{ "cells": [ { "cell_type": "markdown", "id": "82c10597", "metadata": {}, "source": [ "# Signal statistics for beamformer and correlator\n", "\n", "Author: Eric Kooistra, Aug - Dec 2022\n", "\n", "Purpose: Model the SNR of a beamformer and a correlator\n", "\n", "Description:\n", "* SNR: This model shows two different SNR measures. one regarding the 'coherent' SNR of the coherent signal versus the incoherent signal (e.g. in a voltage beamformer, in a correlator) that indicates the strength of the coherent signal with respect to the incoherent noise, and one regarding the 'incoherent' SNR of the power measurement itself, that indicates the accuracy if the measured power (e.g. in power statistics, in a powers beamformer). The 'coherent' SNR makes use of phase information of the input voltage signals. The 'incoherent' SNR is based on input powers, so the input phase information is lost, and therefore the 'incoherent' SNR can only improve the accuracy of the mean power measurement, it cannot improve (distinguish) between signal and noise.\n", "* Coherent summator (sums voltages, e.g. voltage beamformer): The 'coherent' SNR of coherent input versus the incoherent input improves by the number of inputs N.\n", "* Incoherent summator (sums powers, e.g. auto power statistics, power beamformer): The 'coherent' SNR of coherent input versus incoherent input does not improve, because the coherent phase information is lost in the powers. However, the accuracy of mean power measurement, so the 'incoherent' SNR, does improve by factor N, because the std of the mean power measurement reduces by N.\n", "* Correlator: The 'coherent' SNR of coherent input versus the incoherent input improves by sqrt(N) for integration over N cross powers in time. The mean correlation of the coherent input is constant and non-zero. The mean correlation of the incoherent input is zero. The power of the mean correlation of the incoherent input reduces by N, so the std of the mean correlation of the incoherent input reduces by sqrt(N). For example, if the input SNR of the input signal is -20 dB (i.e. sigma_coh / sigma_sys = 0.1), then it takes integration over N = 10000 cross powers in time to improve the SNR of the correlator output by a factor 100 = +20 dB to 0 dB.\n", "\n", "Remarks:\n", "* Summing powers from N inputs (like in an incoherent array beamformer = IAB) or summing N powers in time from 1 input (like in auto power statistics of subbands = SST or of beamlets = BST) is equivalent.\n", "* The field of view of a voltage beamformer reduces by a factor N, to accomodate for the 'coherent' SNR improvement. The field of view of the incoherent array power beam (IAB) is the same as the field of view of one input, because the 'coherent' SNR of the IAB does not improve.\n", "\n", "Usage:\n", "* On command line start: > jupyter notebook\n", "* In browser open the ipynb and run it\n", "\n", "References:\n", "\n", "1. Understanding digital signal processing, R.G. Lyons" ] }, { "cell_type": "code", "execution_count": 1, "id": "2b477516", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "4ddef2d8", "metadata": {}, "source": [ "## 1 Statistics basics:\n", "\n", "Signal statistics\n", "\n", "* dc = mean # direct current, average value of a signal\n", "* sigma = std = sqrt(var) # standard deviation, measure for fluctuating portion of a signal\n", "* var = std**2 # variance, power of the fluctuating portion of a signal\n", "* power = var + mean**2\n", "* rms = sqrt(power) = sqrt(var + mean**2)\n", "\n", "If mean = 0 then var = power and std = rms.