import math import numpy as np import matplotlib.pyplot as plt def AWGN_channel(x, sigma2): noise = np.sqrt(sigma2) * np.random.randn(x.size) return x + noise def AWGNdemapper(y, const, varN): apps = np.exp(-np.abs(np.transpose([y]) - const) ** 2 / (2 * varN)) return apps / np.transpose([np.sum(apps, 1)]) def sampler(prob, n): samples = np.empty(0) for idx, p in enumerate(prob): occurrences = np.round(n * p) samples = np.concatenate((samples, np.ones(occurrences.astype(int)) * idx)) indexes = np.random.permutation(samples.shape[0]) return samples[indexes] def xesmd(apps, idx): ''' Estimates symbolwise equivocation from reference symbols indices and a posteriori probabilities. ''' eq = -np.log(np.take_along_axis(apps, idx[:, None], axis=1) / np.transpose([np.sum(apps, 1)])) eq[eq == np.inf] = 1000 return np.mean(eq) n = 100_000 SNR_dBs = np.arange(5,22) np.arange(0,2.5,0.01).shape M = 8 plots_dict = np.empty(shape=(17,25000)) for idx, shaping in enumerate(np.arange(0,2.5,0.0001)): alphabet = np.arange(-7,8,2) alphabet = alphabet / np.sqrt(np.mean(alphabet**2)) scaling = (alphabet[1]-alphabet[0])/2 # scaling = 0.21821789023599236 # print('Scaling: ', scaling) denominator = np.sum(np.exp(-shaping*np.square(alphabet))) probs = 1/denominator * np.exp(-shaping*np.square(alphabet)) power = np.sum(np.square(np.arange(-7,8,2)*(scaling))*probs) # print('Power: ', power) indices = sampler(probs, n).astype(int) norm_factor = np.sqrt(np.sum(np.square(alphabet) * probs)) alphabet = alphabet / norm_factor symbols = alphabet[indices] scaling = (alphabet[1]-alphabet[0])/2 # print('Scaling: ', scaling) H = np.sum(-np.log2(probs)*probs) # print('Entropy: ',H) power = np.mean(symbols**2) # print('Power: ', power) # plt.rcParams['figure.figsize'] = [4, 4] # plt.hist(symbols, bins=100) # plt.show() for jdx, snrdB in enumerate(SNR_dBs): sigma2 = 1/(10**(snrdB/10)) sigma2 = sigma2 y = AWGN_channel(symbols, sigma2) apps = AWGNdemapper(y, alphabet, sigma2) xe = xesmd(apps, indices) plots_dict[jdx][idx] = (2*(H - (xe) / np.log(2))) print(np.max(plots_dict, 1).tolist()) mb = np.max(plots_dict, 1) mb = [2.0193916630846918, 2.2654022278277393, 2.5231306887622242, 2.7943201472250596, 3.0806359602235873, 3.3809640408051758, 3.69383842699387, 4.010358520455199, 4.318829495451576, 4.61704902872525, 4.895880050688773, 5.151007989533582, 5.376996748960784, 5.569021543421744, 5.722730806499707, 5.841398311333901, 5.9200053405287045] from numpy import genfromtxt my_data = genfromtxt('/home/ddeandres/Projects/internship_pcs/documentation/figs/mb_8_ask.csv', delimiter=',') plt.plot(my_data[:,0], my_data[:,1]) # Plot plt.rcParams['figure.figsize'] = [8, 6] for value in plots_dict: # print(key, value) plt.plot(SNR_dBs, mb) plt.plot(my_data[:,0], 2*my_data[:,1]) plt.plot(SNR_dBs, np.log2(1+10**(SNR_dBs/10)), color='black', label='Capacity') plt.grid() 解释代码，并进行注释，请注意，可以对代码进行规范化，但不要修改原本的结构。另外，将原本的信噪比SNR_dBs = np.arange(5,22)修改为仅包含5,10,15,20.增加星座点可视化，可参考下列代码： 3. 星座图可视化 plt.figure(figsize=(4, 4)) # 计算二维网格点（实部+虚部，本例为实数调制） alph = alphabet_norm.detach().numpy() a = np.array([(d, c) for c in np.flip(alph) for d in alph]) # 计算联合概率 joint_probs = (probs.reshape(-1, 1) * probs.reshape(1, -1)).flatten().detach().numpy() # 绘制散点图（点大小表示概率） plt.scatter(a[:, 0], a[:, 1], s=joint_probs * 2000, alpha=0.6) plt.title(“Constellation Diagram”) plt.xlabel(“In-phase”) plt.ylabel(“Quadrature”) # 保存为TikZ格式（用于LaTeX文档） tikzplotlib_save(f"aref_pcs_{SNR_dB}dB.tex") plt.show()

import numpy as np import matplotlib.pyplot as plt import math

import matplotlib.pyplot as plt import math # 解决图标题中文乱码问题 import matplotlib as mpl mpl.rcParams['font.sans-serif'] = ['SimHei'] # 指定默认字体 mpl.rcParams['axes.unicode_minus'] = False #...

python 3.74 运行import numpy as np 报错lib\site-packages\numpy\init.py

import numpy as np import os,sys #获取当前文件夹，并根据文件名 def path(fileName): p=sys.path[0]+'\\'+fileName return p #读文件 def readFile(fileName): f=open(path(fileName)) str=f.read() ...

import numpy as np(2).py

import numpy as np import matplotlib.pyplot as plt import torch from torch import nn, optim def one_hot(a, M): onehot = np.zeros(M) onehot[a] = 1 return onehot def normalization(x, P): c = torch.mean(x**2) return torch.sqrt(P / c) * x def awgn(x, sigma2): noise_t = np.sqrt(sigma2)*torch.randn(x.shape) return torch.add(x, noise_t) class Mapper(nn.Module): def init(self): super().init() self.lin1 = nn.Linear(16, 32) self.lin2 = nn.Linear(32, 32) self.lin3 = nn.Linear(32, 2) def forward(self, y): return self.lin3(self.lin2(self.lin1(y))) class Demapper(nn.Module): def init(self): super().init() self.lin1 = nn.Linear(2, 32) self.lin2 = nn.Linear(32, 32) self.lin3 = nn.Linear(32, 16) def forward(self, y): return self.lin3(self.lin2(self.lin1(y))) # Generate data M = 16 n = 10000 a = np.random.choice(range(M), size= n) onehot = np.array([one_hot(a[i], M) for i in range(n)]) # convert array to tensors onehot_t = torch.tensor(onehot).float() a_t = torch.tensor(a) a_t = a_t.type(torch.LongTensor) # loss function loss_fn = nn.CrossEntropyLoss() P = 1 # normalization parameter SNRdBs = np.array([0, 2, 4, 6, 8, 10]) #SNRdBs = np.array([10]) SNRs = 10(SNRdBs/10) # Initialize network mapper = Mapper() demap = Demapper() for (k,snr) in enumerate(SNRs): sigma2 = P/snr print(f'---SNR = {SNRdBs[k]} dB---') # Optimizer optimizer = optim.Adam(list(mapper.parameters()) + list(demap.parameters()), lr=0.01) # Training loop for j in range(4001): xhat = mapper(onehot_t) xhat = normalization(xhat, P) yhat = awgn(xhat, sigma2) l = demap(yhat) loss = loss_fn(l, a_t) optimizer.zero_grad() loss.backward() optimizer.step() # Printout and visualization if j % 500 == 0: print(f'epoch {j}: Loss = {loss.detach().numpy()/np.log(2) :.4f} dB') if loss < 1e-3: break # Data for the plots a_plot = np.arange(M) onehot_plot = np.array([one_hot(a_plot[i], M) for i in range(M)]) learned_x = mapper(torch.tensor(onehot_plot).float()) learned_x = normalization(learned_x, P).detach().numpy() plt.scatter(learned_x[:,0], learned_x[:,1]) plt.title(f'Learned Constellation for SNR = {SNRdBs[k]} dB') plt.grid() plt.show() class Mapper3(nn.Module): def init(self): super().init() self.lin1 = nn.Linear(16, 2) def forward(self, y): return self.lin1(y) class Demapper3(nn.Module): def init(self): super().init() self.lin1 = nn.Linear(2, 16) #self.act1 = nn.ReLU() #self.lin2 = nn.Linear(32, 32) #self.act2 = nn.ReLU() #self.lin3 = nn.Linear(32, 32) #self.act3 = nn.ReLU() #self.lin4 = nn.Linear(32, 32) #self.act4 = nn.ReLU() #self.lin5 = nn.Linear(32, 16) def forward(self, y): #y = self.act1(self.lin1(y)) #y = self.act2(self.lin2(y)) #y = self.act3(self.lin3(y)) #return self.lin5(self.act4(self.lin4(y))) return self.lin1(y) P = 1 # normalization parameter SNRdBs = np.array([0, 2, 4, 6, 8, 10]) SNRs = 10(SNRdBs/10) # Initialize network mapper = Mapper3() demap = Demapper3() for (k,snr) in enumerate(SNRs): sigma2 = P/snr print(f'---SNR = {SNRdBs[k]} dB---') # Optimizer optimizer = optim.Adam(list(mapper.parameters()) + list(demap.parameters()), lr=0.01) # Training loop for j in range(4001): xhat = mapper(onehot_t) xhat = normalization(xhat, P) yhat = awgn(xhat, sigma2) l = demap(yhat) loss = loss_fn(l, a_t) optimizer.zero_grad() loss.backward() optimizer.step() # Printout and visualization if j % 500 == 0: print(f'epoch {j}: Loss = {loss.detach().numpy()/np.log(2) :.4f} dB') if loss < 1e-3: break # Data for the plots a_plot = np.arange(M) onehot_plot = np.array([one_hot(a_plot[i], M) for i in range(M)]) learned_x = mapper(torch.tensor(onehot_plot).float()) learned_x = normalization(learned_x, P).detach().numpy() plt.scatter(learned_x[:,0], learned_x[:,1]) plt.title(f'Learned Constellation for SNR = {SNRdBs[k]} dB') plt.grid() plt.show() class Mapper2(nn.Module): def init(self): super().init() self.lin1 = nn.Linear(4, 10) self.act1 = nn.ReLU() self.lin2 = nn.Linear(10, 10) self.act2 = nn.ReLU() self.lin3 = nn.Linear(10, 2) def forward(self, y): y = self.act1(self.lin1(y)) y = self.act2(self.lin2(y)) return self.lin3(y) class Demapper2(nn.Module): def init(self): super().init() self.lin1 = nn.Linear(2, 20) self.act1 = nn.ReLU() self.lin2 = nn.Linear(20, 20) self.act2 = nn.ReLU() self.lin3 = nn.Linear(20, 20) self.act3 = nn.ReLU() self.lin4 = nn.Linear(20, 20) self.act4 = nn.ReLU() self.lin5 = nn.Linear(20, 4) def forward(self, y): y = self.act1(self.lin1(y)) y = self.act2(self.lin2(y)) y = self.act3(self.lin3(y)) return self.lin5(self.act4(self.lin4(y))) def get_labeling(msg): label = np.array([[0,0,0,0], [0,0,0,1], [0,0,1,1], [0,0,1,0], [0,1,1,0], [0,1,1,1], [0,1,0,1], [0,1,0,0], [1,0,0,0], [1,0,0,1], [1,0,1,1], [1,0,1,0], [1,1,1,0], [1,1,1,1], [1,1,0,1], [1,1,0,0]]) return label[msg, :] # Generate data N = 40000 bits = np.random.choice(range(2), size= N) bits = bits.reshape(-1,4) # convert array to tensors bits_t = torch.tensor(bits).float() # loss function loss_fn = nn.BCEWithLogitsLoss() # Batches batch_size = 1000 num_epochs = 5001 dataloader = torch.utils.data.DataLoader(bits_t, batch_size=batch_size) P = 1 # normalization parameter SNRdBs = np.array([6, 10, 12, 16]) SNRs = 10**(SNRdBs/10) # Initialize network mapper = Mapper2() demap = Demapper2() for (k,snr) in enumerate(SNRs): sigma2 = P/snr print(f'---SNR = {SNRdBs[k]} dB---') # Optimizer optimizer = optim.Adam(list(mapper.parameters()) + list(demap.parameters()), lr=0.01) # Training loop for j in range(num_epochs): for b_t in (dataloader): xhat = mapper(b_t) xhat = normalization(xhat, P) yhat = awgn(xhat, sigma2) l = demap(yhat) loss = loss_fn(l, b_t) optimizer.zero_grad() loss.backward() optimizer.step() # Printout and visualization if j % 500 == 0: print(f'epoch {j}: Loss = {loss.detach().numpy()/np.log(2) :.4f} dB') if loss < 1e-3: break # Data for the plots a_plot = np.arange(M) b_plot = get_labeling(a_plot) learned_x = mapper(torch.tensor(b_plot).float()) learned_x = normalization(learned_x, P).detach().numpy() plt.scatter(learned_x[:,0], learned_x[:,1]) for i in range(M): plt.annotate(f'{b_plot[i,:]}', (learned_x[i,0], learned_x[i,1]) ) plt.title(f'Learned Constellation for SNR = {SNRdBs[k]} dB') plt.grid() plt.show() # Covariance and mean cov = np.array([[1, 0.5],[0.5, 2]]) mean = np.array([1, 2]) # generate data x = np.random.multivariate_normal(mean, cov, 100000) # Plot plt.scatter(x[:, 0], x[:, 1], s=1) plt.gca().set_aspect('equal') plt.grid() class PCA(torch.nn.Module): def init(self): super().init() self.lin1 = torch.nn.Linear(2, 1) self.lin2 = torch.nn.Linear(1, 2) def forward(self, x): z = self.lin1(x) return self.lin2(z), z pca = PCA() _x = torch.tensor(x).float() optimizer = torch.optim.Adam(list(pca.parameters())) loss_fn = torch.nn.MSELoss() for i in range(6001): _xhat, _ = pca(_x) optimizer.zero_grad() loss = loss_fn(_x, _xhat) loss.backward() optimizer.step() if i % 500 == 0: print(f'(epoch {i}) loss = {loss :.4f}') # Plot _xhat, _z = pca(_x) xhat = _xhat.detach().numpy() plt.scatter(x[:, 0], x[:, 1], s=1, label='data x') plt.scatter(xhat[:, 0], xhat[:, 1], s=1, label='principal component') plt.legend() plt.gca().set_aspect('equal') plt.grid() from sklearn.decomposition import PCA pca = PCA(n_components=1) pca.fit(x) x_pca = pca.transform(x) x_new = pca.inverse_transform(x_pca) # Plot plt.scatter(x[:, 0], x[:, 1], s=1, label='data x') plt.scatter(x_new[:, 0], x_new[:, 1], s=1, label='principal component') plt.legend() plt.gca().set_aspect('equal') plt.grid() 解释并注释上述代码

