newtonized orthog- onal matching pursuit: Frequency estimation over the continuum,” IEEE Transactions on Signal Processing , vol. 64, no. 19, pp. 5066–5081, Oct. 2016

2016
[16]

Millimeter wave channel modeling and cellular capacity evaluation,

M. R. Akdeniz, Y . Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter wave channel modeling and cellular capacity evaluation,” IEEE Journal on Selected Areas in Communications, vol. 32, no. 6, pp. 1164–1179, Jun. 2014

2014
[17]

Tse and P

D. Tse and P. Viswanath, Fundamentals of Wireless Communication . New York, NY , USA: Cambridge University Press, 2005

2005
[18]

Adapting to unknown smoothness via wavelet shrinkage,

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” Journal of the American Statistical Association , vol. 90, no. 432, pp. 1200–1224, Dec. 1995

1995
[19]

Regression shrinkage and selection via the LASSO,

R. Tibshirani, “Regression shrinkage and selection via the LASSO,” Journal of the Royal Statistical Society. Series B (Methodological) , vol. 58, no. 1, pp. 267–288, 1996

1996
[20]

Asymptotic analysis of complex LASSO via complex approximate message passing (CAMP),

A. Maleki, L. Anitori, Z. Yang, and R. G. Baraniuk, “Asymptotic analysis of complex LASSO via complex approximate message passing (CAMP),” IEEE Transactions on Information Theory , vol. 59, no. 7, pp. 4290–4308, Jul. 2013

2013
[21]

Parameterless optimal approximate message passing,

A. Mousavi, A. Maleki, and R. G. Baraniuk, “Parameterless optimal approximate message passing,” Oct. 2013. [Online]. Available: http://arxiv.org/abs/1311.0035

2013 arXiv
[22]

QuaDRiGa - Quasi Deterministic Radio Channel Generator User Manual and Documentation,

S. Jaeckel, L. Raschkowski, K. Börner, L. Thiele, F. Burkhardt, and E. Eberlein, “QuaDRiGa - Quasi Deterministic Radio Channel Generator User Manual and Documentation,” Fraunhofer Heinrich Hertz Institute, Tech. Rep. v2.0.0, 2017

2017
[23]

Consistent parameter estimation for LASSO and approximate message passing,

A. Mousavi, A. Maleki, and R. G. Baraniuk, “Consistent parameter estimation for LASSO and approximate message passing,”arXiv preprint: 1511.01017 [math.ST] , Nov. 2015

2015 arXiv

Pith tools

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

[1] [1]

Massive MIMO for next generation wireless systems,

E. G. Larsson, O. Edfors, F. Tufvesson, and T. L. Marzetta, “Massive MIMO for next generation wireless systems,” IEEE Communications Magazine, vol. 52, no. 2, pp. 186–195, Feb. 2014

work page 2014

[2] [2]

Millimeter wave mobile communications for 5G cellular: It will work!

T. S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y . Azar, K. Wang, G. N. Wong, J. K. Schulz, M. Samimi, and F. Gutierrez, “Millimeter wave mobile communications for 5G cellular: It will work!” IEEE Access , vol. 1, pp. 335–349, May 2013

work page 2013

[3] [3]

Rappaport, R

T. Rappaport, R. Heath, R. Daniels, and J. Murdock, Millimeter Wave Wireless Communications. Prentice Hall, 2015

work page 2015

[4] [4]

Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design,

T. S. Rappaport, G. R. MacCartney, M. K. Samimi, and S. Sun, “Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design,” IEEE Transactions on Communications , vol. 63, no. 9, pp. 3029–3056, Sep. 2015

work page 2015

[5] [5]

Channel estimation for millimeter- wave massive MIMO with hybrid precoding over frequency-selective fading channels,

Z. Gao, C. Hu, L. Dai, and Z. Wang, “Channel estimation for millimeter- wave massive MIMO with hybrid precoding over frequency-selective fading channels,” IEEE Communications Letters , vol. 20, no. 6, pp. 1259–1262, Jun. 2016

work page 2016

[6] [6]

Throughput analysis of massive MIMO uplink with low-resolution ADCs,

S. Jacobsson, G. Durisi, M. Coldrey, U. Gustavsson, and C. Studer, “Throughput analysis of massive MIMO uplink with low-resolution ADCs,” IEEE Transactions on Wireless Communications , vol. 16, no. 6, pp. 4038–4051, Jun. 2017

work page 2017

[7] [7]

Channel estimation and hybrid precoding for millimeter wave cellular systems,

A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE Journal of Selected Topics in Signal Processing , vol. 8, no. 5, pp. 831–846, Oct. 2014

work page 2014

[8] [8]

Channel estimation and precoder design for millimeter-wave communications: The sparse way,

P. Schniter and A. Sayeed, “Channel estimation and precoder design for millimeter-wave communications: The sparse way,” in Proceedings of the 48th Asilomar Conference on Signals, Systems and Computers , Nov. 2014, pp. 273–277

work page 2014