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Expand file tree/ Copy pathModulationPy.pyMore file actions 451 lines (389 loc) · 15.5 KB / Copy pathModulationPy.pyFile metadata and controls451 lines (389 loc) · 15.5 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 # coding: utf-8 import numpy as np import matplotlib.pyplot as plt class Modem: def __init__(self, M, gray_map=True, bin_input=True, soft_decision=True, bin_output=True): N = np.log2(M) # bits per symbol if N != np.round(N): raise ValueError("M should be 2**n, with n=1, 2, 3...") if soft_decision == True and bin_output == False: raise ValueError("Non-binary output is available only for hard decision") self.M = M # modulation order self.N = int(N) # bits per symbol self.m = [i for i in range(self.M)] self.gray_map = gray_map self.bin_input = bin_input self.soft_decision = soft_decision self.bin_output = bin_output ''' SERVING METHODS ''' def __gray_encoding(self, dec_in): """ Encodes values by Gray encoding rule. Parameters ---------- dec_in : list of ints Input sequence of decimals to be encoded by Gray. Returns ------- gray_out: list of ints Output encoded by Gray sequence. """ bin_seq = [np.binary_repr(d, width=self.N) for d in dec_in] gray_out = [] for bin_i in bin_seq: gray_vals = [str(int(bin_i[idx]) ^ int(bin_i[idx - 1])) if idx != 0 else bin_i[0] for idx in range(0, len(bin_i))] gray_i = "".join(gray_vals) gray_out.append(int(gray_i, 2)) return gray_out def create_constellation(self, m, s): """ Creates signal constellation. Parameters ---------- m : list of ints Possible decimal values of the signal constellation (0 ... M-1). s : list of complex values Possible coordinates of the signal constellation. Returns ------- dict_out: dict Output dictionary where key is the bit sequence or decimal value and value is the complex coordinate. """ if self.bin_input == False and self.gray_map == False: dict_out = {k: v for k, v in zip(m, s)} elif self.bin_input == False and self.gray_map == True: mg = self.__gray_encoding(m) dict_out = {k: v for k, v in zip(mg, s)} elif self.bin_input == True and self.gray_map == False: mb = self.de2bin(m) dict_out = {k: v for k, v in zip(mb, s)} elif self.bin_input == True and self.gray_map == True: mg = self.__gray_encoding(m) mgb = self.de2bin(mg) dict_out = {k: v for k, v in zip(mgb, s)} return dict_out def llr_preparation(self): """ Creates the coordinates where either zeros or ones can be placed in the signal constellation.. Returns ------- zeros : list of lists of complex values The coordinates where zeros can be placed in the signal constellation. ones : list of lists of complex values The coordinates where ones can be placed in the signal constellation. """ code_book = self.code_book zeros = [[] for i in range(self.N)] ones = [[] for i in range(self.N)] bin_seq = self.de2bin(self.m) for bin_idx, bin_symb in enumerate(bin_seq): if self.bin_input == True: key = bin_symb else: key = bin_idx for possition, digit in enumerate(bin_symb): if digit == '0': zeros[possition].append(code_book[key]) else: ones[possition].append(code_book[key]) return zeros, ones ''' DEMODULATION ALGORITHMS ''' def __ApproxLLR(self, x, noise_var): """ Calculates approximate Log-likelihood Ratios (LLRs) [1]. Parameters ---------- x : 1-D ndarray of complex values Received complex-valued symbols to be demodulated. noise_var: float Additive noise variance. Returns ------- result: 1-D ndarray of floats Output LLRs. Reference: [1] Viterbi, A. J., "An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes," IEEE Journal on Selected Areas in Communications, vol. 16, No. 2, pp 260–264, Feb. 1998 """ zeros = self.zeros ones = self.ones LLR = [] for (zero_i, one_i) in zip(zeros, ones): num = [((np.real(x) - np.real(z)) ** 2) + ((np.imag(x) - np.imag(z)) ** 2) for z in zero_i] denum = [((np.real(x) - np.real(o)) ** 2) + ((np.imag(x) - np.imag(o)) ** 2) for o in one_i] num_post = np.amin(num, axis=0, keepdims=True) denum_post = np.amin(denum, axis=0, keepdims=True) llr = np.transpose(num_post[0]) - np.transpose(denum_post[0]) LLR.append(-llr / noise_var) result = np.zeros((len(x) * len(zeros))) for i, llr in enumerate(LLR): result[i::len(zeros)] = llr return result ''' METHODS TO EXECUTE ''' def modulate(self, msg): """ Modulates binary or decimal stream. Parameters ---------- x : 1-D ndarray of ints Decimal or binary stream to be modulated. Returns ------- modulated : 1-D array of complex values Modulated symbols (signal envelope). """ if (self.bin_input == True) and ((len(msg) % self.N) != 0): raise ValueError("The length of the binary input should be a multiple of log2(M)") if (self.bin_input == True) and ((max(msg) > 1.) or (min(msg) < 0.)): raise ValueError("The input values should be 0s or 1s only!") if (self.bin_input == False) and ((max(msg) > (self.M - 1)) or (min(msg) < 0.)): raise ValueError("The input values should be in following range: [0, ... M-1]!") if self.bin_input: msg = [str(bit) for bit in msg] splited = ["".join(msg[i:i + self.N]) for i in range(0, len(msg), self.N)] # subsequences of bits modulated = [self.code_book[s] for s in splited] else: modulated = [self.code_book[dec] for dec in msg] return np.array(modulated) def demodulate(self, x, noise_var=1.): """ Demodulates complex symbols. Yes, MathWorks company provides several algorithms to demodulate BPSK, QPSK, 8-PSK and other M-PSK modulations in hard output manner: https://www.mathworks.com/help/comm/ref/mpskdemodulatorbaseband.html However, to reduce the number of implemented schemes the following way is used in our project: - calculate LLRs (soft decision) - map LLR to bits according to the sign of LLR (inverse of NRZ) We guess the complexity issues are not the critical part due to hard output demodulators are not so popular. This phenomenon depends on channel decoders properties: e.g., Convolutional codes, Turbo convolutional codes and LDPC codes work better with LLR. Parameters ---------- x : 1-D ndarray of complex symbols Decimal or binary stream to be demodulated. noise_var: float Additive noise variance. Returns ------- result : 1-D array floats Demodulated message (LLRs or binary sequence). """ if self.soft_decision: result = self.__ApproxLLR(x, noise_var) else: if self.bin_output: llr = self.__ApproxLLR(x, noise_var) result = (np.sign(-llr) + 1) / 2 # NRZ-to-bin else: llr = self.__ApproxLLR(x, noise_var) result = self.bin2de((np.sign(-llr) + 1) / 2) return result class PSKModem(Modem): def __init__(self, M, phi=0, gray_map=True, bin_input=True, soft_decision=True, bin_output=True): super().__init__(M, gray_map, bin_input, soft_decision, bin_output) self.phi = phi # phase rotation self.s = list(np.exp(1j * self.phi + 1j * 2 * np.pi * np.array(self.m) / self.M)) self.code_book = self.create_constellation(self.m, self.s) self.zeros, self.ones = self.llr_preparation() def de2bin(self, decs): """ Converts values from decimal to binary representation. If the input is binary, the conversion from binary to decimal should be done before. Therefore, this supportive method is implemented. This method has an additional heuristic: the bit sequence of "even" modulation schemes (e.g., QPSK) should be read right to left. Parameters ---------- decs : list of ints Input decimal values. Returns ------- bin_out : list of ints Output binary sequences. """ if self.N % 2 == 0: bin_out = [np.binary_repr(d, width=self.N)[::-1] for d in decs] else: bin_out = [np.binary_repr(d, width=self.N) for d in decs] return bin_out def bin2de(self, bin_in): """ Converts values from binary to decimal representation. Parameters ---------- bin_in : list of ints Input binary values. Returns ------- dec_out : list of ints Output decimal values. """ dec_out = [] N = self.N # bits per modulation symbol (local variables are tiny bit faster) Ndecs = int(len(bin_in) / N) # length of the decimal output for i in range(Ndecs): bin_seq = bin_in[i * N:i * N + N] # binary equivalent of the one decimal value str_o = "".join([str(int(b)) for b in bin_seq]) # binary sequence to string if N % 2 == 0: str_o = str_o[::-1] dec_out.append(int(str_o, 2)) return dec_out def