Text from the interactive explanation

Sparse Array Design for Near-Field MU-MIMO: Reconfigurable Array Thinning Approach

Hussain, Ahmed, Abdallah, Asmaa, Celik, Abdulkadir, Björnson, Emil, Eltawil, Ahmed M.

Near-field MU-MIMO · arXiv 2026

Future wireless networks may deploy arrays with thousands of antennas and operate in the , where a can separate users by distance as well as by direction. But every active antenna needs its own , and thousands of them are costly. Hussain and colleagues keep the full array fixed and switch on only a subset, re-chosen electronically as people move. In their simulations this reaches about 75% of the full array's with 10% of the antennas active.

Thinned and adapting: the swarm keeps re-choosing which 10 antennas are on as the phones move.

If only a few antennas can have radios, where should they go?

1 Five ways to build a sparse array

A conventional array places an antenna every half wavelength and gives each one its own radio chain. To make a beam narrow enough to focus at a distance you need a long array — and with half-wavelength spacing that means thousands of antennas and thousands of radios. Sparse arrays use far fewer antennas spread over the same length. Wider gaps also make the channels of different users less alike, which helps the base station keep their signals apart. The paper compares several ways to build one. Watch them serve the same small crowd; every few seconds the people move.

The design gallery

Full array (FULA). All 100 on. The best beams, but 100 radio chains. In the paper this is the upper bound.

Evenly spaced sparse (SULA). 10 antennas with equal, wide gaps. Cheap and long — but evenly spaced gaps create ghost beams.

Fixed irregular, pre-optimized. 10 antennas in an uneven pattern chosen in advance (coprime arrays and the paper's pre-optimized PTA and GTA designs are of this kind). No ghosts, tuned for typical conditions, but it never adapts.

Movable antennas (MA). 10 antennas on a rail, moved to the best positions for the current users. Adapts, but physical repositioning "introduces latency overheads and system-level complexity". The motor speed here is illustrative.

Reconfigurable thinning (this paper). 100 antennas fixed in place, 10 switched on; the set is re-chosen electronically when people move. Adapts, and nothing moves.

What “reconfigurable array thinning” means

Thinning starts from a full, dense array and switches most of it off. The full array stays physically fixed; only a subset of NT out of N antennas is active, a thinning ratio NT/N. In the paper, 32 of 320 antennas are on: one in ten, as on this page (10 of 100). Reconfigurable means the choice can be redone at any moment — by flipping switches, not by moving hardware.

How do 10 radios reach 100 antennas? Through an RF switch network . In a dynamic sub-array, each antenna can be connected to any radio chain, and inactive antennas are terminated to ground. A more power-efficient alternative is a fixed sub-array: each radio chain can only reach its own predefined group of antennas. The authors note a fundamental trade-off between spectral efficiency and power efficiency here, and leave its detailed analysis for future work.

Inside the switch box

Sum-rate with this wiring: –

Swarm's best pattern for these five users — –

Classic antenna selection uses channel measurements to pick the antennas that contribute most, by metrics such as singular values of the channel matrix, channel norms, spatial correlation or minimum signal-to-noise ratio. It is not posed as designing a sparse array. Array thinning designs a structured sparse array: either offline, before deployment, from channel statistics, or online, adapting to where users are (for example, learned through beam training). To the best of the authors' knowledge, this is the first work to consider array thinning for near-field communication.

Why not simply spread the 10 antennas evenly over the whole length?

2 Ghosts in direction — none in distance

Spreading a fixed number of antennas over a longer stretch narrows the beam, and in the it is the long aperture that lets a beam focus at a particular distance. Slide the same 10 antennas apart and watch one phone's beam.

Spread them out

Those extra spots are — ghost beams. They are the main problem of evenly spaced sparse arrays: they shine full power at people who should be getting someone else's signal. Ghosts in direction are textbook physics. The paper's first question is whether a near-field beam also has ghosts in distance. Its answer is no. Let's hunt for them.

Predict first. Antennas 2 wavelengths apart, beam pointed straight ahead. Where does the first ghost appear?

