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"""
Near-field vs far-field beamforming comparison.
Near-field user at 8 m (well within Fresnel distance) β focused SPOT
Far-field user at 500 m (beyond Fresnel distance) β STRIP along angle
Each beamformer uses the appropriate steering model for its user.
Beam patterns are evaluated on a polar (range, azimuth) grid.
Usage:
python plot_nf_vs_ff_beam.py
python plot_nf_vs_ff_beam.py --Nh 128 --Nv 64 --fc 12e9
"""
import argparse
import math
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np
import torch
# ββββββββββββββββββββββββββββββββββββββββββββββ
# UPA geometry
# ββββββββββββββββββββββββββββββββββββββββββββββ
def make_upa(Nh, Nv, dx, dy):
"""Uniform Planar Array in x-z plane, centered at origin."""
x = (torch.arange(Nh, dtype=torch.float32) - (Nh - 1) / 2) * dx
z = (torch.arange(Nv, dtype=torch.float32) - (Nv - 1) / 2) * dy
X, Z = torch.meshgrid(x, z, indexing="ij")
return torch.stack([X, torch.zeros_like(X), Z], dim=-1).reshape(-1, 3)
# ββββββββββββββββββββββββββββββββββββββββββββββ
# Steering vectors
# ββββββββββββββββββββββββββββββββββββββββββββββ
def nf_steering(p, r, az, k):
"""Near-field: a_n = exp(jk βp_target β p_nβ) (spherical wave)"""
px = r * torch.sin(az)
py = -r * torch.cos(az)
dist = torch.sqrt(
(px.unsqueeze(-1) - p[:, 0]) ** 2
+ py.unsqueeze(-1) ** 2
+ p[:, 2] ** 2
)
return torch.exp(1j * k * dist)
def ff_steering(p, az, k):
"""Far-field: a_n = exp(βjk x_n sinΞΈ) (planar wave, angle only)"""
return torch.exp(-1j * k * p[:, 0] * torch.sin(az).unsqueeze(-1))
# ββββββββββββββββββββββββββββββββββββββββββββββ
# Beam pattern on polar (range, azimuth) grid
# ββββββββββββββββββββββββββββββββββββββββββββββ
@torch.no_grad()
def beam_pattern_polar(w, p, r_grid, az_grid, k, batch=2000):
"""P(r, ΞΈ) = |w^H a_nf(r, ΞΈ)|Β² normalised to peak = 1."""
R, AZ = torch.meshgrid(r_grid, az_grid, indexing="ij")
Rf, AZf = R.reshape(-1), AZ.reshape(-1)
wc = w.conj()
parts = []
for i in range(0, Rf.shape[0], batch):
a = nf_steering(p, Rf[i:i + batch], AZf[i:i + batch], k)
parts.append((a @ wc).abs().square().cpu())
P = torch.cat(parts).reshape(len(r_grid), len(az_grid))
return P / P.max()
# ββββββββββββββββββββββββββββββββββββββββββββββ
# Plot: 2D heatmaps + 1D cuts + phase profiles
# ββββββββββββββββββββββββββββββββββββββββββββββ
def plot_comparison(P_nf_db, P_ff_db,
r_nf, az_nf, r0_nf, az0_nf_deg,
r_ff, az_ff, r0_ff, az0_ff_deg,
w_nf, w_ff, p, info, path):
"""3-row figure: heatmaps, range cuts, phase profiles."""
