equalization.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "equalization.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/github/planewave/coherent_receiver_with_CNN/blob/master/equalization.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "BJ1kM7UQan4C",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "# from matplotlib import pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "8IkAZQKaZ-2-",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "def rrcosdesign(beta, span, sps):\n",
        "    \"\"\"\n",
        "    returns the coefficients, that correspond to a square-root raised \n",
        "    cosine FIR filter with rolloff factor specified by beta. The filter \n",
        "    is truncated to span symbols, and each symbol period contains sps \n",
        "    samples. The order of the filter, sps*span, must be even. \n",
        "    modified from:\n",
        "    https://github.com/veeresht/CommPy/blob/master/commpy/filters.py\n",
        "    \"\"\"\n",
        "    n = sps*span\n",
        "    rrc = np.zeros(n, dtype=float)\n",
        "        \n",
        "    for x in np.arange(n):\n",
        "        t = (x-n/2)/sps\n",
        "        if t == 0.0:\n",
        "            rrc[x] = 1.0 - beta + (4*beta/np.pi)\n",
        "        elif beta != 0 and t == 1/(4*beta):\n",
        "            rrc[x] = ((beta/np.sqrt(2))*(((1+2/np.pi)*(np.sin(np.pi/\n",
        "                     (4*beta)))) + ((1-2/np.pi)*(np.cos(np.pi/(4*beta))))))\n",
        "        elif beta != 0 and t == -1/(4*beta):\n",
        "            rrc[x] = ((beta/np.sqrt(2))*(((1+2/np.pi)*(np.sin(np.pi/\n",
        "                     (4*beta)))) + ((1-2/np.pi)*(np.cos(np.pi/(4*beta))))))\n",
        "        else:\n",
        "            rrc[x] = ((np.sin(np.pi*t*(1-beta))+4*beta*(t)*np.cos(np.pi*\n",
        "                     t*(1+beta)))/(np.pi*t*(1-(4*beta*t)*(4*beta*t))))\n",
        "        \n",
        "    return rrc\n",
        "\n",
        "def demod_qpsk(sig):\n",
        "    \"\"\"\n",
        "    demodulation of QPSK signal\n",
        "    complex 1D array input\n",
        "    soft max decision output\n",
        "    \"\"\"\n",
        "    out = np.zeros((sig.size, 4))\n",
        "    x = sig.real\n",
        "    y = sig.imag\n",
        "    out[:, 0] = y*(x>y)+x*(x<=y)\n",
        "    out[:, 1] = y*(-x>y)-x*(-x<=y)\n",
        "    out[:, 2] = -y*(-x>-y)-x*(-x<=-y)\n",
        "    out[:, 3] = -y*(x>-y)+x*(x<=-y)\n",
        "    e_x = np.exp(out-out.max(axis = 1).reshape(-1,1))\n",
        "    soft_dc = e_x/e_x.sum(axis = 1).reshape(-1,1)\n",
        "    hard_dc = np.argmax(soft_dc, axis=1)\n",
        "    return hard_dc, soft_dc\n",
        "\n",
        "def upsample(x, n):\n",
        "    \"\"\"\n",
        "    increase sample rate by integer factor\n",
        "    y = upsample(x,n) increases the sample rate of x by \n",
        "    inserting n – 1 zeros between samples.\n",
        "    input is 1D numpy array\n",
        "    \n",
        "    \"\"\"\n",
        "    zo = np.zeros((len(x), n), dtype=x.dtype)\n",
        "    zo[:,0] += x\n",
        "    return zo.flatten()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "7sK94qW7bQZQ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "M = 4\n",
        "SYMB = 512 # num of symbols\n",
        "msg = np.random.randint(0, M, SYMB)\n",
        "sig_mod = np.exp(1j*(np.pi/M+msg*(2*np.pi/M)))\n",
        "# pluse shaping \n",
        "beta = 0.4\n",
        "span = 8\n",
        "sps = 16\n",
        "rrc = rrcosdesign(beta, span, sps)\n",
        "sig_up = upsample(sig_mod, sps)\n",
        "sig_pulse = np.convolve(sig_up, rrc)\n",
        "# plt.plot(sig_pulse.real)\n",
        "# plt.plot(sig_pulse.imag)\n",
        "# plt.show()\n",
        "\n",
        "\n",
        "# up convert\n",
        "fc = 7.1e3\n",
        "baud = 1e3\n",
        "fs = baud*sps # 24kHz\n",
        "samp_len = len(sig_pulse)\n",
        "time = np.arange(samp_len)/fs\n",
        "carrier = np.exp(1j*(2*np.pi*fc*time))\n",
