#!/usr/bin/env python3 import matplotlib.pyplot as plt import numpy as np from itertools import chain, combinations, product c_light = 3e8 f_beacon = 50e6 class Antenna: """ Simple Antenna class """ def __init__(self,x=0,y=0,z=0,t0=0,name=""): self.x = x self.y = y self.z = z self.t = t0 self.name = name def __repr__(self): cls = self.__class__.__name__ return f'{cls}(x={self.x!r},y={self.y!r},z={self.z!r},t0={self.t!r},name={self.name!r})' def phase_mod(phase, low=np.pi): """ Modulo phase such that it falls within the interval $[-low, 2\pi - low)$. """ return (phase + low) % (2*np.pi) - low def dist(a,b): return ((a.x-b.x)**2+(a.y-b.y)**2+(a.z-b.z)**2)**0.5 def phase(a,b,f=f_beacon,wrap=False): t = dist(a,b)/c_light phase = t*f*2*np.pi if wrap: phase = phase_mod(phase) return phase def grid_plot(grid, ax=None, **plot_kwargs): if ax is None: ax = plt.gca() x = [a.x for a in grid] y = [a.y for a in grid] l = [a.name for a in grid] ax.plot(x,y,'kx', **plot_kwargs) for x_,y_,l_ in zip(x,y,l): ax.annotate(l_,(x_,y_)) def antenna_combinations(ants, ref_ant=None): if ref_ant is not None: # use only one reference antenna for the baselines ref = ref_ant ant_combi = [ (ref, j) for j in ants if j is not ref ] else: # use all baselines ant_combi = combinations(ants, 2) return list(ant_combi) def calculate_field(field, tx, ant_combi, ref_ant=None, calculate_phase=True): if plot_phase: p_ij = [ (phase(tx,i) - phase(tx,j)) for i,j in ant_combi ] else: t_ij = [ (dist(tx,i) - dist(tx, j))/c_light for i,j in ant_combi ] val = [] xx = [] yy = [] xs = field[0] ys = field[1] for x in xs: for y in ys: tx_t = Antenna(x=x,y=y) if plot_phase: # phase dp_ij = np.array([ (phase(tx_t,i) - phase(tx_t,j)) - p_ij[k] for k,(i,j) in enumerate(ant_combi) ]) if True: # phase wrap dp_ij = phase_mod(dp_ij) val.append(np.sum(dp_ij**2)**0.5) else: # time dt_ij = np.array([ (dist(tx_t,i) - dist(tx_t, j))/c_light - t_ij[k] for k,(i,j) in enumerate(ant_combi) ]) val.append(np.sum(dt_ij**2)**0.5) xx.append(x) yy.append(y) return np.array(xx), np.array(yy), np.array(val) def plot_field(tx, ants, xx, yy, val, ax=None, ref_ant=None, color_label='$\\left( t - \\tau \\right)^2$', plot_phase=None, mask=None,**scatter_kwargs): if ax is None: ax = plt.gca() default_scatter_kwargs = {} default_scatter_kwargs['cmap'] = 'Spectral_r' if mask is not None: val[mask] = np.nan if plot_phase is None: pass elif plot_phase: default_scatter_kwargs['vmax'] = len(ants)*np.pi #default_scatter_kwargs['cmap'] = 'gray' pass else: val *=1e9 # to ns default_scatter_kwargs['vmax'] = 100 scatter_kwargs = {**default_scatter_kwargs, **scatter_kwargs} grid_plot([tx] + ants, ax=ax) if ref_ant is not None: ax.set_title("Single reference antenna: {}, f: {}MHz".format(ref_ant.name, f_beacon/1e6)) else: ax.set_title("All baselines f: {} MHz".format(f_beacon/1e6)) sc = ax.scatter(xx,yy,c=val, **scatter_kwargs) fig = ax.get_figure() fig.colorbar(sc, ax=ax, label=color_label) return ax def square_grid(dx=1, N_x=10, dy=None, N_y=None, x_start=0, y_start=0): N_y = N_x if N_y is None else N_y dy = dx if dy is None else dy print([(N_x,N_y), (dx,dy), (x_start,y_start)]) return product( (x_start + n*dx for n in range(N_x)), (y_start + n*dy for n in range(N_y)), ) def triangular_grid(dx=1, N_x=10, dy=None, N_y=None, x_start=0, y_start=0): return chain( square_grid(dx=dx,dy=dy,N_x=N_x,N_y=N_y,x_start=x_start,y_start=y_start), square_grid(dx=dx,dy=dy,N_x=N_x,N_y=N_y,x_start=x_start + dx/2,y_start=y_start + dy/2), ) if __name__ == "__main__": ### ### Field ### x_low, x_high, N_x = -1203, 300, 81 y_low, y_high, N_y = -x_low, -x_high, N_x ### ### Geometry ### tx = Antenna(x=-800,y=300,z=0,name="tx") if True: # single baseline ants = [ Antenna(x=-50,y=0,z=0,name="a"), Antenna(x=50,y=0,z=0,name="b"), ] tx = Antenna(x=-000,y=200,z=0,name="tx") x_low, x_high, N_x = -300, 300, 81 y_low, y_high, N_y = -300, 300, 81 elif not True: # from grid definition x_start, dx, ant_N_x = 0, 50, 2 y_start, dy, ant_N_y = 0, dx, ant_N_x if not True: # square grid grid_func = square_grid elif True: # triangular grid_func = triangular_grid grid = grid_func(dx=dx, dy=dy, N_x=ant_N_x, N_y=ant_N_y, x_start=x_start, y_start=y_start) ants = [ Antenna(x=x,y=y,z=0,name=i) for i, (x,y) in enumerate(grid) ] else: ants = [ Antenna(x=100,y=0,z=0,name="a"), Antenna(x=0,y=-50,z=0,name="b"), Antenna(x=+50,y=-180,z=0,name="c"), Antenna(x=125,y=180,z=0,name="d"), ] ### ### Options ### plot_phase = True ref_ant = None ant_combi = antenna_combinations(ants, ref_ant=ref_ant) print("Antenna Combinations calculated") xs = np.linspace(x_low, x_high, N_x) ys = np.linspace(y_low, y_high, N_y) xx, yy, val = calculate_field((xs, ys), tx, ant_combi, calculate_phase=plot_phase) mask = None if False and plot_phase: mask = abs(val) > np.pi if plot_phase: color_label='$\\sqrt{ \\sum \\left(\\varphi(x) - \\Delta \\varphi\\right)^2}$' else: color_label='$\\sqrt{ \\sum \\left(t(x) - \\Delta t\\right)^2}$ [ns]' val *= 1e9 ax = plot_field(tx, ants, xx, yy, val, ax=None, ref_ant=ref_ant, mask=mask, color_label=color_label) # if plot_phase: # N_lowest = np.min(len(ant_combi)-1, 10) # lowest_idx = np.argpartition(val, N_lowest)[:N_lowest] # # print(lowest_idx) # print(val[lowest_idx]) # print( list(zip(np.array(xx)[lowest_idx], np.array(yy)[lowest_idx])) ) plt.show()