\n", "\n", "For a complex signal (like subbands and beamlets):\n", "\n", "* power complex = power real + power imag = (std real)^2 + (std imag)^2\n", "* power real = power imag = power complex / 2\n", "* std real = std imag = std complex / sqrt(2)\n", "* std complex = sqrt(power complex)\n", "* ampl real = ampl imag = std complex = std real * sqrt(2) = std imag * sqrt(2)\n", "\n", "Coherent and incoherent signals. With S signals, the std of their sum signal:\n", "\n", "* increases by S for coherent signals\n", "* increases by sqrt(S) for incoherent signals\n", "\n", "Coherent averaging by summing voltage signals improves the 'coherent' SNR of a signal by a factor N^2 / N = N, because the coherent signal power increases by a factor N^2, while the incoherent noise adds as powers, so the noise power increases by a factor N.\n", "\n", "Incoherent averaging by summing power signals does not improve the 'coherent' SNR, because the phase information of the signal is lost in the powers. Incoherent averaging does reduce the std of the signal power estimate by a factor N, so incoherent averaging does inprove the 'incoherent' SNR, so it makes the signal power measurement more accurate." ] }, { "cell_type": "code", "execution_count": 2, "id": "9c55fb7b", "metadata": {}, "outputs": [], "source": [ "def rms(arr):\n", " \"\"\"Root mean square of values in arr\n", " \n", " rms = sqrt(mean powers) = sqrt(std**2 + mean**2)\n", " \n", " The rms() also works for complex input thanks to using np.abs().\n", " \"\"\"\n", " return np.sqrt(np.mean(np.abs(arr)**2.0))" ] }, { "cell_type": "code", "execution_count": 3, "id": "74edfe32", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean(si) = -0.192589, expected -0.2\n", "std(si) = 0.500000, expected 0.5\n", "rms(si) = 0.535808, expected 0.538516\n" ] } ], "source": [ "N_samples = 10000\n", "sigma = 0.5\n", "var = sigma**2\n", "dc = -0.2\n", "\n", "# Signal input voltages\n", "si = np.random.randn(N_samples)\n", "si *= sigma / np.std(si) # apply requested sigma\n", "si += dc # add offset\n", "\n", "print(f\"mean(si) = {np.mean(si):.6f}, expected {dc}\")\n", "print(f\"std(si) = {np.std(si):.6f}, expected {sigma}\")\n", "print(f\"rms(si) = {rms(si):.6f}, expected {np.sqrt(var + dc**2):.6f}\") " ] }, { "cell_type": "markdown", "id": "17d333f1", "metadata": {}, "source": [ "## 2 Summator\n", "\n", "Two types:\n", "\n", "1. Coherent summation in voltage beamformer (e.g. digital BF in LOFAR2 Station, tied array beamformer = TAB in ARTS)\n", "2. Incoherent summation in power statistics (e.g. SST, BST), power beamformer (e.g. IAB in ARTS)" ] }, { "cell_type": "markdown", "id": "96de4cb4", "metadata": {}, "source": [ "### 2.1 Coherent summation (voltages beamformer)\n", "\n", "Two signal input types:\n", " \n", "1. Coherent signals, add up as voltages\n", "2. Incoherent signal, add up as powers\n", "\n", "In the voltage beamformer the sky signal in the beamlet direction adds coherently and the sky\n", "signals from other directions and the signals from the receivers noise add incoherently." ] }, { "cell_type": "code", "execution_count": 4, "id": "89845ec3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Signal inputs\n", "# . Warning: do use not too high values for N_samples and S_max to avoid too long compute time.