import matplotlib.pyplot as plt import torch from torch import nn, optim # 辅助函数：将整数转换为one-hot编码向量 def one_hot(a, M): """ 将整数转换为one-hot编码向量 Args: a: 整数索引 M: 向量长度...

import math import numpy as np import matplotlib.pyplot as plt import torch import torch.nn as nn import torch.optim as optim import tikzplotlib def my_bisection(f, a, b, P, tol): # approximates a root, R, of f bounded # by a and b to within tolerance # | f(m) | < tol with m the midpoint # between a and b Recursive implementation # check if a and b bound a root if (f(a) > P and f(b) > P) or (f(a) < P and f(b) < P): raise Exception( "The scalars a and b do not bound P") # get midpoint m = (a + b)/2 if np.abs(f(m)-P) < tol: # stopping condition, report m as root return m elif f(m) > P and f(m) < f(a): # case where m is an improvement on a. # Make recursive call with a = m return my_bisection(f, m, b, P, tol) elif f(m) < P and f(m) > f(b): # case where m is an improvement on b. # Make recursive call with b = m return my_bisection(f, a, m, P, tol) def AWGN_channel(x, sigma2): noise = np.sqrt(sigma2) * np.random.randn(x.size) return x + noise’ def AWGNdemapper(y, const, varN): apps = np.exp(-np.abs(np.transpose([y])-const)**2/(2varN)) return apps / np.transpose([np.sum(apps, 1)]) def sampler(prob, n): samples = np.empty(0) for idx, p in enumerate(prob): occurrences = np.round(n p) samples = np.concatenate((samples, np.ones(occurrences.astype(int)) * idx)) indexes = np.random.permutation(samples.shape[0]) return samples[indexes] def xesmd(apps, idx): ‘’’ Estimates symbolwise equivocation from reference symbols indices and a posteriori probabilities. ‘’’ eq = -np.log(np.take_along_axis(apps, idx[:, None], axis=1) / np.transpose([np.sum(apps, 1)])) eq[eq==np.inf] = 1000 return np.mean(eq) n = 100_000 SNR_dBs = np.arange(5,25) 16 QAM M = 4 alphabet = np.arange(-3,4,2) alphabet = alphabet / np.sqrt(np.mean(alphabet2)) indices = np.random.choice(np.arange(M), n) symbols = alphabet[indices] mi_16 = [] for snrdB in SNR_dBs: sigma2 = 1/(10(snrdB/10)) sigma2 = sigma2 y = AWGN_channel(symbols, sigma2) apps = AWGNdemapper(y, alphabet, sigma2) xe = xesmd(apps, indices) mi_16.append(2(2 - xe / np.log(2))) 64 QAM M = 8 alphabet = np.arange(-7,8,2) alphabet = alphabet / np.sqrt(np.mean(alphabet2)) indices = np.random.choice(np.arange(M), n) symbols = alphabet[indices] print('Power: ',np.mean(np.square(symbols))) mi_64 = [] for snrdB in SNR_dBs: sigma2 = 1/(10(snrdB/10)) sigma2 = sigma2 y = AWGN_channel(symbols, sigma2) apps = AWGNdemapper(y, alphabet, sigma2) xe = xesmd(apps, indices) mi_64.append(2(3 - (xe) / np.log(2))) def power_for_shaping(shaping): alphabet = np.arange(-7,8,2) # alphabet = alphabet / np.sqrt(np.mean(alphabet**2)) scaling = (alphabet[1]-alphabet[0])/2 denominator = np.sum(np.exp(-shapingnp.square(alphabet))) probs = 1/denominator np.exp(-shapingnp.square(alphabet)) power = np.sum(np.square(np.arange(-7,8,2)(scaling))*probs) return power power = [] for i in np.arange(0,1,0.1): power.append(power_for_shaping(i)) plt.plot(np.arange(0,1,0.1), power) M = 8 shaping = 2.5 alphabet = np.arange(-7,8,2) alphabet = alphabet / np.sqrt(np.mean(alphabet**2)) scaling = (alphabet[1]-alphabet[0])/2 scaling = 0.21821789023599236 print('Scaling: ', scaling) denominator = np.sum(np.exp(-shapingnp.square(alphabet))) probs = 1/denominator * np.exp(-shapingnp.square(alphabet)) power = np.sum(np.square(np.arange(-7,8,2)(scaling))probs) print('Power: ', power) indices = sampler(probs, n).astype(int) norm_factor = np.sqrt(np.sum(np.square(alphabet) * probs)) alphabet = alphabet / norm_factor symbols = alphabet[indices] scaling = (alphabet[1]-alphabet[0])/2 print('Scaling: ', scaling) H = np.sum(-np.log2(probs)probs) print('Entropy: ',H) power = np.mean(symbols2) print('Power: ', power) plt.rcParams[‘figure.figsize’] = [4, 4] plt.hist(symbols, bins=100) plt.show() mi_mb_64 = [] for snrdB in SNR_dBs: sigma2 = 1/(10(snrdB/10)) sigma2 = sigma2 y = AWGN_channel(symbols, sigma2) apps = AWGNdemapper(y, alphabet, sigma2) xe = xesmd(apps, indices) mi_mb_64.append((H - (xe) / np.log(2))) 256 QAM M = 16 alphabet = np.arange(-15,16,2) alphabet = alphabet / np.sqrt(np.mean(alphabet2)) indices = np.random.choice(np.arange(M), n) symbols = alphabet[indices] print('Power: ',np.mean(np.square(symbols))) mi_256 = [] for snrdB in SNR_dBs: sigma2 = 1/(10(snrdB/10)) sigma2 = sigma2 y = AWGN_channel(symbols, sigma2) apps = AWGNdemapper(y, alphabet, sigma2) xe = xesmd(apps, indices) mi_256.append(2(4 - (xe) / np.log(2))) Plot plt.rcParams[‘figure.figsize’] = [8, 6] plt.plot(SNR_dBs, mi_16, label = ‘16QAM’) plt.plot(SNR_dBs, mi_64, label = ‘64QAM’) plt.plot(SNR_dBs, mi_mb_64, label = ‘64-MB’) plt.plot(SNR_dBs, mi_256, label = ‘256QAM’) plt.plot(SNR_dBs, np.log2(1+10(SNR_dBs/10)), color=‘black’, label=‘Capacity’) plt.legend() plt.grid() plt.title(‘AIR of QAM constellation’) plt.ylabel(‘bits per channel use’) plt.xlabel(‘SNR in dB’) tikzplotlib.save(“QAM_MI.tex”) SNR_dBs = np.arange(5,25) plt.plot(SNR_dBs, np.log2(1+10(SNR_dBs/10)), color=‘black’, label=‘ C ( P / σ 2 ) C(P/σ 2 )’) plt.plot(SNR_dBs, np.log2(1+10**(SNR_dBs/10)) - 0.5np.log2((np.pinp.e)/6) , linestyle=‘dashed’, color=‘C1’, label=‘ C ( P / σ 2 ) − 1 2 log ⁡ 2 π e 6 C(P/σ 2 )− 2 1 log 2 6 πe ’) plt.grid() plt.ylabel(‘bits per channel use’) plt.xlabel(‘SNR in dB’) plt.xlim([5, 25]) plt.ylim([1, 8]) plt.title(‘AWGN channel capacity gap’) plt.legend() tikzplotlib.save(“SNR_GAP.tex”) f = lambda x: -np.log10(x) P = 0.4 p1 = my_bisection(f, 0.2, 0.8, P, 0.1) print(“P1 =”, p1) p01 = my_bisection(f, 0.2, 0.8, P, 0.01) print(“P01 =”, p01) print(“f(r1) =”, f(p1)) print(“f(r01) =”, f(p01)) 解释代码，并进行注释，请注意，可以对代码进行规范化，但不要修改原本的结构。另外，将原本的信噪比SNR_dBs = np.arange(5,22)修改为仅包含5,10,15,20.增加星座点可视化，可参考下列代码：星座图可视化 plt.figure(figsize=(4, 4)) 计算二维网格点（实部+虚部，本例为实数调制） alph = alphabet_norm.detach().numpy() a = np.array([(d, c) for c in np.flip(alph) for d in alph]) 计算联合概率 joint_probs = (probs.reshape(-1, 1) * probs.reshape(1, -1)).flatten().detach().numpy() 绘制散点图（点大小表示概率） plt.scatter(a[:, 0], a[:, 1], s=joint_probs * 2000, alpha=0.6) plt.title(“Constellation Diagram”) plt.xlabel(“In-phase”) plt.ylabel(“Quadrature”) 保存为TikZ格式（用于LaTeX文档） tikzplotlib_save(f"aref_pcs_{SNR_dB}dB.tex") plt.show()

noise = np.sqrt(sigma2) * np.random.randn(x.size) return x + noise def AWGNdemapper(y, const, varN): """计算后验概率""" apps = np.exp(-np.abs(np.transpose([y]) - const)**2 / (2 * varN)) return ...