Ghost hunter

Probe gain –

Phase clocks — one per antenna: how far each wave is off, at the probe

Phasor chain: the 32 waves added head to tail

Phase across the array

Step between neighbours: –

Predicted ghost directions: – · 2D = 124λ

Why ghosts appear in direction…

At the focus, all 32 waves arrive in step: the phasor chain is a straight line, the gain is 0 dB. Move the probe sideways along the ring and each antenna's wave slips by the same extra amount relative to its neighbour — the phase grows linearly along the array (the dots form a straight, wrapping staircase). Equal slips curl the chain into a circle, and the waves cancel. But when the slip between neighbours reaches a whole turn, every wave is back in step: the chain straightens again, a full-strength copy of the beam. That is the grating-lobe condition of the paper, sin θq = sin θ0 + qλ/d. Wider spacing or steering toward the side packs more ghosts into view — try 3λ, or steer to 40°.

…but not in distance

Now move the probe outward along the beam. A change of distance shifts the waves by an amount that grows quadratically along the array, like a bowl: the middle antennas barely change, the edge ones change a lot. The steps between neighbours are no longer equal, so at any realistic distance they cannot all become whole turns at once. The chain coils into a spiral and never straightens. The paper shows that the only distances where the formula would allow re-alignment (its eq. 14) are negative or a few wavelengths from the antennas: here r₁ ≈ 1.98λ, r₂ ≈ 0.99λ, r₃ ≈ 0.66λ. That is far inside 2D, where the near-field model does not even apply — and even there, the phases still don't re-align; the sum gives only small ripples. So along distance you find a single focus and weak ripples, never a copy.

The consequence. Grating lobes need fighting only in the angle domain. And the angle pattern is the same in the near and far field, with ghost directions that do not depend on distance — so a sparse array can be designed against ghosts using the simple far-field angle pattern alone.

If even spacing makes ghosts, can an uneven choice of 10 antennas avoid them?

3 Break the rhythm

Ghosts come from regularity. Break the regular pattern and they dissolve into weaker, scattered sidelobes. The paper's first design, the grating-lobe-based thinned array (GTA) , picks which antennas to keep on so that the worst stray lobe is as low as possible for every steering direction in the coverage (here ±60°), keeping the two edge antennas on to preserve the full aperture. Try it by hand: start from the evenly spaced pattern, whose ghost sits at full strength (0 dB), and get the score below −4 dB.

Thin it yourself

Worst stray lobe: 0.0 dB

Click a lit antenna, then an empty slot, to move it. Keyboard: ← → and Enter.

Ghost at full strength.

How the swarm searches

There are about 1011 ways to choose 8 more antennas out of 98 — far too many to test. The paper uses particle swarm optimization (its Algorithm 1). A flock of candidate designs (“particles”) flies through the space of possibilities. Each one remembers the best design it has ever seen, and every step it is pulled partly toward its own best and partly toward the flock's best, with some inertia and randomness.

The clever part is how a smooth flight becomes an on/off choice: each particle carries a priority between 0 and 1 for every switchable antenna, and the design is “the two edges plus the 8 highest-priority antennas”. The update rule is v ← ωv + c1u1(Pbest − x) + c2u2(Gbest − x), then x ← x + v, clipped to [0, 1]. Here the swarm uses 24 particles, 150 iterations, ω = 0.72 and c1 = c2 = 1.49. The cost grows as (iterations) × (particles) × (switchable antennas).

The result is a GTA: designed once, offline, and then fixed. With only 10 of 100 antennas the swarm reaches a worst stray lobe of about −5 to −6 dB. Although the ghosts are gone, the paper notes that a GTA's sidelobes stay relatively high, because the spacing is irregular and few antennas are active. Its own GTA uses 32 of 320 antennas:

A ghost-free pattern is good on average. Can we do better for the people who are actually there?

4 Serve the crowd

The paper's second design, the sum-rate-based thinned array (STA) , assumes the base station knows each user's direction and distance. It runs the same swarm, but now the score is the itself, with beams computed by . It is re-run whenever users move. The benchmark it should match is the movable-antenna array (MULA), whose 10 antennas can sit anywhere along the same length. Drag the phones, switch designs, and compare.