\n", "N_samples = 10000 # >= 3\n", "S_max = 100\n", "S_arr = np.arange(1, S_max + 1)\n", "S_arr_log = np.log10(S_arr)\n", "\n", "sigma_coh = 0.05\n", "sigma_incoh = 0.5\n", "\n", "si_coh = np.random.randn(N_samples)\n", "si_coh *= sigma_coh / np.std(si_coh)\n", "\n", "# Voltage beamformer sum(S)\n", "bf_coh_std_arr = []\n", "bf_incoh_std_arr = []\n", "bf_sys_std_arr = []\n", "coh_SNR_dB_arr = []\n", "for S in S_arr:\n", " # The coh signal in the beamlet direction adds coherently for all signal inputs\n", " bf_coh = S * si_coh\n", " bf_coh_std = np.std(bf_coh)\n", " bf_coh_std_arr.append(bf_coh_std)\n", " \n", " # The incoh signals from other directions and from the receivers noise add incoherently\n", " bf_incoh = np.zeros(N_samples)\n", " for si in range(1, S + 1):\n", " si_incoh = np.random.randn(N_samples)\n", " si_incoh *= sigma_incoh / np.std(si_incoh)\n", " bf_incoh += si_incoh\n", " bf_incoh_std = np.std(bf_incoh)\n", " bf_incoh_std_arr.append(bf_incoh_std)\n", " \n", " # Total BF output\n", " bf_sys_std = np.std(bf_coh + bf_incoh)\n", " bf_sys_std_arr.append(bf_sys_std)\n", " \n", " # SNR of the coherent sum\n", " coh_SNR_dB = 20 * np.log10(bf_coh_std / bf_incoh_std)\n", " coh_SNR_dB_arr.append(coh_SNR_dB)\n", "\n", "plt.figure(1)\n", "plt.plot(S_arr, bf_coh_std_arr, 'g', S_arr, bf_incoh_std_arr, 'b', S_arr, bf_sys_std_arr, 'r')\n", "plt.title(\"Summator\")\n", "plt.xlabel(\"Number of signal inputs\")\n", "plt.ylabel(\"BF std\")\n", "plt.legend(['bf_coh', 'bf_incoh', 'bf_sys'])\n", "plt.grid()\n", "\n", "plt.figure(2)\n", "plt.plot(S_arr_log, coh_SNR_dB_arr, 'r-o')\n", "plt.title(\"Summator\")\n", "plt.xlabel(\"Number of signal inputs (log10)\")\n", "plt.ylabel(\"SNR of voltage signal [dB]\")\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "71aa6647", "metadata": {}, "source": [ "**Conclusion:**\n", "The voltage beamformer improves the 'coherent' SNR of the beamlet signal by factor S, because the coherent signal power increases by S^2 while the incoherent noise power increases by S. For very weak astronomical signals this 'coherent' SNR improvement is not enough to make them appear above the system noise, so then additional voltage beamforming is needed or integration in time using a correlator is needed." ] }, { "cell_type": "markdown", "id": "9dafd903", "metadata": {}, "source": [ "### 2.2 Incoherent summation (powers beamformer)\n" ] }, { "cell_type": "markdown", "id": "fd6ffb94", "metadata": {}, "source": [ "Incoherent summation of powers from S inputs is equivalent to incoherent summation of S powers in time from a single input. Incoherent summation does not improve the 'coherent' SNR of the signal, but it does improve the accuracy of the power measurement by a factor S. Hence instead of measuring with one dish for S intervals it is equivalent to sum the powers of S dishes for 1 interval. Hence the field of view of the summed incoherent array power beam (IAB) is the same as the field of view of one signal input." ] }, { "cell_type": "markdown", "id": "84b8930c", "metadata": {}, "source": [ "## 3 