class Receiver(nn.Module): def init(self, M): super().init() self.lin1 = nn.Linear(1, M) def forward(self, y): y = self.lin1(y) return y class Encoder(nn.Module): def init(self, M): super().init() self.lin1 = nn.Linear(1, M, bias=False) nn.init.constant_(self.lin1.weight, 1 / M) self.out = nn.Softmax(dim=0) def forward(self, y): return self.out(self.lin1(y)) def gradient_correction_factor(app, idx, prob, M): (nn,M)= app.shape cf = torch.zeros(M) for j in range(M): tmp = app[:, j] cf[j] = torch.sum(torch.log(tmp[idx==j])) / (nnprob[j]) # tmp[idx==j] selects the ll of those xy pairs which belong to the current symbol j return cf def AWGN_channel(x, sigma2): noise_t = np.sqrt(sigma2)torch.randn(x.shape) return x + noise_t def tanh_channel(x, sigma2): noise_t = np.sqrt(sigma2)torch.randn(x.shape) return torch.tanh(x) + noise_t M = 8 n = 10_000 SNR_dB = 5 SNR = 10(SNR_dB/10) sigma2 = 1/SNR nepochs = 4000 dec = Receiver(M) enc = Encoder(M) loss_fn = nn.CrossEntropyLoss() alphabet = np.arange(-(M-1),M,2) #alphabet = np.array([-10, -6, -3, -1, 1, 3, 6, 10]) <-- Non-uniform alphabet alphabet = alphabet / np.sqrt(np.mean(alphabet2)) alphabet_t = torch.tensor(alphabet).float() lr = 0.1 opt = optim.Adam( list(enc.parameters()) + list(dec.parameters()), lr=lr) def sampler(prob, n): samples = torch.empty(0) for idx, p in enumerate(prob): occurrences = (n p).type(torch.LongTensor) samples = torch.cat((samples, torch.ones(occurrences, dtype=torch.int64) * torch.tensor(idx))) indexes = torch.randperm(samples.shape[0]) return samples[indexes] for j in range(nepochs): # logits = enc(torch.tensor([1], dtype=torch.float)) probs = enc(torch.tensor([1], dtype=torch.float)) # probs = nn.functional.softmax(logits, -1) probs.retain_grad() # Sample indexes indices = sampler(probs, n) indices = indices.type(torch.LongTensor) # Modulation # with torch.no_grad(): #alternatively detach() norm_factor = torch.rsqrt(torch.sum(torch.pow(torch.abs(alphabet_t), 2) * probs)) alphabet_norm = alphabet_t * norm_factor onehot = nn.functional.one_hot(indices, M).float() symbols = torch.matmul(onehot, torch.transpose(input=alphabet_norm.reshape(1,-1), dim0=0, dim1=1)) # Channel y = AWGN_channel(symbols, sigma2) # Demodulator ll = dec(y.reshape(-1,1).float()) # Loss loss = -(torch.sum(-probstorch.log(probs)) - loss_fn(ll, indices.detach()))# -(H(X) - CE(P,Q)), the gradient descent minimizes, therefore we minimize the opposite to maximize the MI in the end. opt.zero_grad() # 2nd option loss.backward(retain_graph=True) # correction factor app = nn.functional.softmax(ll, 1) #Q(X|Y) cf = - (gradient_correction_factor(app, indices, probs, M) - torch.log(probs)) # 1st option # probs.register_hook(lambda grad: grad + cf) # loss.backward() # 2nd option probs.grad = cf # loss.backward() probs.backward(torch.tensor([1., 1., 1., 1., 1., 1., 1., 1.])) opt.step() # Printout and visualization if j % 500 == 0: print(f'epoch {j}: Loss = {loss.detach().numpy() / np.log(2) :.4f}') enc.lin1._parameters['weight']AWGN_channel probs plt.rcParams['figure.figsize'] = [4, 4] plt.hist(symbols.detach().numpy(), bins=100) plt.xlim(-2.5, 2.5) plt.show() # Scatterplot plt.rcParams['figure.figsize'] = [4, 4] pp = (probs.reshape(-1,1)probs.reshape(1,-1)).reshape(-1,1).detach().numpy() alph = alphabet_norm.detach().numpy() a = [] for c in np.flip(alph): for d in alph: a.append(d+1jc) plt.scatter(np.real(a), np.imag(a), pp2000) tikzplotlib.save("/home/ddeandres/Projects/internship_pcs/documentation/figs/aref_pcs_{}dB.tex".format(SNR_dB)) plt.show() def AWGN_channel_np(x, sigma2): noise = np.sqrt(sigma2) * np.random.randn(x.size) return x + noise def AWGNdemapper(y, const, varN): apps = np.exp(-np.abs(np.transpose([y])-const)**2/(2varN)) return apps / np.transpose([np.sum(apps, 1)]) def xesmd(apps, idx): """ Estimates symbolwise equivocation from reference symbols indices and a posteriori probabilities. """ eq = -np.log(np.take_along_axis(apps, idx[:, None], axis=1) / np.transpose([np.sum(apps, 1)])) eq[eq==np.inf] = 1000 return np.mean(eq) n = 10_000 SNR_dBs = np.arange(5,22) M = 8 alphabet = np.arange(-7,8,2) alphabet = alphabet / np.sqrt(np.mean(alphabet2)) indices = np.random.choice(np.arange(M), n) symbols = alphabet[indices] mi_64 = [] for snrdB in SNR_dBs: sigma2 = 1/(10(snrdB/10)) sigma2 = sigma2 y = AWGN_channel_np(symbols, sigma2) apps = AWGNdemapper(y, alphabet, sigma2) xe = xesmd(apps, indices) mi_64.append(2(3 - (xe) / np.log(2))) print((-2*loss.detach()/np.log(2)).detach().numpy()) # Plot plt.rcParams['figure.figsize'] = [8, 6] plt.plot(SNR_dBs, mi_64, label = '64QAM') plt.plot(SNR_dBs, np.log2(1+10**(SNR_dBs/10)), color='black', label='Capacity') plt.plot(SNR_dB, -2loss.detach()/np.log(2), color='red', marker='o', markersize=3) xy = (SNR_dB, (-2loss.detach()/np.log(2)).detach().numpy()) plt.annotate('(%s, %s)' % xy, xy=xy, textcoords='data') plt.legend() plt.grid()def one_hot(a, M): onehot = np.zeros(M) onehot[a] = 1 return onehot # Data for the plots a_plot = np.arange(M) onehot_plot = np.array([one_hot(a_plot[i], M) for i in range(M)]) learned_x = mapper(torch.tensor(onehot_plot).float()) yy_plot = torch.tanh(learned_x) # Plot plt.scatter(np.real(learned_x.detach().numpy()), np.imag(learned_x.detach().numpy())) plt.title('Learned constellation') plt.grid() plt.scatter(np.real(yy_plot.detach().numpy()), np.imag(yy_plot.detach().numpy())) plt.title('Constellation after tanh') plt.grid() SNR_dBs = np.arange(0,20) plt.plot(SNR_dBs, np.log2(1+10(SNR_dBs/10)), color='C0', label='$C(P/\sigma^2)$') plt.plot(SNR_dBs, np.log2(1+10(SNR_dBs/10)) - 0.5np.log2((np.pinp.e)/6) , linestyle='dashed', color='C1', label='$C(P/\sigma^2) - \dfrac{1}{2}\log_2\dfrac{\pi e}{6}$') plt.grid() plt.ylabel('bits per channel use') plt.xlabel('SNR in dB') plt.xlim([0, 20]) plt.ylim([0, 5]) # plt.title('AWGN channel capacity gap') plt.legend() 解释上述代码，并注释

def AWGN_channel_np(x, sigma2): """NumPy实现的AWGN信道""" noise = np.sqrt(sigma2) * np.random.randn(x.size) return x + noise def AWGNdemapper(y, const, varN): """计算后验概率（软解调）""" # 计算...

