This is a 2D companion to the 3D 5G beamforming simulator, using the same real array and link-budget math:
- Array factor: AF(θ) = |Σₙ exp(j·n·k·d·(sinθ − sinθ₀))| / N, with k = 2π/λ and half-wavelength element spacing d = λ/2. Elements combine constructively toward the steering angle θ₀ and destructively (nulls) elsewhere — no lenses, just phase offsets per antenna.
- Half-power beamwidth ≈ 0.886·λ/(N·d)/cos θ₀ radians — more elements make a narrower, more directional beam; steering off-broadside widens it (scan loss).
- Free-space path loss: FSPL(dB) = 20log₁₀(d) + 20log₁₀(f) + 20log₁₀(4π/c) — loss grows with the square of frequency, so mmWave (28 GHz) attenuates far faster than Sub-6 (3.5 GHz) at the same distance, plus extra atmospheric absorption.
- Array gain ≈ 10log₁₀(N) offsets that loss — this is exactly why massive-MIMO beamforming is what makes mmWave 5G viable at all.
- Shannon capacity: C = B·log₂(1 + SNR) — mmWave's much wider channel bandwidth (800 MHz vs 100 MHz) can still win on throughput once the beam is narrow enough to close the link.