Correlation\n" ] }, { "cell_type": "markdown", "id": "94dce0e2", "metadata": {}, "source": [ "### 3.1 Auto powers" ] }, { "cell_type": "code", "execution_count": 5, "id": "8713e865", "metadata": {}, "outputs": [ { "data": { "image/png": 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eI4UxEXEGcEbRwfQFj5JqZlZdnqRwoaSxwN3ArcC0iJhRbFi9z6OkmpnVluc+hf0ljQD2JHtozvWSNoyIzYoOzszM+lbNpCBpP+B96bUJcB3ZEYOZmQ0yebqPSsC9wHeBP0bEqkIjMjOzhsmTFEYD+wLvB06RtBb4W0T8Z6GRmZlZn8tzTuElSU8AWwFjgX8AhhcdmJmZ9b085xSeAB4BbgPOA05wF5KZ2eCUp/vo7RFR97AWki4EDgUWR8Q7qyzTBpxDduSxJCL2r7eeennobDOz6vLc0byFpD9IWpxeV6T7FmqZDBxUbaakTYBfAIdFxDuAT+YJuKc8dLaZWW15ksJFwDXAFul1bSrrVkRMA17oZpGjgSsj4pm0/OIcsZiZWYHydB+9OSIqk8BkSaf2Qt07AMMllYCNgJ9ExCVdLShpAjABoKWlhVKpVHdlCxYuAGD27NmUlte//kDV3t7eo89rIHObm4PbXIw8SeF5Sf9ENhgewHjg+V6q+z3AgcAGwN8k3RERj3ZeMCImAZMAWltbo62tre7KLlt+GSyEHXfckbb31L/+QFUqlejJ5zWQuc3NwW0uRp7uo88ARwKL0usI4IReqHsecGNErIiIJcA0YNde2K6ZmfVQnvsUngYOK6Duq4FzJQ0DRgB7Az8uoB4zM8spz30K2wE/AfYBAvgb8MWIeKLGelPIBtAbLWkecCbppreImBgRD0u6AXiQ7Elu50fEzHVoSy4eOtvMrLo85xQuA34OfDxNH0V2fmHv7laKiPG1NhwRPwB+kCOGdeahs83MastzTmFkRPw6Itak12+A9YsOzMzM+l6eI4U/Sfoq8Fuy7qNPAX+UtBlARHR3L4KZmQ0geZLCkenfz3YqP4osSWzXqxGZmVnD5Ln6aNu+CMTMzBovzzkFMzNrEk2XFDxKqplZdU2TFDxKqplZbXlONCPpMLLHcQLcEhHXFheSmZk1Ss0jBUnfBb4AzEqvUyR9p+jAzMys7+U5UvgIsFvH09ckXQzcD3ytyMDMzKzv5T2nsEnF+40LiMPMzPqBPEcK3wXulzQVENm5hdMLjcrMzBoiz81rU9LT0fZMRadFxKJCoyqQR0k1M6suz4nmmyNiYURck16LJN3cF8H1Jo+SamZWW9UjBUnrAyPJnoewKZS/Vd8EbNkHsZmZWR/rrvvos8CpwBbAfRXly4BzC4zJzMwapGpSiIifAD+RdHJE/KwPYzIzswbJc/XRUknHdS6MiEsKiKdwHvvIzKy6PElhz4r36wMHknUnDaik4LGPzMxqy3NJ6smV05I2IXsK24DkS1LNzKrrySipK4CaD96RdKGkxZJm1lhuT0lrJB3Rg1hy8yWpZma11TxSkHQtlDvihwC7AJfn2PZksquUqnYzSRoKnA38Ocf2zMysYHnOKfxPxfs1wNMRMa/WShExTdK4GoudDFzB689bmJlZg+Q5p3BL5bSk/SSdHhGfX5eKJW0JfBw4ACcFM7N+Ie9DdnYHjgY+CTwJXNkLdZ9DNo7S2lpXBkmaAEwAaGlpoVQq1V3Z/AXzAXj0sUcpvVz/+gNVe3t7jz6vgcxtbg5uczG6G+ZiB2B8ei0BfgcoIg7opbpbgd+mhDAaOETSmoi4qvOCETEJmATQ2toabW1tdVd2+YrLYQHssP0OtO1V//oDValUoief10DmNjcHt7kY3R0pPALcChwaEXMAJH2xtyqOiPIVTJImA9d1lRB6m29eMzOrrruk8AngKGCqpBvI7k3IfV2npClAG9mAevOAM4HhABExsacB95RvXjMzq627sY+uAq6SNAr4GNngeG+RdB7wh4jo9jLSiBifN4iI+HTeZc3MrDg1b16LiBURcVlEfBQYS/Z85tMKj8zMzPpcXXc0R8SLETEpIg4sKiAzM2ucngxzYWZmg5STgpmZlTVdUvAoqWZm1TVNUvAoqWZmtTVNUjAzs9qcFMzMrMxJwczMypwUzMyszEnBzMzKmi4peJRUM7PqmiYpeJRUM7PamiYpmJlZbU2TFP78eDbS95wX5jQ4EjOz/qtpksLSlUsBWLlmZYMjMTPrv5omKZiZWW1OCmZmVtZ0ScGXpJqZVdc0ScGjpJqZ1dY0ScHMzGorLClIulDSYkkzq8w/RtKDkmZIul3SrkXFYmZm+RR5pDAZOKib+U8C+0fEu4D/AiYVGIuZmeUwrKgNR8Q0SeO6mX97xeQdwNiiYjEzs3wKSwp1OhH4U7WZkiYAEwBaWloolUp1V7Bq1SoAFixc0KP1B6r29vamai+4zc3CbS5Gw5OCpAPIksJ+1ZaJiEmk7qXW1tZoa2uru54R946AVTDmrWPoyfoDValUaqr2gtvcLNzmYjQ0KUh6N3A+cHBEPF9wXUVu3sxsUGjYJamStgauBI6NiEeLrm/FqhUALHllSdFVmZkNWIUdKUiaArQBoyXNA84EhgNExETgG8DmwC/Sr/g1EdFaVDwdA+Jd9chVRVVhZjbgFXn10fga808CTiqqfjMzq5/vaDYzszInBTMzK3NSMDOzMicFMzMrc1IwM7MyJwUzMytzUjAzszInBTMzK3NSMDOzMicFMzMrc1IwM7MyJwUzMytzUjAzszInBTMzK3NSMDOzMicFMzMrc1IwM7MyJwUzMytzUjAzszInBTMzK3NSMDOzssKSgqQLJS2WNLPKfEn6qaQ5kh6UtEdRsXQ2f9n8vqrKzGxAKfJIYTJwUDfzDwa2T68JwHkFxvI6Y388lkMvO5RLH7yUw397OA8seoC1sZaHn3sYgIjoq1DMzPqVYUVtOCKmSRrXzSIfAy6J7Bv4DkmbSBoTEQuLiqnS9Y9dz/WPXQ/A1bOvLpevP2x9Xl3zKgBbvWkrhg8dzhANoX1VO4vaF7HT6J2Yv2w+y1ctZ9P1N2XE0BFsMHwDVr+2mvWHrc8QZXlWUjm5DNGQcnlnQbEJ6OWXX2bkQyPfWG8/S3ySXj+NqixZW7U2D2Zuc3Noe1MbbbQVWkdhSSGHLYG5FdPzUtkbkoKkCWRHE7S0tFAqlequ7A/v/QMf