        "sig_pass = np.real(sig_pulse*carrier)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "jmeZMKbmMI--",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# channel\n",
        "hp = np.zeros(5*32) # 5 ms\n",
        "hp[0], hp[38], hp[90], hp[127] = 1, 0.0, 0.0, 0.0\n",
        "hp[0], hp[38], hp[90], hp[127] = 1, 0.4, 0.6, 0.3\n",
        "sig_ch = np.convolve(sig_pass, hp)[0:sig_pass.size]+ \\\n",
        "        0.3*np.random.randn(sig_pass.size)\n",
        "# plt.plot(hp)\n",
        "# plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "-caaiCzI7ZK_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 380
        },
        "outputId": "b66bf82a-d320-4cad-ab8c-1a3ebe36dbd1"
      },
      "cell_type": "code",
      "source": [
        "# receiver side\n",
        "# down convert to baseband\n",
        "sig_base = sig_ch*np.conj(carrier)\n",
        "# sig_filt = sig.upfirdn(rrc, sig_base)\n",
        "# sig_dn = sig.upfirdn(rrc, sig_base, 1, sps)[span:-span]\n",
        "\n",
        "sig_filt = np.convolve(sig_base, rrc)\n",
        "sig_timing = sig_filt[span*sps:-span*sps:sps]\n",
        "\n",
        "# plt.scatter(sig_base.real, sig_base.imag, marker='.')\n",
        "plt.scatter(sig_timing.real, sig_timing.imag, marker='.')\n",
        "plt.axis('equal')\n",
        "plt.title('Constellation diagram')\n",
        "# plt.ylim(-20, 20)\n",
        "# plt.xlim(-20, 20)\n",
        "plt.show()\n",
        "\n",
        "# deodulation\n",
        "demod  = demod_qpsk(sig_timing)[0]\n",
        "symb_acc = np.sum(msg == demod)/SYMB\n",
        "symb_acc\n",
        "# print(msg, demod)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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o8U4QrFas0sHMynxlOdiLyVLOvbGqcSw1aeAOnH39IRw91YTC8VlD9vPV8znw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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fe60770ea58>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.85546875"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "metadata": {
        "id": "r9rTUiIeoaAv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 55
        },
        "outputId": "715ce81e-14e1-4796-91c8-bc60282465eb"
      },
      "cell_type": "code",
      "source": [
        "from os import path\n",
        "from wheel.pep425tags import get_abbr_impl, get_impl_ver, get_abi_tag\n",
        "platform = '{}{}-{}'.format(get_abbr_impl(), get_impl_ver(), get_abi_tag())\n",
        "\n",
        "accelerator = 'cu90' if path.exists('/opt/bin/nvidia-smi') else 'cpu'\n",
        "\n",
        "!pip -q install http://download.pytorch.org/whl/{accelerator}/torch-0.4.0-{platform}-linux_x86_64.whl\n",
        "import torch\n",
        "from torch import nn\n",
        "device = torch.device(\"cuda:0\")\n",
        "dtype = torch.float\n"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tcmalloc: large alloc 1073750016 bytes == 0x5dc2e000 @  0x7f422fe591c4 0x46d6a4 0x5fcbcc 0x4c494d 0x54f3c4 0x553aaf 0x54e4c8 0x54f4f6 0x553aaf 0x54efc1 0x54f24d 0x553aaf 0x54efc1 0x54f24d 0x553aaf 0x54efc1 0x54f24d 0x551ee0 0x54e4c8 0x54f4f6 0x553aaf 0x54efc1 0x54f24d 0x551ee0 0x54efc1 0x54f24d 0x551ee0 0x54e4c8 0x54f4f6 0x553aaf 0x54e4c8\r\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "S6WqIUahfVZH",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class NET(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(NET, self).__init__()\n",
        "        self.cnn = nn.Sequential(\n",
        "            nn.Conv1d(2, 32, 5, 1, 2),\n",
        "            nn.ReLU(),\n",
        "#             nn.MaxPool1d(2),\n",
        "            nn.Conv1d(32, 32, 5, 1, 2),\n",
        "            nn.ReLU(),\n",
        "            nn.MaxPool1d(2),\n",
        "            nn.Conv1d(32, 32, 3, 1, 1),\n",
        "            nn.ReLU(),\n",
        "            nn.MaxPool1d(2),\n",
        "            nn.Conv1d(32, 16, 3, 1, 1),\n",
        "            nn.ReLU(),\n",
        "            nn.MaxPool1d(2),\n",
        "            nn.Conv1d(16, 8, 3, 1, 1),\n",
        "            nn.ReLU(),\n",
        "            )\n",
        "\n",
        "        self.lin = nn.Linear(32, 2) # [512, 2]\n",
        "        self.feedback = nn.Linear(4, 1)\n",