fig, axes = plt.subplots(3, 2, figsize=(14, 15))
vmin = -40
# ββ Row 1: 2D heatmaps ββ
for col, (Z, r_ax, az_ax, r0, az0, label) in enumerate([
(P_nf_db, r_nf, az_nf, r0_nf, az0_nf_deg,
f"Near-Field BF β SPOT\n(target r={r0_nf:.0f} m, ΞΈ={az0_nf_deg}Β°)"),
(P_ff_db, r_ff, az_ff, r0_ff, az0_ff_deg,
f"Far-Field BF β STRIP\n(target r={r0_ff:.0f} m, ΞΈ={az0_ff_deg}Β°)"),
]):
ax = axes[0, col]
pcm = ax.pcolormesh(
az_ax, r_ax, np.clip(Z, vmin, 0),
cmap="jet", shading="auto", vmin=vmin, vmax=0)
fig.colorbar(pcm, ax=ax, label="dB")
ax.axhline(r0, color="w", ls="--", lw=0.8, alpha=0.7)
ax.axvline(az0, color="w", ls="--", lw=0.8, alpha=0.7)
ax.plot(az0, r0, "r*", ms=14, mec="white", mew=0.6)
ax.set_xlabel("Azimuth (Β°)")
ax.set_ylabel("Range (m)")
ax.set_title(label, fontsize=11)
# ββ Row 2: range cuts at target azimuth ββ
az_nf_np = az_nf.numpy() if isinstance(az_nf, torch.Tensor) else az_nf
az_ff_np = az_ff.numpy() if isinstance(az_ff, torch.Tensor) else az_ff
r_nf_np = r_nf.numpy() if isinstance(r_nf, torch.Tensor) else r_nf
r_ff_np = r_ff.numpy() if isinstance(r_ff, torch.Tensor) else r_ff
idx_nf = np.argmin(np.abs(az_nf_np - az0_nf_deg))
idx_ff = np.argmin(np.abs(az_ff_np - az0_ff_deg))
for col, (Z, r_ax, idx, r0, label) in enumerate([
(P_nf_db, r_nf_np, idx_nf, r0_nf,
f"NF range cut at ΞΈ={az0_nf_deg}Β°"),
(P_ff_db, r_ff_np, idx_ff, r0_ff,
f"FF range cut at ΞΈ={az0_ff_deg}Β°"),
]):
ax = axes[1, col]
ax.plot(r_ax, Z[:, idx], "b-", lw=1.5)
ax.axvline(r0, color="r", ls="--", lw=1, label=f"target r={r0:.0f} m")
ax.set_xlabel("Range (m)")
ax.set_ylabel("Power (dB)")
ax.set_title(label, fontsize=11)
ax.set_ylim(vmin, 3)
ax.legend(fontsize=9)
ax.grid(True, ls=":", alpha=0.3)
# ββ Row 3: weight phase profiles ββ
p_np = p.numpy()
x_elem = p_np[:, 0]
sort_idx = np.argsort(x_elem)
for col, (w, label) in enumerate([
(w_nf, "NF weight phase (curved = spherical)"),
(w_ff, "FF weight phase (linear = planar)"),
]):
ax = axes[2, col]
phase = np.angle(w.numpy())[sort_idx]
phase_unwrap = np.unwrap(phase)
ax.plot(x_elem[sort_idx] * 1e3, phase_unwrap, "g-", lw=1)
ax.set_xlabel("Element x-position (mm)")
ax.set_ylabel("Phase (rad)")
ax.set_title(label, fontsize=11)
ax.grid(True, ls=":", alpha=0.3)
fig.suptitle(info, fontsize=13, fontweight="bold")
plt.tight_layout()
plt.savefig(path, dpi=150, bbox_inches="tight")
plt.close()
print(f"Saved β {path}")
# ββββββββββββββββββββββββββββββββββββββββββββββ
# 3D surface plots
# ββββββββββββββββββββββββββββββββββββββββββββββ
def plot_3d(P_nf_db, P_ff_db,
r_nf, az_nf, r0_nf, az0_nf_deg,
r_ff, az_ff, r0_ff, az0_ff_deg,
info, path):
fig = plt.figure(figsize=(18, 8))
vmin = -40
for col, (Z, r_ax, az_ax, r0, az0, label) in enumerate([
(P_nf_db, r_nf, az_nf, r0_nf, az0_nf_deg,
f"(a) Near-Field BF (target {r0_nf:.0f} m, {az0_nf_deg}Β°)"),
(P_ff_db, r_ff, az_ff, r0_ff, az0_ff_deg,
f"(b) Far-Field BF (target {r0_ff:.0f} m, {az0_ff_deg}Β°)"),
]):
ax = fig.add_subplot(1, 2, col + 1, projection="3d")
R, AZ = np.meshgrid(r_ax, az_ax, indexing="ij")
Z_clip = np.clip(Z, vmin, 0)
ax.plot_surface(
AZ, R, Z_clip,
cmap="jet", vmin=vmin, vmax=0,
rstride=2, cstride=2,
linewidth=0, antialiased=True, alpha=0.9,
)
ax.scatter([az0], [r0], [3],
color="red", marker="*", s=300,
zorder=10, depthshade=False)
ax.set_xlabel("Azimuth (Β°)", fontsize=10, labelpad=8)
ax.set_ylabel("Range (m)", fontsize=10, labelpad=8)
ax.set_zlabel("Power (dB)", fontsize=10, labelpad=6)
ax.set_zlim(vmin, 5)
ax.set_title(label, fontsize=12, fontweight="bold", y=-0.02)