/9vHay73vs3ex9xX5rLo1UVst952DNdw1sZalg9fzls2fgubaTNGjhwJI2HUsFGMGjaK1WtXI8SaWMOQdPAVRPbFJlgba7v98l+XL8Ba1qy3hmHqYjer2Hrr0fmzecNnFVBPqFXbPIi5zc1h5NqRPfr+q8eA+EQjYhIwCaC1tTXa2tp6tJ2pI6bS03UHqlKp5DY3Abe5OfRFmxt59dF8YKuK6bGpzMzMGqSRSeEa4Lh0FdI+wNK+Op9gZmZdK6z7SNIUoA0YLWkecCYwHCAiJgJ/BA4B5gAvAycUFYuZmeVT5NVH42vMD+DzRdVvZmb18x3NZmZW5qRgZmZlTgpmZlbmpGBmZmXqb8Md1CLpOeDpHq4+GljSi+EMBG5zc3Cbm8O6tHmbiHhzrYUGXFJYF5LuiYjWRsfRl9zm5uA2N4e+aLO7j8zMrMxJwczMypotKUxqdAAN4DY3B7e5ORTe5qY6p2BmZt1rtiMFMzPrhpOCmZmVNU1SkHSQpNmS5kj6aqPjqYekrSRNlTRL0kOSvpDKN5N0k6TH0r+bpnJJ+mlq64OS9qjY1vFp+cckHV9R/h5JM9I6P1Xn52M2iKShku6XdF2a3lbSnSnO30kakcrXS9Nz0vxxFds4PZXPlvThivJ+9zeRHkv7v5IekfSwpPcO9v0s6Yvp73qmpCmS1h9s+1nShZIWS5pZUVb4fq1WR7ciYtC/gKHA48B2wAjgAWCXRsdVR/xjgD3S+42AR4FdgO8DX03lXwXOTu8PAf5E9hDLfYA7U/lmwBPp303T+03TvLvSskrrHtzodqe4/h24DLguTf8eOCq9nwj8S3r/r8DE9P4o4Hfp/S5pf68HbJv+Dob2178J4GLgpPR+BLDJYN7PZI/gfRLYoGL/fnqw7Wfg/cAewMyKssL3a7U6uo210f8J+miHvBe4sWL6dOD0Rse1Du25GvhHYDYwJpWNAWan978ExlcsPzvNHw/8sqL8l6lsDPBIRfnrlmtgO8cCNwMfAK5Lf/BLgGGd9ytwI/De9H5YWk6d93XHcv3xbwLYOH1BqlP5oN3P/P1Z7Zul/XYd8OHBuJ+Bcbw+KRS+X6vV0d2rWbqPOv7wOsxLZQNOOlzeHbgTaIm/P61uEdCS3ldrb3fl87oob7RzgK8Aa9P05sBLEbEmTVfGWW5bmr80LV/vZ9FI2wLPARelLrPzJY1iEO/niJgP/A/wDLCQbL/dy+Dezx36Yr9Wq6OqZkkKg4KkDYErgFMjYlnlvMh+Cgya64slHQosjoh7Gx1LHxpG1sVwXkTsDqwgO+QvG4T7eVPgY2QJcQtgFHBQQ4NqgL7Yr3nraJakMB/YqmJ6bCobMCQNJ0sIl0bElan4WUlj0vwxwOJUXq293ZWP7aK8kfYFDpP0FPBbsi6knwCbSOp4YmBlnOW2pfkbA89T/2fRSPOAeRFxZ5r+X7IkMZj38weBJyPiuYhYDVxJtu8H837u0Bf7tVodVTVLUrgb2D5d0TCC7ATVNQ2OKbd0JcEFwMMR8aOKWdcAHVcgHE92rqGj/Lh0FcM+wNJ0CHkj8CFJm6ZfaB8i629dCCyTtE+q67iKbTVERJweEWMjYhzZ/vq/iDgGmAockRbr3OaOz+KItHyk8qPSVSvbAtuTnZTrd38TEbEImCtpx1R0IDCLQbyfybqN9pE0MsXU0eZBu58r9MV+rVZHdY08ydTHJ3kOIbtq53HgjEbHU2fs+5Ed9j0ITE+vQ8j6Um8GHgP+AmyWlhfw89TWGUBrxbY+A8xJrxMqyluBmWmdc+l0srPB7W/j71cfbUf2n30OcDmwXipfP03PSfO3q1j/jNSu2VRcbdMf/yaA3YB70r6+iuwqk0G9n4FvAo+kuH5NdgXRoNrPwBSycyaryY4IT+yL/Vqtju5eHubCzMzKmqX7yMzMcnBSMDOzMicFMzMrc1IwM7MyJwUzMytzUrB+RVJI+mHF9JclndVL254s6YjaS65zPZ9UNsLp1KLrqhHHU5JGNzIGG3icFKy/WQl8or99mVXcXZvHicA/R8QBRcVjVhQnBetv1pA9h/aLnWd0/qUvqT392ybpFklXS3pC0vckHSPprjTG/NsqNvNBSfdIejSNr9TxzIYfSLo7jV//2Yrt3irpGrK7bDvHMz5tf6aks1PZN8huNrxA0g86LT9G0jRJ09M670vl56WYHpL0zYrln5L03bT8PZL2kHSjpMclfa4ixmmSrlf2zICJkt7w/1rSP6XPY7qkX6Y2D02f6czUjjd85tZ86vn1Y9ZXfg48KOn7dayzK7Az8ALZOPPnR8Reyh5IdDJwalpuHLAX8DZgqqS3kw0LsDQi9pS0HvBXSX9Oy+8BvDMinqysTNIWwNnAe4AXgT9LOjwiviXpA8CXI+KeTjEeTTYswX9LGgqMTOVnRMQLqexmSe+OiAfTvGciYjdJPwYmk40LtD7Z3asT0zJ7kT1P4GngBuATZOMmdcS6M/ApYN+IWC3pF8AxwEPAlhHxzrTcJrU/ZhvsfKRg/U5kI8BeApxSx2p3R8TCiFhJdqt/x5f6DLJE0OH3EbE2Ih4jSx47kY0hc5yk6WRDkm9ONnYOwF2dE0KyJ1CKbCC3NcClZA9S6TZG4IR0juRdEbE8lR8p6T7gfuAdZF/wHTrG6ZlB9rCV5RHxHLCy4kv8roh4IiJeIxtOYb9O9R5IlrzuTm08kGwYiSeA7ST9TNJBwDKs6flIwfqrc4D7gIsqytaQfsikLpIRFfNWVrxfWzG9ltf/nXce1yXIxpo5OSJurJwhqY1s+OpeERHTJL0f+AgwWdKPgFuBLwN7RsSLkiaTHQl0qGxH5zZ2tKurNlUScHFEnN45Jkm7kj3U5nPAkWRj61gT85GC9UsR8QLZIxlPrCh+iuwXL8BhwPAebPqTkoak8wzbkQ2ediPwL8qGJ0fSDsoebtOdu4D9JY1O3T7jgVu6W0HSNsCzEfEr4Hyyrqk3kSWepZJagIN70Ka9lI0COoSsm+i2TvNvBo6Q9JYUx2aStkkn84dExBXA11M81uR8pGD92Q+Bf6uY/hVwtaQHyPrOe/Ir/hmyL/Q3AZ+LiFclnU/WxXRfGnr4OeDw7jYSEQuVPQR+Ktkv8esjotawxG3Af0haDbQDx0XEk5LuJxsldC7w1x606W6ykTHfnuL5Q6dYZ0n6Otl5jyFkI3V+HniF7ClvHT8O33AkYc3Ho6SaDWCpi+vLEXFog0OxQcLdR2ZmVuYjBTMzK/ORgpmZlTkpmJlZmZOCmZmVOSmYmVmZk4KZmZX9f5lOHQg+0jf5AAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Number