import numpy as np import matplotlib.pyplot as plt import torch from torch import nn, optim import torch.nn.functional as F from scipy.stats import entropy from sklearn.neighbors import KernelDensity # 设置字体 plt.rcParams["font.family"] = "Times New Roman" plt.rcParams["axes.labelsize"] = 12 plt.rcParams["axes.titlesize"] = 14 # 辅助函数：将整数转换为one-hot编码向量 def one_hot(a, M): onehot = np.zeros(M) onehot[a] = 1 return onehot # 模值归一化函数 def magnitude_normalization(x): """ 模值归一化：将星座点缩放到单位圆内确保所有点的模值不超过1 """ # 计算每个点的模值 (sqrt(real^2 + imag^2)) magnitudes = torch.sqrt(torch.sum(x**2, dim=1)) # 找到最大模值 max_magnitude = torch.max(magnitudes) # 避免除以零 if max_magnitude < 1e-6: return x # 归一化所有点 return x / max_magnitude.unsqueeze(1) def awgn(x, sigma2): noise_t = np.sqrt(sigma2) * torch.randn(x.shape) return torch.add(x, noise_t) # 计算互信息 def calculate_mutual_information(x, y, n_bins=50): """ 计算两个连续变量x和y之间的互信息使用直方图方法估计联合分布和边际分布 """ # 将PyTorch张量转换为NumPy数组 if isinstance(x, torch.Tensor): x = x.detach().numpy() if isinstance(y, torch.Tensor): y = y.detach().numpy() # 确保输入是二维数组 if x.ndim == 1: x = x.reshape(-1, 1) if y.ndim == 1: y = y.reshape(-1, 1) # 合并数据 joint_data = np.hstack((x, y)) # 计算联合直方图 hist_result = np.histogramdd( joint_data, bins=n_bins, density=True ) # 解析返回值 if len(hist_result) == 2: # 2D情况: (H, edges) joint_hist = hist_result[0] edges = hist_result[1] x_edges = edges[0] y_edges = edges[1] elif len(hist_result) == 3: # 3D情况: (H, x_edges, y_edges) joint_hist, x_edges, y_edges = hist_result else: raise ValueError("Unsupported histogramdd return format") # 确保直方图是二维的 if joint_hist.ndim != 2: joint_hist = joint_hist.reshape(n_bins, n_bins) # 计算边际直方图 - 确保返回一维数组 x_hist, _ = np.histogram(x.flatten(), bins=x_edges, density=True) y_hist, _ = np.histogram(y.flatten(), bins=y_edges, density=True) # 确保边际直方图是一维的 x_hist = x_hist.flatten() y_hist = y_hist.flatten() # 计算互信息 mi = 0.0 # 计算箱宽（假设等间距） dx = np.diff(x_edges)[0] if len(x_edges) > 1 else 1.0 dy = np.diff(y_edges)[0] if len(y_edges) > 1 else 1.0 # 遍历所有箱子 for i in range(joint_hist.shape[0]): for j in range(joint_hist.shape[1]): # 获取标量值 p_xy_val = joint_hist[i, j] * dx * dy # 确保索引在范围内 if i < len(x_hist) and j < len(y_hist): p_x_val = x_hist[i] * dx p_y_val = y_hist[j] * dy else: # 如果索引超出范围，跳过 continue # 避免除以零和log(0) - 现在所有值都是标量 if p_xy_val > 1e-10 and p_x_val > 1e-10 and p_y_val > 1e-10: mi += p_xy_val * np.log2(p_xy_val / (p_x_val * p_y_val)) return mi # 生成标准32QAM星座图（均匀分布） def generate_uniform_32qam(): # 创建6x6网格 levels = np.array([-1.5, -0.9, -0.3, 0.3, 0.9, 1.5]) x, y = np.meshgrid(levels, levels) # 展平网格 points = np.vstack((x.flatten(), y.flatten())).T # 移除四个角点（32QAM标准） corners = [ [0, 0], # (-1.5, -1.5) [0, 5], # (-1.5, 1.5) [5, 0], # (1.5, -1.5) [5, 5] # (1.5, 1.5) ] # 移除角点 mask = np.ones(len(points), dtype=bool) for corner in corners: idx = corner[0] * 6 + corner[1] mask[idx] = False uniform_32qam = points[mask] # 模值归一化 magnitudes = np.sqrt(np.sum(uniform_32qam**2, axis=1)) max_magnitude = np.max(magnitudes) uniform_32qam = uniform_32qam / max_magnitude return uniform_32qam # 计算平均功率 def calculate_average_power(constellation): """ 计算星座图的平均功率平均功率 = (1/N) * Σ |x_i|^2 """ magnitudes_sq = np.sum(constellation2, axis=1) return np.mean(magnitudes_sq) class Mapper(nn.Module): """ 映射器网络（带隐藏层） """ def init(self): super().init() self.lin1 = nn.Linear(32, 64) self.lin2 = nn.Linear(64, 64) self.lin3 = nn.Linear(64, 2) def forward(self, y): y = F.relu(self.lin1(y)) y = F.relu(self.lin2(y)) return self.lin3(y) class Demapper(nn.Module): """ 解映射器网络（带隐藏层） """ def init(self): super().init() self.lin1 = nn.Linear(2, 64) self.lin2 = nn.Linear(64, 64) self.lin3 = nn.Linear(64, 32) def forward(self, y): y = F.relu(self.lin1(y)) y = F.relu(self.lin2(y)) return self.lin3(y) # 生成训练数据 M = 32 n = 10000 a = np.random.choice(range(M), size=n) onehot = np.array([one_hot(a[i], M) for i in range(n)]) # 转换为PyTorch张量 onehot_t = torch.tensor(onehot).float() a_t = torch.tensor(a).long() # 直接转换为长整型 # 整个星座图的one-hot编码（用于计算最小距离） onehot_plot = np.array([one_hot(i, M) for i in range(M)]) onehot_plot_t = torch.tensor(onehot_plot).float() # 损失函数 loss_fn = nn.CrossEntropyLoss() # 生成均匀星座图并计算其平均功率 uniform_32qam = generate_uniform_32qam() P_uniform = calculate_average_power(uniform_32qam) # 均匀星座图的平均功率 print(f"Uniform constellation average power: {P_uniform:.4f}") SNRdBs = np.array([5, 10, 15]) SNRs = 10 (SNRdBs / 10) # 初始化网络 mapper = Mapper() demap = Demapper() # 存储互信息结果 mi_results = [] # 训练循环（针对不同SNR） for (k, snr) in enumerate(SNRs): # 使用均匀星座图的平均功率计算噪声方差 sigma2 = P_uniform / snr # 噪声方差 print(f'\n---SNR = {SNRdBs[k]} dB---') print(f'Using uniform constellation average power: {P_uniform:.4f}') print(f'Noise variance: {sigma2:.6f}') # 优化器 optimizer = optim.Adam(list(mapper.parameters()) + list(demap.parameters()), lr=0.005) # 训练循环 for j in range(10001): optimizer.zero_grad() # 1. 生成训练批次的星座点 xhat = mapper(onehot_t) # 2. 生成整个星座图的星座点（用于计算最小距离） x_plot = mapper(onehot_plot_t) # 3. 模值归一化（使用整个星座图的最大模值） magnitudes = torch.sqrt(torch.sum(x_plot**2, dim=1)) max_mag = torch.max(magnitudes) if max_mag > 0: xhat_norm = xhat / max_mag x_plot_norm = x_plot / max_mag else: xhat_norm = xhat x_plot_norm = x_plot # 4. 通过AWGN信道 yhat = awgn(xhat_norm, sigma2) # 5. 解映射 l = demap(yhat) ce_loss = loss_fn(l, a_t) # 6. 安全计算最小距离（避免就地操作） # 计算所有点对之间的欧氏距离 dist_matrix = torch.cdist(x_plot_norm, x_plot_norm, p=2) # 创建对角线掩码（避免就地操作） eye_mask = torch.eye(M, dtype=torch.bool, device=dist_matrix.device) # 将对角线位置设为无穷大（非就地操作） dist_matrix_masked = dist_matrix.masked_fill(eye_mask, float('inf')) # 找到最小距离 min_dist = torch.min(dist_matrix_masked) # 7. 计算正则化项（惩罚过小的最小距离） d_min_threshold = 0.3 # 最小距离阈值（模值归一化后需要更大阈值） reg_loss = 10.0 * F.relu(d_min_threshold - min_dist) # 使用ReLU避免条件判断 total_loss = ce_loss + reg_loss # 反向传播 total_loss.backward() optimizer.step() # 每500次迭代打印损失 if j % 500 == 0: ce_bits = ce_loss.item() / np.log(2) reg_val = reg_loss.item() # 计算当前星座点平均模值 avg_magnitude = torch.mean(magnitudes).item() # 计算当前星座图平均功率 with torch.no_grad(): avg_power = torch.mean(torch.sum(x_plot_norm2, dim=1)).item() print(f'Epoch {j}: CE Loss = {ce_bits:.4f} bits, Reg Loss = {reg_val:.4f}, ' f'Min Dist = {min_dist.item():.4f}, Avg Mag = {avg_magnitude:.4f}, ' f'Avg Power = {avg_power:.4f}') # 提前终止条件 if total_loss < 1e-3 and min_dist > d_min_threshold: print(f"Early stopping at epoch {j}") break # 可视化学习到的星座图 with torch.no_grad(): # 生成星座点 learned_x = mapper(onehot_plot_t) # 模值归一化 magnitudes = torch.sqrt(torch.sum(learned_x2, dim=1)) max_mag = torch.max(magnitudes) if max_mag > 0: learned_x = learned_x / max_mag learned_x = learned_x.numpy() # 计算模值 learned_magnitudes = np.sqrt(learned_x[:, 0]2 + learned_x[:, 1]2) # 计算平均功率 learned_avg_power = np.mean(learned_magnitudes**2) plt.figure(figsize=(10, 8)) # 绘制星座图 plt.scatter(learned_x[:, 0], learned_x[:, 1], s=30, c=learned_magnitudes, cmap='viridis') # 绘制单位圆 theta = np.linspace(0, 2*np.pi, 100) plt.plot(np.cos(theta), np.sin(theta), 'r--', alpha=0.5) # 标记星座点索引 for i, (x, y) in enumerate(learned_x): plt.text(x, y, str(i), fontsize=8, ha='center', va='center') plt.title(f'32QAM, SNR = {SNRdBs[k]} dB') plt.xlabel('In-phase Component') plt.ylabel('Quadrature Component') plt.grid(True, linestyle='--', alpha=0.6) plt.axis('equal') plt.xlim(-1.2, 1.2) plt.ylim(-1.2, 1.2) # 添加颜色条显示模值 cbar = plt.colorbar() cbar.set_label('Magnitude') plt.tight_layout() # plt.savefig(f'optimized_constellation_snr_{SNRdBs[k]}dB.png', dpi=300) plt.show() # 打印模值统计信息 print(f"Magnitude statistics for SNR={SNRdBs[k]}dB:") print(f" Max magnitude: {np.max(learned_magnitudes):.4f}") print(f" Min magnitude: {np.min(learned_magnitudes):.4f}") print(f" Avg magnitude: {np.mean(learned_magnitudes):.4f}") print(f" Std magnitude: {np.std(learned_magnitudes):.4f}") print(f" Average power: {learned_avg_power:.4f} (Uniform: {P_uniform:.4f})") # ================= 互信息计算 ================= # 生成测试数据（10000个样本） test_a = np.random.choice(range(M), size=10000) test_onehot = np.array([one_hot(test_a[i], M) for i in range(10000)]) test_onehot_t = torch.tensor(test_onehot).float() with torch.no_grad(): # 优化后星座图的发送信号 test_xhat = mapper(test_onehot_t) # 模值归一化 test_x_plot = mapper(onehot_plot_t) test_magnitudes = torch.sqrt(torch.sum(test_x_plot**2, dim=1)) test_max_mag = torch.max(test_magnitudes) if test_max_mag > 0: test_xhat_norm = test_xhat / test_max_mag else: test_xhat_norm = test_xhat # 通过AWGN信道 test_yhat = awgn(test_xhat_norm, sigma2) # 计算优化后星座图的互信息 mi_optimized = calculate_mutual_information( test_xhat_norm, test_yhat, n_bins=50 ) # 计算标准均匀分布星座图的互信息 # 为测试数据选择星座点 uniform_x = uniform_32qam[test_a] # 添加AWGN噪声 - 使用相同的噪声方差 uniform_y = uniform_x + np.sqrt(sigma2) * np.random.randn(uniform_x.shape) # 计算均匀分布星座图的互信息 mi_uniform = calculate_mutual_information( uniform_x, uniform_y, n_bins=50 ) # 存储结果 mi_results.append({ 'SNR_dB': SNRdBs[k], 'mi_uniform': mi_uniform, 'mi_optimized': mi_optimized, 'optimized_power': learned_avg_power, 'uniform_power': P_uniform }) # 打印互信息结果 print(f"\nMutual Information (SNR={SNRdBs[k]}dB):") print(f" Uniform Constellation: {mi_uniform:.4f} bits (Avg Power: {P_uniform:.4f})") print(f" Optimized Constellation: {mi_optimized:.4f} bits (Avg Power: {learned_avg_power:.4f})") print(f" Improvement: {(mi_optimized - mi_uniform):.4f} bits ({100(mi_optimized - mi_uniform)/mi_uniform:.2f}%)") # 绘制互信息随SNR变化的曲线 plt.figure(figsize=(10, 6)) snrs = [res['SNR_dB'] for res in mi_results] mi_uni = [res['mi_uniform'] for res in mi_results] mi_opt = [res['mi_optimized'] for res in mi_results] plt.plot(snrs, mi_uni, 'bo-', label=f'Uniform Constellation (Avg Power: {P_uniform:.4f})') plt.plot(snrs, mi_opt, 'ro-', label='Optimized Constellation') plt.xlabel('SNR (dB)') plt.ylabel('Mutual Information (bits)') plt.title('Mutual Information Comparison (Using Uniform Constellation Power)') plt.grid(True, linestyle='--', alpha=0.6) plt.legend() plt.tight_layout() # plt.savefig('mutual_information_comparison_uniform_power.png', dpi=300) plt.show() # 绘制功率比较 plt.figure(figsize=(10, 6)) opt_power = [res['optimized_power'] for res in mi_results] uni_power = [res['uniform_power'] for res in mi_results] plt.bar([s - 0.2 for s in snrs], uni_power, width=0.4, label='Uniform Constellation', alpha=0.7) plt.bar([s + 0.2 for s in snrs], opt_power, width=0.4, label='Optimized Constellation', alpha=0.7) plt.xlabel('SNR (dB)') plt.ylabel('Average Power') plt.title('Average Power Comparison') plt.grid(True, axis='y', linestyle='--', alpha=0.6) plt.legend() plt.tight_layout() # plt.savefig('power_comparison.png', dpi=300) plt.show() # 保存互信息结果 # import pandas as pd # mi_df = pd.DataFrame(mi_results) # mi_df.to_csv('mutual_information_results_uniform_power.csv', index=False) # print("\nMutual information results saved to 'mutual_information_results_uniform_power.csv'") 代码运行之后显示： --------------------------------------------------------------------------- ValueError Traceback (most recent call last) ~\AppData\Local\Temp\ipykernel_9024\1337079151.py in <module> 381 test_xhat_norm, 382 test_yhat, --> 383 n_bins=50 384 ) 385 ~\AppData\Local\Temp\ipykernel_9024\1337079151.py in calculate_mutual_information(x, y, n_bins) 84 # 确保直方图是二维的 85 if joint_hist.ndim != 2: ---> 86 joint_hist = joint_hist.reshape(n_bins, n_bins) 87 88 # 计算边际直方图 - 确保返回一维数组 ValueError: cannot reshape array of size 6250000 into shape (50,50)

在函数中，我们通过 x = x.reshape(-1,1) 和 y = y.reshape(-1,1) 确保它们都是二维（列向量），然后 joint_data = np.hstack((x,y)) 的形状为 (n,2)。因此，数据确实是二维的。那么，为什么返回的直方图...

