方形16QAM的C语言仿真

本文首先给出16QAM的原理，再给出对应方形星座的C语言设计过程，并附代码。

一、16QAM调制方式原理

为改善进制数较大情况下噪声容限减小的问题，发展出了QAM技术。QAM表示正交幅度调制，其对振幅和相位两个参量同时调制，其具有很高的频谱利用率和抗干扰能力，但对器件参数要求较高。
研究QAM技术主要从其最明显的特征——星座图入手。一般的，我们可以将QPSK视为4QAM，其为最简单的QAM，扩展至16QAM，对比其信号矢量图如下：

可以将16QAM视为两个交错的4ASK。对于每一个点的编码，可以分为对两个4ASK进行级联编码，按格雷码编码如下图所示：
使用格雷码按照上图顺序进行编码可以保证横，纵只有一比特位改变，在保证误码率不变的情况下将减小误比特率。

方形16QAM星座的噪声容限相较于星型16QAM的噪声容限要大，但在衰落信道中，由于星型16QAM的相位，幅度值少，故性能要更好。但是在调制解调的复杂度上，方形更好。

二、16QAM仿真程序

只需要将信号按照两路4ASK在调制判决即可。对于高斯噪声的添加原理，请参考以下博客的第二节：
BPSK，QPSK的C语言仿真
这里信噪比中的Eb计算如下：
方形16QAM的信号平均功率为：
P=A2M∑n=1M(cn2+dn2)=10A2P = \frac{{{A^2}}}{M}\sum\limits_{n = 1}^M {\left( {{c_n}^2 + {d_n}^2} \right)} = 10{A^2}P=MA2n=1∑M(cn2+dn2)=10A2
程序内设置A=1A=1A=1，则单位信号能量为10，则单位比特能量为2.5。

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<time.h>
#define pi 3.14159265
#define data_len 1000000            //比特长
#define M 4                         //进制数
#define k 16                        //符号比特
#define N 2                         //正交路 I Q
#define symbol_len data_len / M
#define EbN0_dB_MAX 15int data_bfcoding[data_len];
int symbol_bfcoding[M][symbol_len];
double symbol_coding[N][symbol_len];
int symbol_decoding[M][symbol_len];
int data_decoding[data_len];
double Eb = 2.5;void Data_produce();
void Symbol_produce();
void Modulation();
double Gauss();
void Gaussnoise(double EbN0_dB);
void Demodulation();
double Erdproduce();
double Mrdproduce();int main()
{double EbN0_dB = 0;srand(unsigned int(time(NULL)));double Erd, Mrd;for (int i = 0; i <= EbN0_dB_MAX; i++){EbN0_dB = i;Data_produce();Symbol_produce();Modulation();Gaussnoise(EbN0_dB);Demodulation();Erd = Erdproduce();Mrd = Mrdproduce();printf("Eb/N0 %d dB\t Symbol_Error: %f \t Bit_Error:%f \n", i, Mrd, Erd);}return 0;
}void Data_produce()
{for (int i = 0; i < data_len; i++){data_bfcoding[i] = rand() % 2;}
}void Symbol_produce()
{int temp = 0;for (int i = 0; i < symbol_len; i++){for (int j = 0; j < M; j++){symbol_bfcoding[j][i] = data_bfcoding[temp];temp++;}}
}void Modulation()
{for (int i = 0; i < symbol_len; i++){if (symbol_bfcoding[0][i] == 0 && symbol_bfcoding[1][i] == 0){symbol_coding[0][i] = -3.0;}if (symbol_bfcoding[0][i] == 0 && symbol_bfcoding[1][i] == 1){symbol_coding[0][i] = -1.0;}if (symbol_bfcoding[0][i] == 1 && symbol_bfcoding[1][i] == 1){symbol_coding[0][i] = 1.0;}if (symbol_bfcoding[0][i] == 1 && symbol_bfcoding[1][i] == 0){symbol_coding[0][i] = 3.0;}}for (int i = 0; i < symbol_len; i++){if (symbol_bfcoding[2][i] == 0 && symbol_bfcoding[3][i] == 0){symbol_coding[1][i] = -3.0;}if (symbol_bfcoding[2][i] == 0 && symbol_bfcoding[3][i] == 1){symbol_coding[1][i] = -1.0;}if (symbol_bfcoding[2][i] == 1 && symbol_bfcoding[3][i] == 1){symbol_coding[1][i] = 1.0;}if (symbol_bfcoding[2][i] == 1 && symbol_bfcoding[3][i] == 0){symbol_coding[1][i] = 3.0;}}
}double Gauss()
{double U, V, Z;U = (double)(rand() + 1.0) / (double)(RAND_MAX + 1.0);V = (double)(rand() + 1.0) / (double)(RAND_MAX + 1.0);Z = sqrt(-2 * log(U)) * sin(2 * pi * V);return Z;
}void Gaussnoise(double EbN0_dB)
{double EbN0 = pow(10, EbN0_dB / 10);double N0 = Eb / EbN0;double sigma = sqrt(N0 / 2);for (int i = 0; i < symbol_len; i++){symbol_coding[0][i] = symbol_coding[0][i] + Gauss() * sigma;symbol_coding[1][i] = symbol_coding[1][i] + Gauss() * sigma;}
}void Demodulation()
{for (int i = 0; i < symbol_len; i++){if (symbol_coding[0][i] > 2.0){symbol_decoding[0][i] = 1;symbol_decoding[1][i] = 0;}if (symbol_coding[0][i] <= 2.0 && symbol_coding[0][i] > 0){symbol_decoding[0][i] = 1;symbol_decoding[1][i] = 1;}if (symbol_coding[0][i] <= 0 && symbol_coding[0][i] > -2.0){symbol_decoding[0][i] = 0;symbol_decoding[1][i] = 1;}if (symbol_coding[0][i] <= -2.0){symbol_decoding[0][i] = 0;symbol_decoding[1][i] = 0;}}for (int i = 0; i < symbol_len; i++){if (symbol_coding[1][i] > 2.0){symbol_decoding[2][i] = 1;symbol_decoding[3][i] = 0;}if (symbol_coding[1][i] <= 2.0 && symbol_coding[1][i] > 0){symbol_decoding[2][i] = 1;symbol_decoding[3][i] = 1;}if (symbol_coding[1][i] <= 0 && symbol_coding[1][i] > -2.0){symbol_decoding[2][i] = 0;symbol_decoding[3][i] = 1;}if (symbol_coding[1][i] <= -2.0){symbol_decoding[2][i] = 0;symbol_decoding[3][i] = 0;}}int temp = 0;for (int i = 0; i < symbol_len; i++){for (int j = 0; j < M; j++){data_decoding[temp] = symbol_decoding[j][i];temp++;}}
}double Erdproduce()
{double Erd;int Nrd = 0;for (int i = 0; i < data_len; i++){if (data_decoding[i] != data_bfcoding[i])Nrd++;}Erd = (double)Nrd / (double)data_len;return Erd;
}double Mrdproduce()
{double Mrd;int Srd = 0;int p[M];int pt;for (int i = 0; i < symbol_len; i++){int pt = 0;for (int j = 0; j < M; j++){if (symbol_decoding[j][i] == symbol_bfcoding[j][i])p[j] = 0;elsep[j] = 1;}for (int j = 0; j < M; j++){pt = pt + p[j];}if (pt > 0)Srd++;}Mrd = (double)Srd / (double)(symbol_len);return Mrd;
}

三、仿真结果

下面给出不同比特信噪比下误码率和误比特率结果。