of samples N_samples in time for input A, try N_samples in N_samples_arr\n", "N_steps = 1000\n", "\n", "N_min = 10\n", "N_max = 100000\n", "n_incr = (N_max / N_min)**(1 / N_steps)\n", "N_samples_arr = []\n", "for s in range(N_steps + 1):\n", " n = int(N_min * n_incr**s)\n", " N_samples_arr.append(n)\n", " \n", "N_samples_arr_log = np.log10(N_samples_arr)\n", "\n", "# Input signal\n", "sigma = 1.0\n", "expected_pow_mean = sigma**2\n", "\n", "# Auto correlator mean(A * A)\n", "auto_mean_arr = []\n", "auto_mean_SNR_arr = []\n", "auto_mean_SNR_dB_arr = []\n", "for N_samples in N_samples_arr:\n", " # Signal input A\n", " sA = np.random.randn(N_samples)\n", " sA *= sigma / np.std(sA)\n", "\n", " # Auto correlate A\n", " # . the auto_mean is the mean power\n", " auto_mean = np.mean(sA * sA)\n", " auto_mean_arr.append(auto_mean)\n", " # . the np.std(sA * sA) is not useful, because for powers all info is already in the auto_mean\n", "\n", " # Accuracy of the power measurement\n", " auto_mean_SNR = auto_mean / np.abs(auto_mean - expected_pow_mean)\n", " auto_mean_SNR_dB = 10 * np.log10(auto_mean_SNR)\n", " auto_mean_SNR_arr.append(auto_mean_SNR)\n", " auto_mean_SNR_dB_arr.append(auto_mean_SNR_dB)\n", " \n", " #print(f\"{N_samples}, {auto_mean:9.6f}, {auto_mean_SNR_dB:.0f}\")\n", " \n", "# Determine accuracy of the auto_mean by using N_measure to measure auto_mean_std using std()\n", "# instead of using auto_mean_SNR = auto_mean - expected_pow_mean\n", "N_measure = 10\n", "\n", "auto_mean_std_log10_arr = []\n", "for N_samples in N_samples_arr:\n", " am_arr = []\n", " for R in range(N_measure):\n", " # Signal input A\n", " sA = np.random.randn(N_samples)\n", " sA *= sigma / np.std(sA)\n", "\n", " # Auto correlate A\n", " am = np.mean(sA * sA)\n", " am_arr.append(am)\n", " auto_mean_std = np.std(np.array(am_arr))\n", " auto_mean_std_log10 = 10 * np.log10(auto_mean_std)\n", " auto_mean_std_log10_arr.append(auto_mean_std_log10)\n", "\n", "\n", "plt.figure(1)\n", "plt.plot(N_samples_arr, auto_mean_arr, 'g')\n", "plt.title(\"Auto correlator mean\")\n", "plt.xlabel(\"Number of samples\")\n", "plt.ylabel(\"Auto power mean\")\n", "plt.grid()\n", "\n", "plt.figure(2)\n", "fit_coef = np.polyfit(N_samples_arr_log, auto_mean_SNR_dB_arr, 1)\n", "fit_p = np.poly1d(fit_coef)\n", "fit_line = fit_p(N_samples_arr_log)\n", "plt.plot(N_samples_arr_log, auto_mean_SNR_dB_arr, 'r', N_samples_arr_log, fit_line, 'b--')\n", "plt.title(\"Auto correlator (%3.1f dB/decade)\" % fit_p[1])\n", "plt.xlabel(\"Number of samples (log10)\")\n", "plt.ylabel(\"SNR of power measurement [dB]\")\n", "plt.grid()\n", " \n", "plt.figure(3)\n", "fit_coef = np.polyfit(N_samples_arr_log, auto_mean_std_log10_arr, 1)\n", "fit_p = np.poly1d(fit_coef)\n", "fit_line = fit_p(N_samples_arr_log)\n", "plt.plot(N_samples_arr_log, auto_mean_std_log10_arr, 'g', N_samples_arr_log, fit_line, 'b--')\n", "plt.title(\"Auto correlator mean power std (%3.1f dB/decade)\" % fit_p[1])\n", "plt.xlabel(\"Number of samples (log10)\")\n", "plt.ylabel(\"Auto mean power std (log10)\")\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "5f5e3a0d", "metadata": {}, "source": [ "**Conclusion:**\n", "The summation of power values does not improve the 'coherent' SNR, but it does improve the 'incoherent' SNR, so