Playground

Sum-rate for these phones (bps/Hz)

FULA all 100 –

STA adaptive thinning –

MULA movable –

GTA fixed, ghost-free –

SULA evenly spaced –

HULA 10 adjacent –

–

Evenly spaced vs full array: –

Predict first. Three phones stand in a line straight ahead, at different distances. Will the evenly spaced array — the one with ghosts — lose to the full array?

Graceful degradation. Turn on “Break an antenna” and knock out lit antennas. The fixed designs lose them for good; the thinned array simply switches on different ones. The paper names this as a strength of thinning: faulty elements can be deactivated, and the thinned configuration can be re-optimized on the fly.

Does it hold up at full scale?

5 What the paper found

The paper's simulations use a base station with 320 antennas at half-wavelength spacing, of which only 32 are active (thinning ratio 1/10), at 30 GHz with 20 dB SNR, and RZF beams. Sixteen users are placed at random between 3.18 m (2D) and 72.6 m (rRD/7), within ±60°. Designs compared: FULA (all 320, the upper bound); MULA (32 movable antennas within ±80λ, optimized by the swarm for each user drop); PTA (32 active, pre-optimized from channel statistics, following earlier work); GTA and STA (this paper); SULA (32 at 5λ, same length); HULA (32 at λ/2, compact).

FULA highest — full aperture, maximum beamforming gain (320 radio chains)

STA ≈ MULA — thinning matches movable antennas, with nothing moving

GTA ≈ PTA — on average about 5% below STA, but designed once, offline

SULA — lower: grating lobes cause interference

HULA — lowest: compact, small aperture

Relations as stated in the paper (Figs. 4–5); no values are re-plotted here.

The price: computation

The swarm's work grows with the number of iterations × particles × switchable antennas. STA needs 100 iterations, while MULA needs 200 because it searches over continuous positions. GTA and PTA are optimized offline, before deployment, so their computing cost matters less. STA, by contrast, must be updated more often, whenever the users' geometry changes.

Back to the wall of antennas

Picture the array at full size: hundreds of antennas fixed to a wall, but only the ones that matter right now are switched on, and the choice changes as people move. No motors, no moving parts. Ghost beams need to be fought only in direction, because distance has none. And when an element fails, the array simply chooses others.

The authors see two next steps: replacing the particle swarm with a deep-learning solution to cut the computation, and analysing the trade-off between spectral and power efficiency in the switch architectures.

Source

Ahmed Hussain, Asmaa Abdallah, Abdulkadir Celik, Emil Björnson, Ahmed M. Eltawil. “Sparse Array Design for Near-Field MU-MIMO: Reconfigurable Array Thinning Approach.” arXiv preprint arXiv:2602.21973v2 [eess.SP], 21 May 2026. arxiv.org/abs/2602.21973 · DOI 10.48550/arXiv.2602.21973

Figures 1–5 are reproduced from the paper under its CC BY 4.0 license, cropped, with credit at each figure.

Methods of this page

Live-simulated (scaled-down, illustrative): every interactive scene runs in your browser. The toy array has 100 antenna positions half a wavelength apart (length 49.5λ) with 10 active, the same one-in-ten ratio as the paper. Waves are modelled as exact spherical waves (no far-field or Fresnel approximation). Path loss is proportional to 1/distance, total transmit power is 1, the toy SNR is 40 dB, and multi-user beams use RZF. STA, GTA and the movable array (MULA) are found with the paper's particle-swarm scheme (24 particles, ω = 0.72, c1 = c2 = 1.49; 100 iterations for STA, 150 for GTA, 200 for MULA); the toy GTA pattern was designed once by that swarm and is reused. The ghost hunter uses 32 antennas 2λ apart, focused at 160λ. Multi-user maps show each phone's beam relative to that beam's strongest point in view (top 4 dB); single-beam maps show 0 to −14 dB (bridge) or 0 to −25 dB (ghost hunter). Movable-antenna motor speed is illustrative. Toy sum-rates are not the paper's numbers.

Reproduced from the paper: the cropped Figures 1–5, the simulation setup, and the stated results (STA ≈ MULA; about 75% of FULA's sum-rate with 10% of the antennas; GTA ≈ PTA, on average about 5% below STA; Fig. 1's ghosts at ±π/6 and −13 dB ripple).