A Genetic Algorithm-based Beamforming Approach

在兹介紹一下所謂Beamforming(波束成型的天線陳列) 的架構,

自LTE通訊啓,基地台為了提供更佳的服務,故使用天線陣列來極化電磁波以利QoS的提升, 在5G的技術中, 幾乎其天缐唯一選項就是波束成型 (beamforming),  波束成型(Beamforming)技術可以大略的分成兩種:

第一種: 藉由量測到的通道係數, 設計傳送參數 (precoder), 最佳化通道

第二種: 透過多天線的相位偏移 (phase shifter), 決定電波傳遞強度模

本章節以Phase shifter 為其架構, 假設以1x9“矩陣”是線性代數來描述波束成型的天線陳列、

本文利用基因工程(Genetic Algorithm-based_來找出每一個Cell 的Weight以利其快速其值。

Source code with Python:

# -*- coding: utf-8 -*-

import numpy as np
import ga
import matplotlib.pyplot as plt
"""
The y=target is to maximize this equation ASAP:
    y = w1x1+w2x2+w3x3+w4x4+w5x5+6wx6+7Wx7+8Wx7+9Wx9
    where (x1,x2,x3,x4,x5,x6,x7,x8,x9)=(4,-2,3.5,5,-11,-4.7,5.0,2.1,3.1)
    What are the best values for the 9 weights w1 to w9?
    We are going to use the genetic algorithm for the best possible values after a number of generations.
"""

# Inputs of the equation.
equation_inputs = [4,-2,3.5,5,-11,-4.7,5.0,2.1,3.1]

# Number of the weights we are looking to optimize.
num_weights = len(equation_inputs)

"""
Genetic algorithm parameters:
    Mating pool size
    Population size
"""
sol_per_pop = 8
num_parents_mating = 4

# Defining the population size.
pop_size = (sol_per_pop,num_weights) # The population will have sol_per_pop chromosome where each chromosome has num_weights genes.
#Creating the initial population.
new_population = np.random.uniform(low=-4.0, high=4.0, size=pop_size)
print("new_population")
print(new_population)

"""
new_population[0,:]=[[ 2.58108145  2.42053643 -3.24720098  0.73414778  2.95861561 -3.95613747
   2.34638506 -1.96226993 -2.4267999 ]
new_population[1,:]= [ 0.50988501  3.66384758 -0.35728906 -3.36106177  0.60748192  0.34572714
   0.63256316  3.59916985  0.5291632 ]
new_population[2,:]= [-3.99726266 -1.05382206 -0.72618039 -0.69354415  3.6819675   1.42235044
   3.21944868  0.56545786 -2.53333267]
new_population[3,:]= [-2.01602033  3.21295543  0.1898793  -2.6094637   1.9595066  -2.04175245
  -0.63172776 -1.84656932 -3.39214779]
new_population[4,:]= [-1.65667992 -3.61456147 -2.08880869  0.51076383  0.06322565 -0.43551276
  -3.4748497  -2.61883376  2.93387284]
new_population[5,:]= [ 3.06194594 -1.81691236 -3.5244207   3.7688676  -0.78804301  1.7642483
  -1.63477098  2.0739781  -3.88904675]
new_population[6,:]= [-0.7733979  -0.59532673  0.22656214 -1.53837445 -1.72333473 -1.32000815
   1.8188883  -0.8669669  -1.29803437]
new_population[7,:]= [-3.52687898 -3.91602606  2.07969841 -2.29166193  0.58104485  0.79150089
  -3.13136887 -0.04240155  2.80654781]]
"""

best_outputs = []
num_generations = 10
for generation in range(num_generations):
    print("Generation : ", generation)
    # Measuring the fitness of each chromosome in the population.
    fitness = ga.cal_pop_fitness(equation_inputs, new_population)
    print("Fitness")
    print(fitness)

    best_outputs.append(np.max(numpy.sum(new_population*equation_inputs, axis=1)))
    # The best result in the current iteration.
    print("Best result : ", np.max(np.sum(new_population*equation_inputs, axis=1)))
    
    # Selecting the best parents in the population for mating.
    parents = ga.select_mating_pool(new_population, fitness, 
                                      num_parents_mating)
    print("Parents")
    print(parents)

    # Generating next generation using crossover.
    offspring_crossover = ga.crossover(parents,
                                       offspring_size=(pop_size[0]-parents.shape[0], num_weights))
    print("Crossover")
    print(offspring_crossover)

    # Adding some variations to the offspring using mutation.
    offspring_mutation = ga.mutation(offspring_crossover, num_mutations=2)
    print("Mutation")
    print(offspring_mutation)

    # Creating the new population based on the parents and offspring.
    new_population[0:parents.shape[0], :] = parents
    new_population[parents.shape[0]:, :] = offspring_mutation
    
# Getting the best solution after iterating finishing all generations.
#At first, the fitness is calculated for each solution in the final generation.
fitness = ga.cal_pop_fitness(equation_inputs, new_population)
# Then return the index of that solution corresponding to the best fitness.
best_match_idx = np.where(fitness == np.max(fitness))

print("Best solution : ", new_population[best_match_idx, :])
print("Best solution fitness : ", fitness[best_match_idx])



plt.plot(best_outputs)
plt.xlabel("Iteration")
plt.ylabel("Fitness")

plt.show()