Wireless 101
M07 · L04
Module 7 · Lesson 4

A Beam You Can Aim in Software

One antenna has one pattern, fixed when it was built. Feed several elements copies of the same signal with chosen delays and the group becomes one antenna — narrower, and steerable with no moving parts.

01 / 11
Wireless 101
M07 · L04
Why bother

N Elements, 10·log₁₀N dB

Coherently fed, N elements add their fields in one direction while noise does not add. A power ratio, so 10·log₁₀ — and every doubling is 3 dB, forever.

N = 4
6.0 dB
N = 16
12.0 dB
N = 64
18.1 dB
02 / 11
Wireless 101
M07 · L04
N in a line, spacing d

The Array Factor

Uniform linear array
\mathrm{AF} = \frac{\sin(N\psi/2)}{N\sin(\psi/2)}, \;\; \psi = kd\cos\theta + \beta

ψ is the phase step between neighbours: the geometric part kd·cosθ plus the part you choose, β. Total pattern = element pattern × array factor.

03 / 11
Wireless 101
M07 · L04
Steering, in one line

Point It With Phase

Beam direction
\beta = -kd\cos\theta_0, \qquad k = \frac{2\pi}{\lambda}

At d = λ/2, kd = π. For θ₀ = 60°: β = −π·cos60° = −π/2 = −90° per element. That is the entire instruction set.

04 / 11
Wireless 101
M07 · L04
Length, not count

How Narrow It Gets

Broadside HPBW
\mathrm{HPBW} \approx \frac{0.886\,\lambda}{N d}\;\left[\text{rad}\right]

N = 16 at d = λ/2 spans 8λ, so 0.886/8 = 0.111 rad = 6.3°. Steer away from broadside and it widens by 1/sinθ₀ — 7.3° at 60°.

05 / 11
Wireless 101
M07 · L04
Try it

Steer the Beam

Real array factor, plotted over the half-plane. Add elements to narrow the beam, move θ₀ to steer it — and push d past λ/2 to watch grating lobes appear.

N N = 16
d/λ d = 0.50 λ
θ₀ θ₀ = 90°
gain 12.0 dB HPBW 6.4° β 0°/elem grating lobe
Interactive: steer a phased-array beam and watch the pattern redraw — AI-generated
06 / 11
Wireless 101
M07 · L04
Nyquist, in space

Why Half a Wavelength

Grating-lobe-free
\frac{d}{\lambda} < \frac{1}{1 + \lvert\cos\theta_0\rvert}

A grating lobe is an alias — two directions with identical element phases. Broadside tolerates d < λ; steering towards endfire tightens it to λ/2.

07 / 11
Wireless 101
M07 · L04
Where the phase is made

Analog, Digital, Hybrid

  • Analog — one transceiver, a phase shifter per element. One beam. Cheapest
  • Digital — a transceiver per element. Up to N beams. Converters dominate the bill
  • Hybrid — M transceivers over sub-arrays: 64 elements behind 4 chains, 4 beams
  • 256 elements, fully digital, hundreds of MHz → hundreds of Gb/s of raw samples
08 / 11
Wireless 101
M07 · L04
Coming in Module 10

Massive MIMO

A 5G panel carries 64 to 256 elements on a 2-D grid, steering in azimuth and elevation. Careful with the words: beamforming focuses energy, while spatial multiplexing runs parallel streams. Same antennas, different purchase.

09 / 11
Wireless 101
Knowledge Check

Check what stuck

Four questions from this lesson. Answer to see why — the explanation appears whether you were right or wrong. Nothing is scored or saved.

Question 1 of 0
Score 0/0

10 / 11
Wireless 101
M07 · L04
Recap

What you learned

  • N coherent elements → 10·log₁₀N dB, and a beam steered in software
  • AF = sin(Nψ/2)/(N·sin(ψ/2)), ψ = kd·cosθ + β; pattern = element × AF
  • β = −kd·cosθ₀ — at d = λ/2, 60° needs −90° per element
  • HPBW ≈ 0.886λ/(N·d); grating lobes are spatial aliasing, hence λ/2
Module 7 complete — up next
Module 8: Propagation →
All lessons Read article
11 / 11