        "\n",
        "    def forward(self, x_in, dcsn):\n",
        "        cnn_out = self.cnn(x_in)\n",
        "        lin_out = self.lin(cnn_out.view(cnn_out.size(0), -1))\n",
        "        return lin_out-self.feedback(dcsn).squeeze() # [512, 2, 1] -> [512, 2]\n",
        "\n",
        "net = NET()\n",
        "net.cuda()\n",
        "LR = 1e-4 # learning rate    \n",
        "optimizer = torch.optim.Adam(net.parameters(), lr=LR)   # optimize all cnn parameters\n",
        "# loss_func = nn.CrossEntropyLoss()\n",
        "# target = torch.tensor(msg, device=device, dtype=torch.long)\n",
        "loss_func = nn.MSELoss()\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "qTtr883KrAFL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "d5370b0d-5a41-4131-b8e3-ac954f3c004f"
      },
      "cell_type": "code",
      "source": [
        "cnn = nn.Sequential(\n",
        "    nn.Conv1d(2, 32, 5, 1, 2),\n",
        "    nn.ReLU(),\n",
        "    nn.MaxPool1d(2),\n",
        "    nn.Conv1d(32, 32, 5, 1, 2),\n",
        "    nn.ReLU(),\n",
        "    nn.MaxPool1d(2),\n",
        "    nn.Conv1d(32, 16, 3, 1, 1),\n",
        "    nn.ReLU(),\n",
        "    nn.MaxPool1d(2),\n",
        "    nn.Conv1d(16, 8, 3, 1, 1),\n",
        "    nn.ReLU(),\n",
        "    ).cuda()\n",
        "\n",
        "feedback = nn.Linear(4, 1).cuda()\n",
        "feedback(dcsn_in_ts).shape\n",
        "# cnn(net_in_ts).shape\n",
        "# dcsn_in_ts.shape"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([512, 2, 1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "metadata": {
        "id": "B_ixyX9hyoUN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "outputId": "449ef737-bf8e-4f10-fb2d-c4d0e15321cd"
      },
      "cell_type": "code",
      "source": [
        "# training\n",
        "net_in = np.zeros((SYMB, 2, span*4)) # span*4: 4 samples per symbol is used\n",
        "dcsn_in = np.zeros((SYMB, 2, 4))\n",
        "step = int(sps/4) # for net_in down sampling\n",
        "for epoch in range(4000):\n",
        "    msg = np.random.randint(0, M, SYMB)\n",
        "    sig_mod = np.exp(1j*(np.pi/M+msg*(2*np.pi/M)))\n",
        "    sig_up = upsample(sig_mod, sps)\n",
        "    sig_pulse = np.convolve(sig_up, rrc)\n",
        "    sig_pass = np.real(sig_pulse*carrier)\n",
        "    sig_ch = np.convolve(sig_pass, hp)[0:sig_pass.size]+ \\\n",
        "        0.5*np.random.randn(sig_pass.size)\n",
        "    sig_base = sig_ch*np.conj(carrier)\n",
        "    sig_filt = np.convolve(sig_base, rrc)\n",
        "#     for symb_ind in range(SYMB):\n",
        "#         net_in[symb_ind, 0, :] = sig_base[symb_ind*sps: symb_ind*sps+span*sps: step].real\n",
        "#         net_in[symb_ind, 1, :] = sig_base[symb_ind*sps: symb_ind*sps+span*sps: step].imag\n",
        "    for symb_ind in range(SYMB):\n",
        "        net_in[symb_ind, 0, :] = sig_filt[64+symb_ind*sps:64+symb_ind*sps+span*sps:step].real\n",
        "        net_in[symb_ind, 1, :] = sig_filt[64+symb_ind*sps:64+symb_ind*sps+span*sps:step].imag\n",
        "    for symb_ind in range(4, SYMB):\n",
        "        dcsn_in[symb_ind, 0, :] = sig_mod[symb_ind-4:symb_ind].real\n",
        "        dcsn_in[symb_ind, 1, :] = sig_mod[symb_ind-4:symb_ind].imag\n",
        "        \n",
        "    net_in_ts = torch.tensor(net_in, device=device, dtype=dtype)/10\n",
        "    dcsn_in_ts = torch.tensor(dcsn_in, device=device, dtype=dtype)\n",
        "        \n",
        "    net_out = net(net_in_ts, dcsn_in_ts)\n",
        "    target = torch.tensor([sig_mod.real, sig_mod.imag], \n",
        "                          dtype=dtype, device=device).transpose(0, 1)\n",
        "    loss = loss_func(net_out, target)\n",
        "    optimizer.zero_grad()               # clear gradients for this training step\n",
        "    loss.backward()                     # backpropagation, compute gradients\n",
        "    optimizer.step()\n",
        "    \n",
        "    if epoch%400 == 0:\n",
        "#         prediction = torch.max(nn.functional.softmax(est, 1), 1)[1]\n",
        "#         accu = torch.sum(prediction == target).item()/prediction.size(0)\n",