alphabet = np.arange(-(8-1),8,2) #alphabet = np.array([-10, -6, -3, -1, 1, 3, 6, 10]) <-- Non-uniform alphabet alphabet = alphabet / np.sqrt(np.mean(alphabet**2)) class Receiver(nn.Module): def init(self, M): super().init() self.lin1 = nn.Linear(1, M) def forward(self, y): y = self.lin1(y) return y class Encoder(nn.Module): def init(self, M): super().init() self.lin1 = nn.Linear(1, M, bias=False) nn.init.constant_(self.lin1.weight, 1 / M) self.out = nn.Softmax(dim=0) def forward(self, y): return self.out(self.lin1(y)) class Mapper(nn.Module): def init(self, M): super().init() self.lin1 = nn.Linear(M, 1) self.lin1.weight = nn.Parameter(torch.Tensor([[i for i in alphabet]])) # set weigths equal to alphabet def forward(self, y): y = self.lin1(y) return y def sampler(prob, n): samples = torch.empty(0) for idx, p in enumerate(prob): occurrences = torch.round(n * p).type(torch.LongTensor) samples = torch.cat((samples, torch.ones(occurrences, dtype=torch.int64) * torch.tensor(idx))) indexes = torch.randperm(samples.shape[0]) return samples[indexes] def gradient_correction_factor(app, idx, prob, M): (nn,M)= app.shape cf = torch.zeros(M) for j in range(M): tmp = app[:, j] cf[j] = torch.sum(torch.log(tmp[idxj])) / (nnprob[j]) # tmp[idxj] selects the ll of those xy pairs which belong to the current symbol j return cf def AWGN_channel(x, sigma2): noise_t = np.sqrt(sigma2)torch.randn(x.shape) return x + noise_t def tanh_channel(x, sigma2): noise_t = np.sqrt(sigma2)torch.randn(x.shape) return torch.tanh(x) + noise_t M = 8 n = 10_000 SNR_dB = 7 SNR = 10(SNR_dB/10) sigma2 = 1/SNR nepochs = 4000 dec = Receiver(M) enc = Encoder(M) mapper = Mapper(M) loss_fn = nn.CrossEntropyLoss() alphabet = np.arange(-(M-1),M,2) alphabet = np.array([-10, -6, -3, -1, 1, 3, 6, 10]) <-- Non-uniform alphabet alphabet = alphabet / np.sqrt(np.mean(alphabet2)) alphabet_t = torch.tensor(alphabet).float() for i in range(0, M): i_onehot = nn.functional.one_hot(torch.tensor(i), 8).float() print(mapper(i_onehot)) enc.lin1._parameters[‘weight’].shape lr = 0.1 opt = optim.Adam( list(enc.parameters()) + list(dec.parameters()) + list(mapper.parameters()), lr=lr) opt = optim.Adam( list(enc.parameters()) + list(dec.parameters()), lr=lr) torch.arange(1,M+1).squeeze() mapper(nn.functional.one_hot(torch.arange(M),M).float()).squeeze().shape for j in range(nepochs): # logits = enc(torch.tensor([1], dtype=torch.float)) probs = enc(torch.tensor([1], dtype=torch.float)) # probs = nn.functional.softmax(logits, -1) probs.retain_grad() # Sample indexes indices = sampler(probs, n) indices = indices.type(torch.LongTensor) # Modulation alphabet_t = mapper(nn.functional.one_hot(torch.arange(M),M).float()).squeeze() norm_factor = torch.rsqrt(torch.sum(torch.pow(torch.abs(alphabet_t), 2) probs)) alphabet_norm = alphabet_t * norm_factor onehot = nn.functional.one_hot(indices, M).float() symbols = torch.matmul(onehot, torch.transpose(input=alphabet_norm.reshape(1,-1), dim0=0, dim1=1)) # Channel # y = AWGN_channel(symbols, sigma2) y = tanh_channel(symbols, sigma2) # Demodulator ll = dec(y.reshape(-1,1).float()) app = nn.functional.softmax(ll, 1) #Q(X|Y) # Loss loss = -(torch.sum(-probstorch.log(probs)) - loss_fn(ll, indices))# -(H(X) - CE(P,Q)), the gradient descent minimizes, therefore we minimize the opposite to maximize the MI in the end. opt.zero_grad() loss.backward(retain_graph=True) # correction factor cf = - (gradient_correction_factor(app, indices, probs, M) - torch.log(probs)).detach() # if j % 500 == 0: # print('missing factors: ', cf.detach().numpy()) # print('current grad: ', probs.grad.detach().numpy()) probs.grad = cf probs.backward(torch.tensor([1., 1., 1., 1., 1., 1., 1., 1.])) # probs.grad += cf.detach() # enc.lin1._parameters['weight'].grad += cf.reshape(-1, 1).detach() opt.step() # Printout and visualization if j % 500 == 0: print(f'epoch {j}: Loss = {loss.detach().numpy() / np.log(2) :.4f}') enc.lin1._parameters[‘weight’] probs plt.rcParams[‘figure.figsize’] = [4, 4] plt.hist(symbols.detach().numpy(), bins=100) tikzplotlib.save(“/home/ddeandres/Projects/internship_pcs/documentation/figs/aref_gcs_{}dB.tex”.format(SNR_dB)) plt.show() plt.savefig(‘/home/ddeandres/Projects/internship_pcs/documentation/figs/aref_gcs_{}dB.pgf’.format(SNR_dB)) Scatterplot pp = (probs.reshape(-1,1)probs.reshape(1,-1)).reshape(-1,1).detach().numpy() alph = alphabet_norm.detach().numpy() a = [] for c in np.flip(alph): for d in alph: a.append(d+1jc) plt.scatter(np.real(a), np.imag(a), pp2000) plt.show() def AWGN_channel_np(x, sigma2): noise = np.sqrt(sigma2) * np.random.randn(x.size) return x + noise def AWGNdemapper(y, const, varN): apps = np.exp(-np.abs(np.transpose([y])-const)**2/(2varN)) return apps / np.transpose([np.sum(apps, 1)]) def xesmd(apps, idx): “”" Estimates symbolwise equivocation from reference symbols indices and a posteriori probabilities. “”" eq = -np.log(np.take_along_axis(apps, idx[:, None], axis=1) / np.transpose([np.sum(apps, 1)])) eq[eq==np.inf] = 1000 return np.mean(eq) n = 100_000 SNR_dBs = np.arange(5,22) M = 8 alphabet = np.arange(-7,8,2) alphabet = alphabet / np.sqrt(np.mean(alphabet2)) indices = np.random.choice(np.arange(M), n) symbols2 = alphabet[indices] mi_64 = [] for snrdB in SNR_dBs: sigma2 = 1/(10(snrdB/10)) sigma2 = sigma2 y = AWGN_channel_np(symbols2, sigma2) apps = AWGNdemapper(y, alphabet, sigma2) xe = xesmd(apps, indices) mi_64.append(2(3 - (xe) / np.log(2))) print((-2*loss.detach()/np.log(2)).detach().numpy()) Plot plt.rcParams[‘figure.figsize’] = [8, 6] plt.plot(SNR_dBs, mi_64, label = ‘64QAM’) plt.plot(SNR_dBs, np.log2(1+10(SNR_dBs/10)), color=‘black’, label=‘Capacity’) plt.plot(SNR_dB, -2loss.detach()/np.log(2), color=‘red’, marker=‘o’, markersize=3) xy = (SNR_dB, (-2loss.detach()/np.log(2)).detach().numpy()) plt.annotate(‘(%s, %s)’ % xy, xy=xy, textcoords=‘data’) plt.legend() plt.grid() SNR_dBs = np.arange(0,20) plt.plot(SNR_dBs, np.log2(1+10(SNR_dBs/10)), color=‘C0’, label=‘ C ( P / σ 2 ) C(P/σ 2 )’) plt.plot(SNR_dBs, np.log2(1+10**(SNR_dBs/10)) - 0.5np.log2((np.pinp.e)/6) , linestyle=‘dashed’, color=‘C1’, label=‘ C ( P / σ 2 ) − 1 2 log ⁡ 2 π e 6 C(P/σ 2 )− 2 1 log 2 6 πe ’) plt.grid() plt.ylabel(‘bits per channel use’) plt.xlabel(‘SNR in dB’) plt.xlim([0, 20]) plt.ylim([0, 5]) plt.title(‘AWGN channel capacity gap’) plt.legend() def one_hot(a, M): onehot = np.zeros(M) onehot[a] = 1 return onehot Data for the plots a_plot = np.arange(M) onehot_plot = np.array([one_hot(a_plot[i], M) for i in range(M)]) learned_x = mapper(torch.tensor(onehot_plot).float()) yy_plot = torch.tanh(learned_x) Plot plt.scatter(np.real(learned_x.detach().numpy()), np.imag(learned_x.detach().numpy())) plt.title(‘Learned constellation’) plt.grid() plt.scatter(np.real(yy_plot.detach().numpy()), np.imag(yy_plot.detach().numpy())) plt.title(‘Constellation after tanh’) plt.grid() 解释上述代码

def AWGN_channel_np(x, sigma2): """NumPy实现的AWGN信道""" noise = np.sqrt(sigma2) * np.random.randn(x.size) return x + noise def AWGNdemapper(y, const, varN): """计算后验概率（软解调）""" # 计算...

--------------------------------------------------------------------------- TypeError Traceback (most recent call last) ~\AppData\Local\Temp\ipykernel_463072\338222022.py in <module> 28 29 # 训练学习型编码器并记录互信息 ---> 30 loss = train_encoder_at_dB(snrdB) 31 mi_geo_pcs.append(-loss.detach().numpy() / np.log(2)) ~\AppData\Local\Temp\ipykernel_463072\2549115607.py in train_encoder_at_dB(dB, report) 25 symbols = torch.matmul(onehot, alphabet_norm.reshape(-1, 1)) 26 # 信道传输 ---> 27 y = AWGN_channel(symbols, sigma2) 28 # 接收机处理 29 ll = dec(y.float()) ~\AppData\Local\Temp\ipykernel_463072\931257074.py in AWGN_channel(x, sigma2) 60 def AWGN_channel(x, sigma2): 61 """添加高斯白噪声""" ---> 62 return x + torch.sqrt(sigma2) * torch.randn(x.shape) 63 64 def AWGN_channel_np(x, sigma2): TypeError: sqrt(): argument 'input' (position 1) must be Tensor, not numpy.float64

def AWGN_channel_np(x, sigma2): """NumPy版高斯白噪声（用于传统方法）""" return x + np.sqrt(sigma2) * np.random.randn(x.size) def AWGNdemapper(y, const, varN): """传统解调器：计算后验概率""" # ...

import numpy as np import matplotlib.pyplot as plt import torch from torch import nn, optim # 设置字体为Times New Roman plt.rcParams["font.family"] = "Times New Roman" plt.rcParams["axes.labelsize"] = 12 plt.rcParams["axes.titlesize"] = 14 # 辅助函数：将整数转换为one-hot编码向量 def one_hot(a, M): onehot = np.zeros(M) onehot[a] = 1 return onehot def normalization(x, P): c = torch.mean(x**2) # 计算当前信号功率 return torch.sqrt(P / c) * x # 缩放信号以达到目标功率 def awgn(x, sigma2): noise_t = np.sqrt(sigma2)*torch.randn(x.shape) return torch.add(x, noise_t) class Mapper(nn.Module): """ 映射器网络（带隐藏层） """ def init(self): super().init() self.lin1 = nn.Linear(32, 32) self.lin2 = nn.Linear(32, 32) self.lin3 = nn.Linear(32, 2) def forward(self, y): return self.lin3(self.lin2(self.lin1(y))) class Demapper(nn.Module): """ 解映射器网络（带隐藏层） """ def init(self): super().init() self.lin1 = nn.Linear(2, 32) self.lin2 = nn.Linear(32, 32) self.lin3 = nn.Linear(32, 32) def forward(self, y): return self.lin3(self.lin2(self.lin1(y))) # 生成训练数据（one-hot编码） M = 32 n = 10000 a = np.random.choice(range(M), size= n) # 随机生成消息索引 onehot = np.array([one_hot(a[i], M) for i in range(n)]) # 转换为one-hot编码 # 转换为PyTorch张量 onehot_t = torch.tensor(onehot).float() # 输入特征（one-hot编码） a_t = torch.tensor(a) # 目标标签（消息索引） a_t = a_t.type(torch.LongTensor) # 转换为长整型（用于交叉熵损失） # 损失函数（交叉熵损失） loss_fn = nn.CrossEntropyLoss() P = 1 SNRdBs = np.array([5,10,15]) SNRs = 10**(SNRdBs/10) # 转换为线性值 # 初始化网络 mapper = Mapper() demap = Demapper() # 训练循环（针对不同SNR） for (k,snr) in enumerate(SNRs): sigma2 = P/snr # 训练循环（针对不同SNR） print(f'---SNR = {SNRdBs[k]} dB---') # 优化器（同时优化映射器和解映射器） optimizer = optim.Adam(list(mapper.parameters()) + list(demap.parameters()), lr=0.01) # 训练循环 for j in range(10001): xhat = mapper(onehot_t) # 映射器生成星座点 xhat = normalization(xhat, P) # 归一化信号功率 yhat = awgn(xhat, sigma2) # 通过AWGN信道 l = demap(yhat) # 解映射器预测消息概率 # 计算损失和反向传播 loss = loss_fn(l, a_t) # 交叉熵损失 optimizer.zero_grad() # 梯度清零 loss.backward() # 反向传播 optimizer.step() # 参数更新 # 每500次迭代打印损失 if j % 500 == 0: # 将损失转换为比特（除以log2） print(f'epoch {j}: Loss = {loss.detach().numpy()/np.log(2) :.4f} dB') # 提前终止条件 if loss < 1e-3: break # 可视化学习到的星座图 a_plot = np.arange(M) # 所有可能的消息索引 onehot_plot = np.array([one_hot(a_plot[i], M) for i in range(M)]) # one-hot编码 learned_x = mapper(torch.tensor(onehot_plot).float()) # 生成星座点 learned_x = normalization(learned_x, P).detach().numpy() # 归一化并转为numpy print("learned_x[0:15,0]:", learned_x[0:15,0]) print("learned_x[16:31,0]:", learned_x[16:31,0]) print("learned_x[0:15,1]:", learned_x[0:15,1]) print("learned_x[16:31,1]:", learned_x[16:31,1]) plt.scatter(learned_x[:,0], learned_x[:,1]) plt.title(f'32QAM, SNR = {SNRdBs[k]} dB') plt.grid() plt.show() 请将代码中的功率归一化修改为幅度归一化，并保证任意两个星座点之间的距离不过小，尽可能保证其在接收端不被误判决

yhat = awgn(xhat, sigma2) l = demap(yhat) ce_loss = loss_fn(l, a_t) total_loss = ce_loss + 10.0 * R # 10.0是正则化系数，可以调整 # 然后反向传播注意：正则化系数需要调整，以确保正则项发挥作用...

BPSK信号在AWGN信道中的性能极限：如何突破

本文系统地探讨了BPSK信号在AWGN信道中的调制与解调技术，并对其在理想和实际条件下的误码率(BER)进行了详细分析。首先介绍了BPSK信号的基础知识和AWGN信道的理论基础，包括信道噪声、信噪比(SNR)和信道容量。接着，...