plot_const(self): """ Plots signal constellation """ const = self.code_book fig = plt.figure(figsize=(6, 4), dpi=150) for i in list(const): x = np.real(const[i]) y = np.imag(const[i]) plt.plot(x, y, 'o', color='green') if x < 0: h = 'right' xadd = -.03 else: h = 'left' xadd = .03 if y < 0: v = 'top' yadd = -.03 else: v = 'bottom' yadd = .03 if abs(x) < 1e-9 and abs(y) > 1e-9: h = 'center' elif abs(x) > 1e-9 and abs(y) < 1e-9: v = 'center' plt.annotate(i, (x + xadd, y + yadd), ha=h, va=v) if self.M == 2: M = 'B' elif self.M == 4: M = 'Q' else: M = str(self.M) + "-" if self.gray_map: mapping = 'Gray' else: mapping = 'Binary' if self.bin_input: inputs = 'Binary' else: inputs = 'Decimal' plt.grid() plt.axvline(linewidth=1.0, color='black') plt.axhline(linewidth=1.0, color='black') plt.axis([-1.5, 1.5, -1.5, 1.5]) plt.title(M + 'PSK, phase rotation: ' + str(round(self.phi, 5)) + \ ', Mapping: ' + mapping + ', Input: ' + inputs) plt.show() class QAMModem(Modem): def __init__(self, M, gray_map=True, bin_input=True, soft_decision=True, bin_output=True): super().__init__(M, gray_map, bin_input, soft_decision, bin_output) if np.sqrt(M) != np.fix(np.sqrt(M)) or np.log2(np.sqrt(M)) != np.fix(np.log2(np.sqrt(M))): raise ValueError('M must be a square of a power of 2') self.m = [i for i in range(self.M)] self.s = self.__qam_symbols() self.code_book = self.create_constellation(self.m, self.s) if self.gray_map: self.__gray_qam_arange() self.zeros, self.ones = self.llr_preparation() def __qam_symbols(self): """ Creates M-QAM complex symbols.""" c = np.sqrt(self.M) b = -2 * (np.array(self.m) % c) + c - 1 a = 2 * np.floor(np.array(self.m) / c) - c + 1 s = list((a + 1j * b)) return s def __gray_qam_arange(self): """ This method re-arranges complex coordinates according to Gray coding requirements. To implement correct Gray mapping the additional heuristic is used: the even "columns" in the signal constellation is complex conjugated. """ for idx, (key, item) in enumerate(self.code_book.items()): if (np.floor(idx / np.sqrt(self.M)) % 2) != 0: self.code_book[key] = np.conj(item) def de2bin(self, decs): """ Converts values from decimal to binary representation. Parameters ---------- decs : list of ints Input decimal values. Returns ------- bin_out : list of ints Output binary sequences. """ bin_out = [np.binary_repr(d, width=self.N) for d in decs] return bin_out def bin2de(self, bin_in): """ Converts values from binary to decimal representation. Parameters ---------- bin_in : list of ints Input binary values. Returns ------- dec_out : list of ints Output decimal values. """ dec_out = [] N = self.N # bits per modulation symbol (local variables are tiny bit faster) Ndecs = int(len(bin_in) / N) # length of the decimal output for i in range(Ndecs): bin_seq = bin_in[i * N:i * N + N] # binary equivalent of the one decimal value str_o = "".join([str(int(b)) for b in bin_seq]) # binary sequence to string dec_out.append(int(str_o, 2)) return dec_out def plot_const(self): """ Plots signal constellation """ if self.M <= 16: limits = np.log2(self.M) size = 'small' elif self.M == 64: limits = 1.5 * np.log2(self.M) size = 'x-small' else: limits = 2.25 * np.log2(self.M) size = 'xx-small' const = self.code_book fig = plt.figure(figsize=(6, 4), dpi=150) for i in list(const): x = np.real(const[i]) y = np.imag(const[i]) plt.plot(x, y, 'o', color='red') if x < 0: h = 'right' xadd = -.05 else: h = 'left' xadd = .05 if y < 0: v = 'top' yadd = -.05 else: v = 'bottom' yadd = .05 if abs(x) < 1e-9 and abs(y) > 1e-9: h = 'center' elif abs(x) > 1e-9 and abs(y) < 1e-9: v = 'center' plt.annotate(i, (x + xadd, y + yadd), ha=h, va=v, size=size) M = str(self.M) if self.gray_map: mapping = 'Gray' else: mapping = 'Binary' if self.bin_input: inputs = 'Binary' else: inputs = 'Decimal' plt.grid() plt.axvline(linewidth=1.0, color='black') plt.axhline(linewidth=1.0, color='black') plt.axis([-limits, limits, -limits, limits]) plt.title(M + '-QAM, Mapping: ' + mapping + ', Input: ' + inputs) plt.show() |
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