        "#         print('Epoch:', epoch, 'accuracy:', accu)\n",
        "        \n",
        "        print('MSE: %7.3f'% loss.item())\n",
        "# \n"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "MSE:   0.091\n",
            "MSE:   0.079\n",
            "MSE:   0.084\n",
            "MSE:   0.085\n",
            "MSE:   0.087\n",
            "MSE:   0.081\n",
            "MSE:   0.074\n",
            "MSE:   0.081\n",
            "MSE:   0.078\n",
            "MSE:   0.082\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "AlY7s-Z9fk4y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 380
        },
        "outputId": "19a5fdf2-cd1e-4c0c-9b47-df14ef9c9755"
      },
      "cell_type": "code",
      "source": [
        "# net_out = net(rec)\n",
        "out_r = net_out[:, 0].detach().cpu().numpy()\n",
        "out_i = net_out[:, 1].detach().cpu().numpy()\n",
        "\n",
        "plt.scatter(out_r, out_i, marker='.')\n",
        "\n",
        "# plt.scatter(sig_base[symb_ind: symb_ind+320].real,\n",
        "#             sig_base[symb_ind: symb_ind+320].imag, marker='.')\n",
        "plt.axis('equal')\n",
        "plt.title('Constellation diagram')\n",
        "# plt.ylim(-20, 20)\n",
        "# plt.xlim(-20, 20)\n",
        "plt.show()\n",
        "\n",
        "# deodulation\n",
        "demod  = np.zeros_like(msg)\n",
        "for ind in range(SYMB):\n",
        "    if out_r[ind] >= 0:\n",
        "        demod[ind] = 0 if out_i[ind] >= 0 else 3\n",
        "    else:\n",
        "        demod[ind] = 1 if out_i[ind] >= 0 else 2\n",
        "        \n",
        "                \n",
        "symb_acc = np.sum(msg == demod)/SYMB\n",
        "print('accuracy: %7.3f'%symb_acc)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PcebMGaSmpmLHjh0oKyvD2LFjsWTJEmzYsAHr1q0DANxyyy0oLi42rNKEALF5Wcea/tPO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\nxMZQUBNCCCE2hoKaEEIIsTH/P/hpkgdc8ZZZAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fe57aaaec88>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "accuracy:   0.949\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Mv6CWhw3WwSk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 380
        },
        "outputId": "acb7bbf1-e9a1-4852-f3b7-4bac67042118"
      },
      "cell_type": "code",
      "source": [
        "# no equalization\n",
        "# plt.scatter(out_r, out_i, marker='.')\n",
        "\n",
        "sig_timing = sig_filt[span*sps:-span*sps:sps]\n",
        "\n",
        "plt.scatter(sig_timing.real, sig_timing.imag, marker='.')\n",
        "plt.axis('equal')\n",
        "plt.title('Constellation diagram')\n",
        "# plt.ylim(-20, 20)\n",
        "# plt.xlim(-20, 20)\n",
        "plt.show()\n",
        "\n",
        "# deodulation\n",
        "demod  = np.zeros_like(msg)\n",
        "for ind in range(SYMB):\n",
        "    if out_r[ind] >= 0:\n",
        "        demod[ind] = 0 if out_i[ind] >= 0 else 3\n",
        "    else:\n",
        "        demod[ind] = 1 if out_i[ind] >= 0 else 2\n",
        "        \n",
        "                \n",
        "demod  = demod_qpsk(sig_timing)[0]\n",
        "symb_acc = np.sum(msg == demod)/SYMB\n",
        "symb_acc"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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YbrqtblS5bW5muNZHFfkwOpBt23N16nKBFrw6Jsq5rJPC4XBY8hsdlJeX4+67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\nQgghDoAKmRBCCHEA/x/H8zy0in+hjwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fe57c7e1e48>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.80078125"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "metadata": {
        "id": "PGXWFScZ3zKe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "e87de5f0-d7cc-4227-afb3-f7a9ed203fae"
      },
      "cell_type": "code",
      "source": [
        "sig_mod[-4:-1:]\n"
      ],
      "execution_count": 195,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.70710678-0.70710678j,  0.70710678+0.70710678j,\n",
              "       -0.70710678+0.70710678j])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 195
        }
      ]
    }
  ]
}