--------------------------------------------------------------------------- FileNotFoundError Traceback (most recent call last) ~/miniconda3/lib/python3.8/site-packages/matplotlib/texmanager.py in _run_checked_subprocess(self, command, tex, cwd) 232 try: --> 233 report = subprocess.check_output( 234 command, cwd=cwd if cwd is not None else self.texcache, ~/miniconda3/lib/python3.8/subprocess.py in check_output(timeout, *popenargs, **kwargs) 414 --> 415 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True, 416 **kwargs).stdout ~/miniconda3/lib/python3.8/subprocess.py in run(input, capture_output, timeout, check, *popenargs, **kwargs) 492 --> 493 with Popen(popenargs, kwargs) as process: 494 try: ~/miniconda3/lib/python3.8/subprocess.py in init(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, encoding, errors, text) 857 --> 858 self._execute_child(args, executable, preexec_fn, close_fds, 859 pass_fds, cwd, env, ~/miniconda3/lib/python3.8/subprocess.py in _execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, start_new_session) 1703 err_msg = os.strerror(errno_num) -> 1704 raise child_exception_type(errno_num, err_msg, err_filename) 1705 raise child_exception_type(err_msg) FileNotFoundError: [Errno 2] No such file or directory: 'latex' The above exception was the direct cause of the following exception: RuntimeError Traceback (most recent call last) ~/miniconda3/lib/python3.8/site-packages/IPython/core/formatters.py in call(self, obj) 339 pass 340 else: --> 341 return printer(obj) 342 # Finally look for special method names 343 method = get_real_method(obj, self.print_method) ~/miniconda3/lib/python3.8/site-packages/IPython/core/pylabtools.py in print_figure(fig, fmt, bbox_inches, base64, kwargs) 149 FigureCanvasBase(fig) 150 --> 151 fig.canvas.print_figure(bytes_io, kw) 152 data = bytes_io.getvalue() 153 if fmt == 'svg': ~/miniconda3/lib/python3.8/site-packages/matplotlib/backend_bases.py in print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, kwargs) 2288 ) 2289 with getattr(renderer, "_draw_disabled", nullcontext)(): -> 2290 self.figure.draw(renderer) 2291 2292 if bbox_inches: ~/miniconda3/lib/python3.8/site-packages/matplotlib/artist.py in draw_wrapper(artist, renderer, args, **kwargs) 71 @wraps(draw) 72 def draw_wrapper(artist, renderer, *args, **kwargs): ---> 73 result = draw(artist, renderer, *args, **kwargs) 74 if renderer._rasterizing: 75 renderer.stop_rasterizing() ~/miniconda3/lib/python3.8/site-packages/matplotlib/artist.py in draw_wrapper(artist, renderer) 48 renderer.start_filter() 49 ---> 50 return draw(artist, renderer) 51 finally: 52 if artist.get_agg_filter() is not None: ~/miniconda3/lib/python3.8/site-packages/matplotlib/figure.py in draw(self, renderer) 2801 2802 self.patch.draw(renderer) -> 2803 mimage._draw_list_compositing_images( 2804 renderer, self, artists, self.suppressComposite) 2805 ~/miniconda3/lib/python3.8/site-packages/matplotlib/image.py in _draw_list_compositing_images(renderer, parent, artists, suppress_composite) 130 if not_composite or not has_images: 131 for a in artists: --> 132 a.draw(renderer) 133 else: 134 # Composite any adjacent images together ~/miniconda3/lib/python3.8/site-packages/matplotlib/artist.py in draw_wrapper(artist, renderer) 48 renderer.start_filter() 49 ---> 50 return draw(artist, renderer) 51 finally: 52 if artist.get_agg_filter() is not None: ~/miniconda3/lib/python3.8/site-packages/matplotlib/axes/_base.py in draw(self, renderer) 3044 artists.remove(spine) 3045 -> 3046 self._update_title_position(renderer) 3047 3048 if not self.axison: ~/miniconda3/lib/python3.8/site-packages/matplotlib/axes/_base.py in _update_title_position(self, renderer) 2994 _log.debug('top of Axes not in the figure, so title not moved') 2995 return -> 2996 if title.get_window_extent(renderer).ymin < top: 2997 _, y = self.transAxes.inverted().transform((0, top)) 2998 title.set_position((x, y)) ~/miniconda3/lib/python3.8/site-packages/matplotlib/text.py in get_window_extent(self, renderer, dpi) 908 909 with cbook._setattr_cm(self.figure, dpi=dpi): --> 910 bbox, info, descent = self._get_layout(self._renderer) 911 x, y = self.get_unitless_position() 912 x, y = self.get_transform().transform((x, y)) ~/miniconda3/lib/python3.8/site-packages/matplotlib/text.py in _get_layout(self, renderer) 307 308 # Full vertical extent of font, including ascenders and descenders: --> 309 _, lp_h, lp_d = renderer.get_text_width_height_descent( 310 "lp", self._fontproperties, 311 ismath="TeX" if self.get_usetex() else False) ~/miniconda3/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py in get_text_width_height_descent(self, s, prop, ismath) 257 texmanager = self.get_texmanager() 258 fontsize = prop.get_size_in_points() --> 259 w, h, d = texmanager.get_text_width_height_descent( 260 s, fontsize, renderer=self) 261 return w, h, d ~/miniconda3/lib/python3.8/site-packages/matplotlib/texmanager.py in get_text_width_height_descent(self, tex, fontsize, renderer) 333 if tex.strip() == '': 334 return 0, 0, 0 --> 335 dvifile = self.make_dvi(tex, fontsize) 336 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1 337 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi: ~/miniconda3/lib/python3.8/site-packages/matplotlib/texmanager.py in make_dvi(self, tex, fontsize) 269 # not support.) 270 with TemporaryDirectory(dir=Path(dvifile).parent) as tmpdir: --> 271 self._run_checked_subprocess( 272 ["latex", "-interaction=nonstopmode", "--halt-on-error", 273 f"../{texfile.name}"], tex, cwd=tmpdir) ~/miniconda3/lib/python3.8/site-packages/matplotlib/texmanager.py in _run_checked_subprocess(self, command, tex, cwd) 235 stderr=subprocess.STDOUT) 236 except FileNotFoundError as exc: --> 237 raise RuntimeError( 238 'Failed to process string with tex because {} could not be ' 239 'found'.format(command[0])) from exc RuntimeError: Failed to process string with tex because latex could not be found

import numpy as np import torch import torch.nn as nn import torch.optim as optim import matplotlib.pyplot as plt import subprocess import os import sys # 重置matplotlib默认设置 plt.rcdefaults() # ...

信道冲击响应和%% 4. OFDM信号仿真与接收 % OFDM参数 (类似5G NR) scs = 15; % 子载波间距15kHz numSC = 960; % 子载波数 (20MHz带宽) cpLen = 144; % 循环前缀长度,循环前缀的时间长度T_cp = cpLen / fs_ofdm,循环前缀的时间长度需要大于信道最大时延扩展 numSym = 14; % 每帧符号数 fs_ofdm = 30.72e6; % 采样率，每个子载波间隔15kHz对应2048个采样点，FFT点数 = 2048 * (scs/15) % 计算资源块数 (RB) nRB = numSC / 12; % 1 RB = 12 子载波,最大支持 275 个资源块（对应 3300 个子载波） % 生成OFDM信号 data = randi([0, 1], numSCnumSym2, 1); % QPSK数据 qpskMod = comm.QPSKModulator('BitInput', true, 'PhaseOffset', pi/4); %创建一个QPSK调制器对象，设置输入为比特，并设置相位偏移为π/4 modData = qpskMod(data); % 使用QPSK调制器将二进制数据调制成频域QPSK符号 % 重塑为OFDM资源网格 ofdmGrid = reshape(modData, numSC, numSym); % txSignal的长度 = numSym * (FFT点数 + cpLen)，函数会为每个OFDM符号添加循环前缀 txSignal = nrOFDMModulate(ofdmGrid, scs, 0, 'CyclicPrefix', 'normal', 'SampleRate', fs_ofdm); % 将OFDM资源网格转换为时域信号，包括循环前缀 % 信号归一化，避免过小 txSignal = txSignal / sqrt(mean(abs(txSignal).^2)); % 归一化到功率1 % 通过信道并添加噪声（8个通道） rxSignals = cell(1,8); snr_dB = 30; % 信噪比 for i = 1:8 fprintf('处理无人机 %d 信道...\n', i); % % 时域卷积版本 % cir_response = cir_data{i}.CIR; % % 通过多径信道（卷积） % channel_output = conv(txSignal, cir_response,'same'); % 获取CIR并统一采样率 cir_time = cir_data{i}.Time; cir_response = cir_data{i}.CIR; % 2. 精确时间对齐 t_start = min(cir_time); t_end = max(cir_time); t_vec = t_start:1/fs_ofdm:t_end; % 在信道传输前添加检查 max_delay = t_end - t_start; T_cp = cpLen / fs_ofdm; if max_delay > T_cp warning('无人机 %d: 最大时延 %.2fμs > CP时间 %.2fμs! 将产生ISI/ICI',... i, max_delay1e6, T_cp1e6); end % 3. 线性插值（保持能量） % cir_interp = interp1(cir_time, cir_response, t_vec, 'linear', 0); cir_interp = interp1(cir_time, cir_response, t_vec, 'spline', 0); % 4. 频域卷积（避免时域截断） L = length(txSignal) + length(cir_interp) - 1; %计算频域卷积所需的FFT长度L NFFT = 2^nextpow2(L); % 计算下一个2的幂次作为FFT大小NFFT，以提高计算效率 % 确保X和H是列向量 X = fft(txSignal(:), NFFT); % (:) 强制列向量化 H = fft(cir_interp(:), NFFT); % (:) Y = X .* H; channel_output = ifft(Y); channel_output = channel_output(1:length(txSignal)); % 截断 % 5. 添加高斯白噪声 rxSignal = awgn(channel_output, snr_dB, 'measured'); % 6. 接收信号放大（解决量级问题） % rx_gain = 1e4; % 根据实际链路预算调整 % rxSignals{i} = rxSignal * rx_gain; rxSignals{i} = rxSignal; % 7. 信号功率记录 tx_power = mean(abs(txSignal).^2); rx_power = mean(abs(rxSignals{i}).^2); fprintf(' 发送功率: %.2f dBm, 接收功率: %.2f dBm, 损耗: %.2f dB\n', ... 10log10(tx_power/1e-3), 10log10(rx_power/1e-3), 10log10(tx_power/rx_power)); end ofdm_params.scs = scs; ofdm_params.cpLen = cpLen; ofdm_params.numSC = numSC; ofdm_params.numSym = numSym; ofdm_params.fs = fs_ofdm; ofdm_params.nRB = nRB; % % OFDM信号可视化 plotofdm(txSignal,rxSignals,ofdm_params,cir_data,ofdmGrid,snr_dB); % 2. 频谱分析 subplot(2,2,2); nfft = 4096; % 提高频谱分辨率 [P_tx, f_tx] = pwelch(txSignal, hanning(nfft), nfft/2, nfft, fs); %使用Welch方法计算发送信号和接收信号的PSD [P_rx, f_rx] = pwelch(rxSignals{1}, hanning(nfft), nfft/2, nfft, fs); plot(f_tx/1e6, 10log10(P_tx1000), f_rx/1e6, 10log10(P_rx*1000)); title('功率谱密度 (dBm/Hz)'); legend('发送信号', '接收信号'); xlabel('频率 (MHz)'); ylabel('PSD (dBm/Hz)'); grid on; 帮我看看我这样画出的功率谱密度图是对的吗？正确的功率谱密度图是什么样的？信道频率响应

import matplotlib.pyplot as plt from scipy.signal import welch N = 1024 # FFT大小 B = 20e6 # 带宽 (Hz) delta_f = B / N t = np.linspace(0, 1, N) s = np.sum([np.exp(1j * 2 * np.pi * k * delta_f * t) ...

仿真后显示：开始仿真...数据长度: 100000 bits, SNR范围: -5.0 dB 到 15.0 dB SNR = -5.0 dB: 编码BER = 2.772e-01, 理论BER = 2.132e-01, 未编码BER = 2.114e-01 SNR = -2.5 dB: 编码BER = 2.212e-01, 理论BER = 1.445e-01, 未编码BER = 1.436e-01 SNR = 0.0 dB: 编码BER = 1.614e-01, 理论BER = 7.865e-02, 未编码BER = 7.905e-02 SNR = 2.5 dB: 编码BER = 1.071e-01, 理论BER = 2.966e-02, 未编码BER = 2.908e-02 SNR = 5.0 dB: 编码BER = 7.463e-02, 理论BER = 5.954e-03, 未编码BER = 5.620e-03 SNR = 7.5 dB: 编码BER = 6.387e-02, 理论BER = 3.988e-04, 未编码BER = 4.600e-04 SNR = 10.0 dB: 编码BER = 6.202e-02, 理论BER = 3.872e-06, 未编码BER = 1.000e-05 SNR = 12.5 dB: 编码BER = 6.193e-02, 理论BER = 1.233e-09, 未编码BER = 0.000e+00 SNR = 15.0 dB: 编码BER = 6.193e-02, 理论BER = 9.124e-16, 未编码BER = 0.000e+00

行2: [0,1,1,1,0,0,0,1,1,1,1, 0,0,1,0] 行3: [0,0,0,0,1,1,1,1,1,1,1, 0,0,0,1] 但注意：我们上面提取的每一行是H矩阵的一行吗？实际上，H矩阵的每一行对应一个校验方程。我们构造的H是： H = [P^T | I4] -> ...