ax.view_init(elev=30, azim=-60)
plt.tight_layout()
plt.savefig(path, dpi=150, bbox_inches="tight")
plt.close()
print(f"Saved β {path}")
# ββββββββββββββββββββββββββββββββββββββββββββββ
# Main
# ββββββββββββββββββββββββββββββββββββββββββββββ
def run(args):
lam = 3e8 / args.fc
k = 2 * math.pi / lam
dx = dy = lam / 2
# If physical aperture is specified, override Nh/Nv to keep aperture fixed
if args.aperture_h > 0:
args.Nh = max(2, round(args.aperture_h / dx))
if args.aperture_v > 0:
args.Nv = max(2, round(args.aperture_v / dy))
N = args.Nh * args.Nv
D_h, D_v = args.Nh * dx, args.Nv * dy
D = math.sqrt(D_h ** 2 + D_v ** 2)
fresnel = 2 * D ** 2 / lam
# NF user: well inside Fresnel distance
r0_nf, az0_nf_deg = 3.0, 45.0
# FF user: beyond Fresnel distance
r0_ff, az0_ff_deg = 500.0, 30.0
az0_nf_rad = az0_nf_deg * math.pi / 180
az0_ff_rad = az0_ff_deg * math.pi / 180
print(f"UPA {args.Nh}Γ{args.Nv} = {N} elements")
print(f"Ξ» = {lam * 1e3:.1f} mm | dx = dy = {dx * 1e3:.2f} mm")
print(f"Aperture {D_h:.3f} Γ {D_v:.3f} m | Fresnel {fresnel:.0f} m")
print(f"NF user: r = {r0_nf} m, ΞΈ = {az0_nf_deg}Β° "
f"(r/Fresnel = {r0_nf / fresnel:.4f})")
print(f"FF user: r = {r0_ff} m, ΞΈ = {az0_ff_deg}Β° "
f"(r/Fresnel = {r0_ff / fresnel:.2f})")
p = make_upa(args.Nh, args.Nv, dx, dy)
# Beamforming weights
w_nf = nf_steering(p, torch.tensor([r0_nf]),
torch.tensor([az0_nf_rad]), k).squeeze(0)
w_ff = ff_steering(p, torch.tensor([az0_ff_rad]), k).squeeze(0)
# Evaluation grids (polar: range Γ azimuth)
ng = args.grid
r_nf_grid = torch.linspace(0.5, 15.0, ng)
az_nf_grid = torch.linspace(0.0, 90.0, ng) # degrees for display
az_nf_rad_grid = az_nf_grid * math.pi / 180
r_ff_grid = torch.linspace(50.0, 1000.0, ng)
az_ff_grid = torch.linspace(0.0, 90.0, ng)
az_ff_rad_grid = az_ff_grid * math.pi / 180
# Smaller batches for large arrays
bsz = max(200, 2000 // max(1, N // 8192))
print(f"\nComputing beam patterns ({ng}Γ{ng} polar grid, batch={bsz}) ...")
P_nf = beam_pattern_polar(w_nf, p, r_nf_grid, az_nf_rad_grid, k, batch=bsz)
print(" Near-field β")
P_ff = beam_pattern_polar(w_ff, p, r_ff_grid, az_ff_rad_grid, k, batch=bsz)
print(" Far-field β")
P_nf_db = 10 * np.log10(P_nf.numpy() + 1e-15)
P_ff_db = 10 * np.log10(P_ff.numpy() + 1e-15)
info = (f"UPA {args.Nh}Γ{args.Nv} @ {args.fc / 1e9:.0f} GHz | "
f"Fresnel = {fresnel:.0f} m")
# 2D heatmaps + range cuts + phase profiles
plot_comparison(
P_nf_db, P_ff_db,
r_nf_grid.numpy(), az_nf_grid.numpy(), r0_nf, az0_nf_deg,
r_ff_grid.numpy(), az_ff_grid.numpy(), r0_ff, az0_ff_deg,
w_nf, w_ff, p, info, args.output)
# 3D surface plots
path_3d = args.output.replace(".png", "_3d.png")
plot_3d(
P_nf_db, P_ff_db,
r_nf_grid.numpy(), az_nf_grid.numpy(), r0_nf, az0_nf_deg,
r_ff_grid.numpy(), az_ff_grid.numpy(), r0_ff, az0_ff_deg,
info, path_3d)
def main():
pa = argparse.ArgumentParser(description="NF vs FF beam comparison")
pa.add_argument("--Nh", type=int, default=128)
pa.add_argument("--Nv", type=int, default=64)
pa.add_argument("--fc", type=float, default=12e9, help="Carrier freq (Hz)")
pa.add_argument("--aperture_h", type=float, default=0,
help="Fixed horizontal aperture (m). Overrides Nh.")
pa.add_argument("--aperture_v", type=float, default=0,
help="Fixed vertical aperture (m). Overrides Nv.")
pa.add_argument("--grid", type=int, default=200, help="Grid points per axis")
pa.add_argument("-o", "--output", default="nf_vs_ff_beam.png")
args = pa.parse_args()
run(args)
if __name__ == "__main__":
main()
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