the accuracy of the power measurement. Therefore the SNR for the auto correlation is defined as the accuracy of the mean power measurement. This 'incoherent' SNR improves by N, so by 10dB / decade, and applies to:\n", "* subband statistics (SST), averaging powers in time\n", "* beamlet statistics (SST), averaging powers in time\n", "* incoherent array (power) beamformer (IAB), averaging powers in space" ] }, { "cell_type": "markdown", "id": "f4be5736", "metadata": {}, "source": [ "### 3.2 Cross powers" ] }, { "cell_type": "code", "execution_count": 6, "id": "470fd269", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SNR input = -20.000 dB\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Number of samples N_samples in time for input A and input B, try N_samples in N_samples_arr\n", "N_steps = 100\n", "\n", "N_min = 100\n", "N_max = 10000000\n", "n_incr = (N_max / N_min)**(1 / N_steps)\n", "N_samples_arr = []\n", "for s in range(N_steps + 1):\n", " n = int(N_min * n_incr**s)\n", " N_samples_arr.append(n)\n", "N_samples_arr_log = np.log10(N_samples_arr)\n", "\n", "# Input signal\n", "sigma_coh = 0.1\n", "pow_coh = sigma_coh**2\n", "sigma_incoh = 1.0\n", "\n", "input_SNR = (sigma_coh / sigma_incoh)**2\n", "input_SNR_dB = 10 * np.log10(input_SNR)\n", "print(f\"SNR input = {input_SNR_dB:.3f} dB\")\n", "\n", "# Correlator mean(A * B)\n", "cross_coh_mean_arr = []\n", "cross_incoh_mean_arr = []\n", "cross_sys_mean_arr = []\n", "cross_SNR_arr = []\n", "cross_SNR_dB_arr = []\n", "for N_samples in N_samples_arr:\n", " si_coh = np.random.randn(N_samples)\n", " si_coh *= sigma_coh / np.std(si_coh)\n", "\n", " # Signal input A\n", " sA_incoh = np.random.randn(N_samples)\n", " sA_incoh *= sigma_incoh / np.std(sA_incoh)\n", " sA_sys = sA_incoh + si_coh\n", "\n", " # Signal input B\n", " sB_incoh = np.random.randn(N_samples)\n", " sB_incoh *= sigma_incoh / np.std(sB_incoh)\n", " sB_sys = sB_incoh + si_coh\n", " \n", " # Correlate A and B\n", " cross_coh_mean = np.mean(si_coh * si_coh)\n", " cross_coh_mean_arr.append(cross_coh_mean)\n", " cross_incoh_mean = np.mean(sA_incoh * sB_incoh)\n", " cross_incoh_mean_arr.append(cross_incoh_mean)\n", " cross_sys_mean = np.mean(sA_sys * sB_sys)\n", " cross_sys_mean_arr.append(cross_sys_mean)\n", " #print(f\"{N_samples}, {cross_coh_mean:9.6f}, {cross_incoh_mean:9.6f}, {cross_sys_mean:9.6f}\")\n", "\n", " # SNR of the coherent correlator.\n", " # * The SNR of the correlator improves with sqrt(N), so factor 10 = 10dB when N increases by\n", " # factor 100 = 20dB. Use select to try different SNR definitions. The SNR definitions are \n", " # equivalent.\n", " # * The cross_sys_mean is available from measured data, but the cross_coh_mean and\n", " # cross_incoh_mean cannot be distinghuised in measured data, therefore the SNR can only be\n", " # calculated in a model.\n", " select = 1\n", " # . using cross_coh_mean / cross_incoh_mean shows the cross_SNR improvement for all N_max\n", " if select == 1:\n", " cross_SNR = np.abs(cross_coh_mean / cross_incoh_mean)\n", " # . the cross_coh_mean and cross_sys_mean become pow_coh, so constant > 0. Therefor it is\n", " # also possible to define relative cross_SNR using 1 divided by the value of cross_incoh_mean\n", " # or the error in cross_coh_mean, which both go to zero.