#include <stdio.h> #include <stdlib.h> #include <math.h> #include <time.h> #include <string.h> // BCH(7,4)编码参数 #define N_BCH 7 #define K_BCH 4 #define T_BCH 1 // 纠错能力 // 高斯随机数生成器（Box-Muller变换） double gaussrand(double mean, double stddev) { static double V1, V2, S; static int phase = 0; double X; if (phase == 0) { do { double U1 = (double)rand() / RAND_MAX; double U2 = (double)rand() / RAND_MAX; V1 = 2.0 * U1 - 1.0; V2 = 2.0 * U2 - 1.0; S = V1 * V1 + V2 * V2; } while (S >= 1.0 || S == 0.0); X = V1 * sqrt(-2.0 * log(S) / S); } else { X = V2 * sqrt(-2.0 * log(S) / S); } phase = 1 - phase; return mean + X * stddev; } // BCH(7,4)编码函数 void bch_encode(const int* input, int* output, int num_blocks) { // 生成矩阵 (系统形式) int G[K_BCH][N_BCH] = { {1, 0, 0, 0, 1, 1, 0}, {0, 1, 0, 0, 1, 0, 1}, {0, 0, 1, 0, 0, 1, 1}, {0, 0, 0, 1, 1, 1, 1} }; for (int i = 0; i < num_blocks; i++) { for (int j = 0; j < N_BCH; j++) { output[i * N_BCH + j] = 0; for (int k = 0; k < K_BCH; k++) { output[i * N_BCH + j] ^= input[i * K_BCH + k] * G[k][j]; } } } } // BCH(7,4)解码函数（带纠错） void bch_decode(const int* input, int* output, int num_blocks) { // 校验矩阵 int H[3][7] = { {1, 1, 0, 1, 1, 0, 0}, // 对应位置：0,1,3,4 {1, 0, 1, 1, 0, 1, 0}, // 对应位置：0,2,3,5 {0, 1, 1, 1, 0, 0, 1} // 对应位置：1,2,3,6 }; // 校正子到错误位置的映射（修正后的） // 索引 = s04 + s12 + s2 int error_pattern[8] = { -1, 6, 5, 2, 4, 1, 0, 3 }; // -1: 无错误 // 0: 位置0错误 // 1: 位置1错误 // 2: 位置2错误 // 3: 位置3错误 // 4: 位置4错误 // 5: 位置5错误 // 6: 位置6错误 for (int i = 0; i < num_blocks; i++) { int received[N_BCH]; memcpy(received, &input[i * N_BCH], N_BCH * sizeof(int)); // 计算校正子（异或运算） int syndrome[3] = { 0 }; for (int j = 0; j < 3; j++) { for (int k = 0; k < N_BCH; k++) { if (H[j][k]) { syndrome[j] ^= received[k]; } } } // 计算错误位置索引 (0-7) int error_index = syndrome[0] * 4 + syndrome[1] * 2 + syndrome[2]; int error_loc = error_pattern[error_index]; // 如果有错误且位置有效，则纠正 if (error_loc >= 0 && error_loc < N_BCH) { received[error_loc] ^= 1; // 翻转错误位 } // 提取信息位 for (int j = 0; j < K_BCH; j++) { output[i * K_BCH + j] = received[j]; } } } // 计算误码率 double calculate_ber(const int* original, const int* received, int length) { if (length <= 0) return 0.0; // 避免除以零 int errors = 0; for (int i = 0; i < length; i++) { if (original[i] != received[i]) { errors++; } } return (double)errors / length; } int main() { // 设置随机种子 srand((unsigned int)time(NULL)); // 参数初始化 const int n = 1000000; // 数据长度（比特数） const double SNR_dB_start = 0.0; const double SNR_dB_end = 10.0; const double SNR_dB_step = 1.0; // 增加步长以加快测试 const int num_snr = (int)((SNR_dB_end - SNR_dB_start) / SNR_dB_step) + 1; // 动态分配存储BER结果的数组 double* BER_encoded = (double)malloc(num_snr sizeof(double)); double* BER_theory = (double)malloc(num_snr sizeof(double)); double* BER_test = (double)malloc(num_snr sizeof(double)); if (!BER_encoded || !BER_theory || !BER_test) { fprintf(stderr, "内存分配失败\n"); exit(1); } // 生成随机数据 int* data = (int)malloc(n sizeof(int)); for (int i = 0; i < n; i++) { data[i] = rand() % 2; } // BCH编码参数 const int num_blocks = n / K_BCH; // 完整块数 // BCH编码 int* encoded_bits = (int)malloc(num_blocks N_BCH * sizeof(int)); if (!encoded_bits) { fprintf(stderr, "编码内存分配失败\n"); exit(1); } bch_encode(data, encoded_bits, num_blocks); const int encoded_length = num_blocks * N_BCH; // BPSK调制（0->-1, 1->1） double* BPSK_encoded = (double)malloc(encoded_length sizeof(double)); for (int i = 0; i < encoded_length; i++) { BPSK_encoded[i] = encoded_bits[i] ? 1.0 : -1.0; } // 未编码数据的BPSK调制 double* BPSK_test = (double)malloc(n sizeof(double)); for (int i = 0; i < n; i++) { BPSK_test[i] = data[i] ? 1.0 : -1.0; } printf("开始仿真...数据长度: %d bits, SNR范围: %.1f dB 到 %.1f dB\n", n, SNR_dB_start, SNR_dB_end); printf("编码方案: BCH(%d,%d), 纠错能力: %d bit\n", N_BCH, K_BCH, T_BCH); // 主循环：针对不同的SNR计算BER for (int z = 0; z < num_snr; z++) { double snr_db = SNR_dB_start + z * SNR_dB_step; double snr_lin = pow(10.0, snr_db / 10.0); // 关键：确保相同Eb/N0下的公平比较 double noise_var = 1.0 / (2.0 * snr_lin); // 未编码的噪声方差 double noise_std = sqrt(noise_var); // 编码系统的噪声方差（考虑码率损失） double noise_var_encoded = 1.0 / (2.0 * snr_lin * (double)K_BCH / N_BCH); double noise_std_encoded = sqrt(noise_var_encoded); // --------------------------------------------------- // 编码部分处理 // --------------------------------------------------- double* noisy_encoded = (double)malloc(encoded_length sizeof(double)); int* demod_encoded = (int)malloc(encoded_length sizeof(int)); int* decoded_bits = (int)malloc(num_blocks K_BCH * sizeof(int)); // 添加高斯噪声 for (int i = 0; i < encoded_length; i++) { noisy_encoded[i] = BPSK_encoded[i] + gaussrand(0.0, noise_std_encoded); } // BPSK解调（硬判决） for (int i = 0; i < encoded_length; i++) { demod_encoded[i] = (noisy_encoded[i] > 0.0) ? 1 : 0; } // BCH解码 bch_decode(demod_encoded, decoded_bits, num_blocks); // 计算编码BER BER_encoded[z] = calculate_ber(data, decoded_bits, num_blocks * K_BCH); // 释放内存 free(noisy_encoded); free(demod_encoded); free(decoded_bits); // --------------------------------------------------- // 未编码部分处理 // --------------------------------------------------- double* noisy_test = (double)malloc(n sizeof(double)); int* demod_test = (int)malloc(n sizeof(int)); // 添加高斯噪声 for (int i = 0; i < n; i++) { noisy_test[i] = BPSK_test[i] + gaussrand(0.0, noise_std); } // BPSK解调（硬判决） for (int i = 0; i < n; i++) { demod_test[i] = (noisy_test[i] > 0.0) ? 1 : 0; } // 计算未编码BER BER_test[z] = calculate_ber(data, demod_test, n); // 计算理论BER (未编码) BER_theory[z] = 0.5 * erfc(sqrt(snr_lin)); // 释放内存 free(noisy_test); free(demod_test); // 打印进度 printf("SNR = %4.1f dB: 编码BER = %8.3e, 未编码BER = %8.3e, 理论BER = %8.3e\n", snr_db, BER_encoded[z], BER_test[z], BER_theory[z]); } // 输出结果文件（用于绘图） FILE* fp = fopen("ber_results.txt", "w"); if (fp) { fprintf(fp, "SNR_dB BER_theory BER_encoded BER_test\n"); for (int z = 0; z < num_snr; z++) { double snr_db = SNR_dB_start + z * SNR_dB_step; fprintf(fp, "%.1f %.6e %.6e %.6e\n", snr_db, BER_theory[z], BER_encoded[z], BER_test[z]); } fclose(fp); printf("\n结果已保存到 ber_results.txt\n"); // 分析编码增益 int coding_gain_point = -1; for (int z = num_snr - 1; z >= 0; z--) { if (BER_encoded[z] < BER_test[z]) { coding_gain_point = z; break; } } if (coding_gain_point >= 0) { double snr_db = SNR_dB_start + coding_gain_point * SNR_dB_step; printf("-> 在 %.1f dB 处观察到编码增益: 编码BER=%.2e < 未编码BER=%.2e\n", snr_db, BER_encoded[coding_gain_point], BER_test[coding_gain_point]); } else { printf("-> 警告: 未检测到编码增益\n"); printf(" 可能原因:\n"); printf(" - 解码算法实现问题\n"); printf(" - SNR范围选择不当（需要在更高SNR区域仿真）\n"); printf(" - 数据长度不足（当前为%d比特）\n", n); printf(" 建议: 尝试设置SNR_dB_end=15.0并增加数据长度\n"); } } else { printf("保存结果到文件失败\n"); } // 释放所有内存 free(BER_encoded); free(BER_theory); free(BER_test); free(data); free(encoded_bits); free(BPSK_encoded); free(BPSK_test); return 0; }

位置2: [0,1,1] -> 0*4 + 1*2 + 1 = 3 -> error_pattern[3]=2 位置3: [1,1,1] -> 1*4 + 1*2 + 1 = 7 -> error_pattern[7] 但表大小只有8，索引0-7，7对应3 -> 正确位置4: [1,0,0] -> 1*4 + 0*2 + 0 = 4 -> error...

完成数字基带信号的生成，及滤波。噪声信号如图 t= 0:1/1000:1: noise=0.1*randn(size(t)):

import matplotlib.pyplot as plt from scipy.signal import upfirdn, firwin # 参数设置 Fs = 1000 Rb = 100 Nsym = 1000 sps = Fs // Rb beta = 0.5 span = 6 # 生成二进制数据 data = np.random.randint(0, 2, ...

--------------------------------------------------------------------------- RuntimeError Traceback (most recent call last) ~\AppData\Local\Temp\ipykernel_381048\701610136.py in <module> 123 124 # 反向传播 --> 125 total_loss.backward() 126 optimizer.step() 127 c:\Users\23740\AppData\Local\Programs\Python\Python37\lib\site-packages\torch\_tensor.py in backward(self, gradient, retain_graph, create_graph, inputs) 487 ) 488 torch.autograd.backward( --> 489 self, gradient, retain_graph, create_graph, inputs=inputs 490 ) 491 c:\Users\23740\AppData\Local\Programs\Python\Python37\lib\site-packages\torch\autograd\init.py in backward(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs) 197 Variable._execution_engine.run_backward( # Calls into the C++ engine to run the backward pass 198 tensors, grad_tensors_, retain_graph, create_graph, inputs, --> 199 allow_unreachable=True, accumulate_grad=True) # Calls into the C++ engine to run the backward pass 200 201 def grad( RuntimeError: one of the variables needed for gradient computation has been modified by an inplace operation: [torch.FloatTensor [32, 32]], which is output 0 of EuclideanDistBackward0, is at version 1; expected version 0 instead. Hint: enable anomaly detection to find the operation that failed to compute its gradient, with torch.autograd.set_detect_anomaly(True).

我们遇到了一个运行时错误，提示一个用于梯度计算的变量被就地操作修改了。错误信息指出，EuclideanDistBackward0输出的一个...import matplotlib.pyplot as plt import torch from torch import nn, optim import...

%% BP算法 clear;close all;clc; %% 程序说明 3.1 % 后向投影算法（BPA） % 扫描模式：条带 % 成像场景几何：正侧视 % 成像坐标：固定场景直角坐标系 % 相干累加截取有效时段 %------------------------------ 参数设置 ---------------------------- %% 基本参数 % 载频信号参数 c = 3e8; fc = 1e9; % 信号载频 lambda = c/fc; % 载波波长 % 平台参数 vr = 100; % SAR搭载平台速度 H = 5000; % 平台高度 %天线参数 D = 4; % 方位向天线长度 %% 快时间参数 % 距离向范围 Rg0 = 10e3; % 中心地距 RgL = 1000; % 测绘带宽 R0 = sqrt(Rg0^2+H^2); % 中心斜距（斜视角零度） % 合成孔径长度 La = lambdaR0/D; % 合成时长 Ta = La/vr; % 距离维/快时间维参数 Tw = 5e-6; % 脉冲持续时间 Br = 30e6; % 发射信号带宽 Kr = Br/Tw; % 调频率 Fr = 2Br; % 快时间维采样频率 Rmin = sqrt((Rg0-RgL/2)^2+H^2); Rmax = sqrt((Rg0+RgL/2)^2+H^2+(La/2)^2); Nfast = ceil(2(Rmax-Rmin)/cFr+TwFr); % 快时间维点数 Nfast = 2^nextpow2(Nfast); % 用于快时间维FFT的点数 tr = linspace(2Rmin/c,2Rmax/c+Tw,Nfast); Fr = 1/((2Rmax/c+Tw-2Rmin/c)/Nfast); % 与快时间维FFT点数相符的采样率 %% 慢时间参数 % 方位向范围 Az0 = 10e3; AL = 1000; Azmin = Az0-AL/2; Azmax = Az0+AL/2; % 方位维/慢时间维参数 Ka = -2vr^2/lambda/R0; % 慢时间维调频率 Ba = abs(KaTa); % 慢时间维带宽 PRF = 1.2Ba; % 脉冲重复频率 Mslow = ceil((Azmax-Azmin+La)/vrPRF); % 慢时间维点数/脉冲数 Mslow = 2^nextpow2(Mslow); % 用于慢时间维FFT的点数 ta = linspace((Azmin-La/2)/vr,(Azmax+La/2)/vr,Mslow); PRF = 1/((Azmax-Azmin+La)/vr/Mslow); % 与慢时间维FFT点数相符的脉冲重复频率 %% 性能参数 % 分辨率参数 Dr = c/2/Br; % 距离分辨率 Da = D/2; % 方位分辨率 %% 目标参数 Ptarget = [Az0-20,Rg0-20,1;Az0-20,Rg0,1;Az0-20,Rg0+20,1; Az0,Rg0-20,1;Az0,Rg0,1;Az0,Rg0+20,1; Az0+20,Rg0-20,1;Az0+20,Rg0,1;Az0+20,Rg0+20,1]; % 目标位置\散射信息 Ntarget = size(Ptarget,1); % 目标数量 fprintf('仿真参数：\n'); fprintf('快时间/距离维过采样率：%.4f\n',Fr/Br); fprintf('快时间/距离维采样点数：%d\n',Nfast); fprintf('慢时间/方位维过采样率：%.4f\n',PRF/Ba); fprintf('慢时间/方位维采样点数：%d\n',Mslow); fprintf('理论距离分辨率：%.1fm\n',Dr); fprintf('理论距离横向分辨率：%.1fm\n',Da); fprintf('合成孔径长度：%.1fm\n',La); disp('目标方位/地距/斜距：'); disp([Ptarget(:,1),Ptarget(:,2),sqrt(Ptarget(:,2).^2+H^2)]); figure; scatter(Ptarget(:,2),Ptarget(:,1),'fill'); grid on axis([Rg0-50,Rg0+50,Az0-50,Az0+50]); xlabel('\rightarrow\it地距/m'); ylabel('\it方位/m\leftarrow'); title('真实目标分布'); %------------------------------ 回波信号生成 ---------------------------- %% 回波信号生成 snr = 0; % 信噪比 Srnm = zeros(Mslow,Nfast); for k = 1:1:Ntarget sigmak = Ptarget(k,3); Azk = tavr-Ptarget(k,1); Rk = sqrt(Azk.^2+Ptarget(k,2)^2+H^2); tauk = 2Rk/c; tk = ones(Mslow,1)tr-tauk'ones(1,Nfast); phasek = piKrtk.^2-(4pi/lambda)(Rk'ones(1,Nfast)); Srnm = Srnm+sigmakexp(1iphasek).(0<tk&tk<Tw).((abs(Azk)<La/2)'ones(1,Nfast)); end Srnm = awgn(Srnm,snr,'measured'); %------------------------------ 距离脉冲压缩 ---------------------------- %% 距离压缩 thr = tr-2Rmin/c; hrc = exp(1ipiKrthr.^2).(0<thr&thr<Tw); % 距离维匹配滤波器 SAR1 =ifft((fft(Srnm,Nfast,2).(ones(Mslow,1)conj(fft(hrc,Nfast,2)))),Nfast,2); figure; imagesc(tr,ta,255-abs(SAR1)); xlabel('快时间'); ylabel('慢时间'); title('快时间维脉压(插值前）'); colormap(gray) %------------------------------ 方位脉冲压缩 ---------------------------- %% 距离插值 L = 8; trs = linspace(min(tr),max(tr),LNfast); SAR1f = fft(SAR1,Nfast,2); SAR11f = [SAR1f(:,1:floor((Nfast+1)/2)),zeros(Mslow,(L-1)Nfast),... SAR1f(:,floor((Nfast+1)/2)+1:end)]; SAR2 = ifft(SAR11f,LNfast,2); figure; imagesc(trs,ta,255-abs(SAR2)); xlabel('快时间'); ylabel('慢时间'); title('快时间维脉压(插值后）'); colormap(gray) %% 网格剖分 % 探测范围离散化 Rg = Rg0-50:0.2:Rg0+50; Nr =length(Rg); Az = Az0-50:0.1:Az0+50; Na = length(Az); %% SAR 成像 SAR3 = zeros(Na,Nr); for i = 1:Na for j = 1:Nr % 距离徙动曲线确定 Rt = sqrt((vrta-Az(i)).^2+Rg(j)^2+H^2); tau = 2Rt/c; nr = round((tau-min(tr))Fr); % 相位补偿 Azi = tavr-Az(i); I = abs(Azi)<La/2; index = find(I~=0); rd = zeros(1,length(index)); for m=index rd(m) = SAR1(m,nr(m)); end rdi = rd(I).exp(1j4pifc/cRt(I)); % 相干累加 SAR3(i,j) = sum(rdi); end disp(i); end %% SAR 成像 SAR4 = zeros(Na,Nr); for i = 1:Na for j = 1:Nr % 距离徙动曲线确定 Rt = sqrt((vrta-Az(i)).^2+Rg(j)^2+H^2); tau = 2Rt/c; nr = round((tau-min(trs))FrL); % 相位补偿 Azi = tavr-Az(i); I = abs(Azi)<La/2; index = find(I~=0); rd = zeros(1,length(index)); for m=index rd(m) = SAR2(m,nr(m)); end rdi = rd(I).exp(1j4pifc/cRt(I)); % 相干累加 SAR4(i,j) = sum(rdi); end disp(i); end figure; mesh(Rg,Az,abs(SAR3)); xlabel('地距R_g/m'); ylabel('方位A_z/m'); title('SAR图像'); colormap(gray) figure; mesh(Rg,Az,abs(SAR4)); xlabel('地距R_g/m'); ylabel('方位A_z/m'); title('SAR图像（插值后）'); colormap(gray) % figure; % imagesc(Rg,Az,255-abs(SAR4)); % xlabel('地距R_g/m'); % ylabel('方位A_z/m'); % title('SAR图像（插值后）'); % colormap(gray) figure; Max = max(max(abs(SAR3))); contourf(Rg,Az,abs(SAR3),[0.707Max,Max],'b'); grid on xlabel('\rightarrow\it地距R_g/m'); ylabel('\it方位A_z/m\leftarrow'); title('地面目标分辨率'); colormap(gray); figure; Max = max(max(abs(SAR4))); contourf(Rg,Az,abs(SAR4),[0.707Max,Max],'b'); grid on xlabel('\rightarrow\it地距R_g/m'); ylabel('\it方位A_z/m\leftarrow'); title('地面目标分辨率(插值后）'); colormap(gray); 帮我添加一段代码，用于计算sar3和sar4的实际分辨率，并与理论分辨率进行比较

import matplotlib.pyplot as plt def calculate_resolution(response, axis_type, params): """ 计算实际分辨率 :param response: 点目标响应曲线 :param axis_type: 'range'或'azimuth' :param params: 包含...

请将下面Matlab代码改写成Python代码：clear all clc t=0:0.01:3; %时间间隔为 0.01 说明采样频率为 100 Hz x=sin(2pi30t)+sin(2pi500t);%产生主要频率为 30Hz 和 500Hz 的信号 4 f=x+3.4randn(1,length(t)); %在信号中加入白噪声 subplot(121); plot(f); %画出原始信号的波形图 ylabel('幅值'); xlabel('时间'); title('原始信号'); y=fft(f,1024); %对原始信号进行离散傅里叶变换，参加 DFT 的采样点个数为 1024 p=y.conj(y); %计算功率谱，conj 表示复共轭，1024 调整放大倍数 ff=100*(0:511)/1024; %计算变换后不同点所对应的频率值 subplot(122); plot(ff,p(1:512)); %画出信号的频谱图 ylabel('功率谱'); xlabel('频率'); title('信号功率谱图')

import matplotlib.pyplot as plt from scipy import signal # 参数设置 fs = 100 # 采样频率(Hz) T = 3 # 总时长(s) t_step = 0.01 # 采样间隔 N = int(T / t_step) # 采样点数 # 生成时间向量 t = np.arange(0, ...

优化算法基于四则运算的算术优化算法原理与Python实现：面向图像分割的全局寻优方法研究

内容概要：本文系统介绍了算术优化算法（AOA）的基本原理、核心思想及Python实现方法，并通过图像分割的实际案例展示了其应用价值。AOA是一种基于种群的元启发式算法，其核心思想来源于四则运算，利用乘除运算进行全局勘探，加减运算进行局部开发，通过数学优化器加速函数（MOA）和数学优化概率（MOP）动态控制搜索过程，在全局探索与局部开发之间实现平衡。文章详细解析了算法的初始化、勘探与开发阶段的更新策略，并提供了完整的Python代码实现，结合Rastrigin函数进行测试验证。进一步地，以Flask框架搭建前后端分离系统，将AOA应用于图像分割任务，展示了其在实际工程中的可行性与高效性。最后，通过收敛速度、寻优精度等指标评估算法性能，并提出自适应参数调整、模型优化和并行计算等改进策略。; 适合人群：具备一定Python编程基础和优化算法基础知识的高校学生、科研人员及工程技术人员，尤其适合从事人工智能、图像处理、智能优化等领域的从业者；; 使用场景及目标：①理解元启发式算法的设计思想与实现机制；②掌握AOA在函数优化、图像分割等实际问题中的建模与求解方法；③学习如何将优化算法集成到Web系统中实现工程化应用；④为算法性能评估与改进提供实践参考；阅读建议：建议读者结合代码逐行调试，深入理解算法流程中MOA与MOP的作用机制，尝试在不同测试函数上运行算法以观察性能差异，并可进一步扩展图像分割模块，引入更复杂的预处理或后处理技术以提升分割效果。

3D感知（4）详解两阶段3D目标检测网络 Voxel R-CNN：Towards High Performance Voxel-based 3D Object Detection

今天介绍一篇两阶段的3D目标检测网络：Voxel R-CNN，论文已收录于AAAI 2021。 Voxel R-CNN论文链接为：https://arxiv.org/pdf/2012.15712.pdf 代码链接为：https://github.com/djiajunustc/Voxel-R-CNN

用于VMwarevSphere67和70版本的SC插件_虚拟机管理_自动化运维_云平台集成_资源监控_性能优化_高可用性配置_备份与恢复_安全策略实施_事件日志分析_存储管.zip

用于VMwarevSphere67和70版本的SC插件_虚拟机管理_自动化运维_云平台集成_资源监控......

相关推荐

import numpy as np import matplotlib.pyplot as plt import math

python 3.74 运行import numpy as np 报错lib\site-packages\numpy\__init__.py

import numpy as np(2).py

BPSK信号在AWGN信道中的性能极限：如何突破

完成数字基带信号的生成，及滤波。噪声信号如图 t= 0:1/1000:1: noise=0.1*randn(size(t)):

优化算法基于四则运算的算术优化算法原理与Python实现：面向图像分割的全局寻优方法研究

3D感知（4）详解两阶段3D目标检测网络 Voxel R-CNN：Towards High Performance Voxel-based 3D Object Detection

用于VMwarevSphere67和70版本的SC插件_虚拟机管理_自动化运维_云平台集成_资源监控_性能优化_高可用性配置_备份与恢复_安全策略实施_事件日志分析_存储管.zip

大家在看

电网两区域动态LFC模型

DateTimePicker自绘

瞬时单位线制作软件，一定要试试，很好用

STM32F10x_StdPeriph_Lib_V3.5.0.zip

opentelnet

最新推荐

优化算法基于四则运算的算术优化算法原理与Python实现：面向图像分割的全局寻优方法研究

【微信小程序源码】图文信息；欢迎页面，音乐控制.zip

bedrock-testing-support-7.0.4.jar中文-英文对照文档.zip

【微信小程序源码】物业管理.zip

Docker化部署TS3AudioBot教程与实践

零售销售数据的探索性分析与DeepAR模型预测

llm agent平台

Docker实现OAuth2代理：安全的HTTPS解决方案

利用AmazonSageMaker进行图像分类：从理论到实践

wed前端开发网页设计

python 3.74 运行import numpy as np 报错lib\site-packages\numpy\init.py