\n", " if select == 20:\n", " cross_SNR = np.abs(1 / cross_incoh_mean)\n", " if select == 21:\n", " cross_SNR = np.abs(1 / (cross_sys_mean - cross_coh_mean)) \n", " # . using cross_sys_mean requires that N_max > input_SNR to see the improvement in cross_SNR,\n", " # because for lower N_samples the cross_sys_mean is still dominated by cross_incoh_mean and\n", " # then thus cross_SNR = 1\n", " if select == 30:\n", " cross_SNR = np.abs(cross_sys_mean / cross_incoh_mean)\n", " if select == 31:\n", " cross_SNR = np.abs(cross_sys_mean / (cross_sys_mean - cross_coh_mean))\n", "\n", " cross_SNR_dB = 10 * np.log10(cross_SNR)\n", " cross_SNR_arr.append(cross_SNR)\n", " cross_SNR_dB_arr.append(cross_SNR_dB)\n", " #print(f\"{N_samples}, correlator SNR = {cross_SNR_dB:.0f} dB\")\n", " \n", "plt.figure(1)\n", "plt.plot(N_samples_arr, cross_coh_mean_arr, 'g', N_samples_arr, cross_incoh_mean_arr, 'b', N_samples_arr, cross_sys_mean_arr, 'r')\n", "plt.title(\"Correlator mean\")\n", "plt.xlabel(\"Number of samples\")\n", "plt.ylabel(\"Cross power mean\")\n", "plt.legend(['cross_coh', 'cross_incoh', 'cross_sys'])\n", "plt.grid()\n", "\n", "plt.figure(2)\n", "fit_coef = np.polyfit(N_samples_arr_log, cross_SNR_dB_arr, 1)\n", "fit_p = np.poly1d(fit_coef)\n", "fit_line = fit_p(N_samples_arr_log)\n", "plt.plot(N_samples_arr_log, cross_SNR_dB_arr, 'r', N_samples_arr_log, fit_line, 'b--')\n", "plt.title(\"Correlator SNR (%3.1f dB/decade)\" % fit_p[1])\n", "plt.xlabel(\"Number of samples (log10)\")\n", "plt.ylabel(\"SNR of coherent correlator [dB]\")\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "48b355ae", "metadata": {}, "source": [ "The expected cross correlation power is the power of the coherent input, because the other terms are uncorrelated and become zero:\n", "\n", "E{(x+a)(y+a)} = E{xy} + E{xa} + E{ya} + E{a^2} = sigma_a^2 = var(a)\n", "\n", "where:\n", "* x = sA_incoh\n", "* y = sB_incoh\n", "* a = si_coh\n", "\n", "The std of E{xy} is a measure of how close E{xy} is to zero. The var of E{xy} reduces with N_samples, so the std(E{xy}) reduces with sqrt(N_samples). Similar for E{xa} and E{ya}. The var(a) is constant and the std of E{xy} has the same (power) units as E{xy}, so therefore the 'coherent' SNR of the correlator depends on the accuracy of E{xy}, and therefore the 'coherent' SNR improves with sqrt(N_samples). This agrees with cross_SNR in the simulation.\n", "\n", "Note that var(E{xy}) is not E{xyxy}." ] }, { "cell_type": "markdown", "id": "4fc1cbf5", "metadata": {}, "source": [ "**Conclusion:**\n", "The expected coherent cross power of the cross correlator is pow_coh. The measurement of cross_coh_mean = pow_coh becomes more accurate when N_samples increases. The incoherent cross power is cross_incoh_mean and goes to zero. The cross power is a power statistics, but the two inputs are voltages so their phase information is preserved and therefore the correlator also has a 'coherent' SNR improvement. The 'coherent' SNR of the coherent correlator is proportional to 1 / cross_incoh_mean. Dividing by almost zero causes the 'coherent' SNR to fluctuate, but on average the 'coherent' SNR of the coherent signal improves by sqrt(N_samples), so by 5dB / decade." ] }, { "cell_type": "code", "execution_count": null, "id": "e271fe26", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }