作为射频工程师的你，是不是对EVM的计算方法也感点兴趣？
在EVM是个什么东东喽？，有说过，EVM衡量的是星座图上理想点和实测点偏移量的大小。
虽说，有这样一个公式，但是光看公式，总是觉得云里雾里的。
最近，因为在琢磨用ADS进行系统仿真的事，然后一步一步下来，发现在ADS的AEL文件里，藏着很多宝藏。
昨天说过，在射频层面仿真EVM的时候，在ADS里面发现两种仿真计算的方法。
一种是在dds文件上，以constellation()函数为基础，一个一个写公式，然后出来EVM的计算结果。
另一种，是在dds文件上，直接调用const_evm()函数来计算EVM的值。
我大概过了一下两种方法的流程，大致差不多。
但是，昨天在仿真的时候，发现当我把Symbol_rate从24.3KHz调整到150KHz，并且输入功率设小的时候，两者仿真出来的结果差很多。
没办法，只能仔细地去看const_evm()函数里面的具体细节。
(2)
先把这个程序贴出来。
defun const_evm(vfund_ideal, vfund_dist, u_symbol_rate,u_sample_delay, u_rotation, u_transient_duration, u_path_delay){if ( vfund_ideal == NULL || vfund_dist == NULL )return;decl symbol_rate = u_symbol_rate == NULL ? 0 : u_symbol_rate;decl transient_duration = u_transient_duration == NULL ? 0 : u_transient_duration;decl tran_time = 0;if ( transient_duration ) // skip integer number of symbolstran_time = ceil(mag(transient_duration)*symbol_rate)/symbol_rate;decl sample_delay = u_sample_delay == NULL ? best_delay_1d(vfund_ideal,symbol_rate,tran_time) : u_sample_delay;decl rotation = u_rotation == NULL ? 0 : u_rotation;decl Path_Delay_default = delay_path(vfund_ideal,vfund_dist);decl path_delay = u_path_delay == NULL ? Path_Delay_default[0] : u_path_delay; // This is a better default than 0.vfund_ideal = vfund_ideal*exp(j*rotation);vfund_dist = vfund_dist*exp(j*rotation);decl vfund_ideal_real = real(vfund_ideal);decl vfund_ideal_imag = imag(vfund_ideal);decl vfund_dist_real = real(vfund_dist);decl vfund_dist_imag = imag(vfund_dist);decl time_values = indep(vfund_ideal);decl time_step = time_values[1]-time_values[0];decl i;decl numPts_i=9;decl min_time_offset = -0.5*time_step;decl time_offset;decl best_evm_rms = 1000; // initialized as an arbitrary large numberdecl evm_rms_this_trial;decl evm_percent;decl best_mean_phase_delta;decl best_vfund_C_dist;decl best_evm;// Ideal trajectorydecl ideal_trajectory = vs(vfund_ideal_imag, vfund_ideal_real);// set interpolation pointsdecl start_time = sample_delay; // removed + tran_time;decl stop_time = max(indep(vfund_ideal));decl incr = NULL;if (symbol_rate)incr = 1/symbol_rate;// Ideal constellationdecl vfund_C_ideal_real = interp(vfund_ideal_real, start_time, stop_time, incr);decl vfund_C_ideal_imag = interp(vfund_ideal_imag, start_time, stop_time, incr);decl vfund_C_ideal = vfund_C_ideal_real+j*vfund_C_ideal_imag;decl vfund_C_ideal_rms = sqrt(mean(mag(vfund_C_ideal)**2));vfund_C_ideal = vfund_C_ideal/vfund_C_ideal_rms;decl ideal_constellation = vs(imag(vfund_C_ideal), real(vfund_C_ideal));set_attr(ideal_constellation,"TraceType","Scatter");for (i=0; i<numPts_i; i++) // Loop to find minimum EVM{time_offset = min_time_offset + i*time_step/8;decl vfund_C_dist_real = interp(vfund_dist_real, start_time+path_delay+time_offset, stop_time, incr); // this length may change with i.decl vfund_C_dist_imag = interp(vfund_dist_imag, start_time+path_delay+time_offset, stop_time, incr); // this length may change with i.decl vfund_C_dist = vfund_C_dist_real +j*vfund_C_dist_imag;decl sn = min([sweep_size(vfund_C_dist_real), sweep_size(vfund_C_ideal_real)]);// phase compensationdecl mean_phase_delta = __phase_delta_calc(vfund_C_ideal[0::sn-1], vfund_C_dist[0::sn-1]);vfund_C_dist = (vfund_C_dist)*exp(-j*mean_phase_delta);// scalingdecl scaling = sqrt(mean(mag(vfund_C_dist[0::sn-1])**2)); // Previously divided this by RMS value of ideal constellation, but this is now 1.vfund_C_dist = vfund_C_dist/scaling;// EVMdecl evm = mag(vfund_C_dist[0::sn-1]-vfund_C_ideal[0::sn-1]);// EVM_percentevm_rms_this_trial = sqrt(mean(evm**2)); // This could be divided by the RMS value of the ideal constellation, but this is now 1.if (evm_rms_this_trial < best_evm_rms){best_evm = evm;best_evm_rms = evm_rms_this_trial;best_mean_phase_delta = mean_phase_delta;best_vfund_C_dist = vfund_C_dist*scaling; // undoing the scaling to generate the distorted constellation}evm_percent = 100*best_evm_rms; // has to be calculated inside the loop because sn could change from one iteration to the next.}// distorted compensated trajectory (phase compensation only)vfund_dist=vfund_dist*exp(-j*best_mean_phase_delta);decl dist_trajectory = vs(imag(vfund_dist),real(vfund_dist));decl distorted_constellation = vs(imag(best_vfund_C_dist), real(best_vfund_C_dist));set_attr(distorted_constellation,"TraceType","Scatter");return list(ideal_constellation, ideal_trajectory, distorted_constellation, dist_trajectory, best_evm, evm_percent);} //fun - const_evm
看上去很长也很难懂，对不对？我也是鼓足很大的勇气，才对着电脑开始研读的。
但是等看完了以后，发现，以后不能自己吓自己。这个程序看上去很长，但是其实只要懂点英文，然后有点数学基础，基本都能看懂。
对于我来说，这上面最大的不懂点，可能就是这条语句。但是现在有AI，分分钟给你解释的清清楚楚。
decl symbol_rate = u_symbol_rate == NULL ? 0 : u_symbol_rate;比如说，上面这条语句，chatgpt是这样给我解释的。
简单理解，就是把u_symbol_rate的值，赋给symbol_rate。
接着，我们一条条看一下const_evm()中的语句哈！
(3)
if ( vfund_ideal == NULL || vfund_dist == NULL )return;decl symbol_rate = u_symbol_rate == NULL ? 0 : u_symbol_rate;decl transient_duration = u_transient_duration == NULL ? 0 : u_transient_duration;decl tran_time = 0;if ( transient_duration ) // skip integer number of symbolstran_time = ceil(mag(transient_duration)*symbol_rate)/symbol_rate;decl sample_delay = u_sample_delay == NULL ? best_delay_1d(vfund_ideal,symbol_rate,tran_time) : u_sample_delay;decl rotation = u_rotation == NULL ? 0 : u_rotation;decl Path_Delay_default = delay_path(vfund_ideal,vfund_dist);decl path_delay = u_path_delay == NULL ? Path_Delay_default[0] : u_path_delay; // This is a better default than 0.
decl，从ADS的help文件可知，是define a variable的意思。
在dds文件中，使用const_evm的时候，会给参数，如下图所示。
vfund_ideal = vfund_ideal*exp(j*rotation);vfund_dist = vfund_dist*exp(j*rotation);decl vfund_ideal_real = real(vfund_ideal);decl vfund_ideal_imag = imag(vfund_ideal);decl vfund_dist_real = real(vfund_dist);decl vfund_dist_imag = imag(vfund_dist);
在const_evm()的参数中，第一个参数，是理想的信号；第二个参数，是经过射频链路后的信号，暂且把它称为失真信号。
上面的语句，主要是把理想信号(vfund_ideal)和失真信号(vfund_dist)都旋转一个角度，这个角度也是在const_evm()的参数中定义。然后取出旋转后信号的实部和虚部。
可以看到，这个旋转对理想信号和失真信号是同时有效的。所以，还没搞清楚，这个参数的主要的作用是啥。不过呢，这个参数主要是影响星座图的旋转角度，和EVM的值，倒是没啥关系。
(5)
decl time_values = indep(vfund_ideal);decl time_step = time_values[1]-time_values[0];decl i;decl numPts_i=9;decl min_time_offset = -0.5*time_step;decl time_offset;decl best_evm_rms = 1000; // initialized as an arbitrary large numberdecl evm_rms_this_trial;decl evm_percent;decl best_mean_phase_delta;decl best_vfund_C_dist;decl best_evm;
因为仿真结果是基于envelope仿真器的，有Tstep设置。所以上面的第一和第二句，就是从信号中恢复出这个Tstep。
接下来的语句，是定义各种各样的变量。
(6)
// Ideal trajectorydecl ideal_trajectory = vs(vfund_ideal_imag, vfund_ideal_real);
这个语句厉害了，没看到这个语句的时候，我觉得，把星座图画出来好难啊！等我看到这个语句的时候，一下子无言，就这么一句话！当然，这里还不是星座图，是符号变化的轨迹。不过离星座图就差一行代码！
不过，我个人觉得这里有个小bug。
因为仿真过程中发现，在dds文件上，想把理想信号的星座图和轨迹放在一张图上的话，轨迹变成一个很小的点。
从代码来看，应该是因为计算星座图的时候，归一化了，但是看计算轨迹的时候，则没有。
再说回上面的语句。
看help文件，vs()是这么解释的。
看上去不太直观哈，但是从最终绘制的结果来看，大概就是在二维矩形坐标上，画出dependent随independent变化的曲线。
（7）
// set interpolation pointsdecl start_time = sample_delay; // removed + tran_time;decl stop_time = max(indep(vfund_ideal));decl incr = NULL;if (symbol_rate)incr = 1/symbol_rate;// Ideal constellationdecl vfund_C_ideal_real = interp(vfund_ideal_real, start_time, stop_time, incr);decl vfund_C_ideal_imag = interp(vfund_ideal_imag, start_time, stop_time, incr);decl vfund_C_ideal = vfund_C_ideal_real+j*vfund_C_ideal_imag;decl vfund_C_ideal_rms = sqrt(mean(mag(vfund_C_ideal)**2));vfund_C_ideal = vfund_C_ideal/vfund_C_ideal_rms;decl ideal_constellation = vs(imag(vfund_C_ideal), real(vfund_C_ideal));set_attr(ideal_constellation,"TraceType","Scatter");
在help文件中，interp()的解释是这样的。
信号的时间间隔原来是Tstep，这个我在原理图中设置的是1/(4*symbolrate)，在程序中，做了个线性插值，使得信号的时间间隔变为1/symbolrate。
然后对理想信号进行归一化，并用vs()画出在二维坐标系上，虚部和实部的关系。并且用set_attr()来设置图形的表现形式，让其以点状的形式显示，从而显示成星座图，而不是轨迹。
(8)
for (i=0; i<numPts_i; i++) // Loop to find minimum EVM{time_offset = min_time_offset + i*time_step/8;decl vfund_C_dist_real = interp(vfund_dist_real, start_time+path_delay+time_offset, stop_time, incr); // this length may change with i.decl vfund_C_dist_imag = interp(vfund_dist_imag, start_time+path_delay+time_offset, stop_time, incr); // this length may change with i.decl vfund_C_dist = vfund_C_dist_real +j*vfund_C_dist_imag;decl sn = min([sweep_size(vfund_C_dist_real), sweep_size(vfund_C_ideal_real)]);// phase compensationdecl mean_phase_delta = __phase_delta_calc(vfund_C_ideal[0::sn-1], vfund_C_dist[0::sn-1]);vfund_C_dist = (vfund_C_dist)*exp(-j*mean_phase_delta);// scalingdecl scaling = sqrt(mean(mag(vfund_C_dist[0::sn-1])**2)); // Previously divided this by RMS value of ideal constellation, but this is now 1.vfund_C_dist = vfund_C_dist/scaling;// EVMdecl evm = mag(vfund_C_dist[0::sn-1]-vfund_C_ideal[0::sn-1]);// EVM_percentevm_rms_this_trial = sqrt(mean(evm**2)); // This could be divided by the RMS value of the ideal constellation, but this is now 1.if (evm_rms_this_trial < best_evm_rms){best_evm = evm;best_evm_rms = evm_rms_this_trial;best_mean_phase_delta = mean_phase_delta;best_vfund_C_dist = vfund_C_dist*scaling; // undoing the scaling to generate the distorted constellation}evm_percent = 100*best_evm_rms; // has to be calculated inside the loop because sn could change from one iteration to the next.}
这个for语句，是代码里面做了一个循环，以time_step/8为步进，来找出最合适的采样点，使得EVM最小。
// phase compensationdecl mean_phase_delta = __phase_delta_calc(vfund_C_ideal[0::sn-1], vfund_C_dist[0::sn-1]);vfund_C_dist = (vfund_C_dist)*exp(-j*mean_phase_delta);// scalingdecl scaling = sqrt(mean(mag(vfund_C_dist[0::sn-1])**2)); // Previously divided this by RMS value of ideal constellation, but this is now 1.vfund_C_dist = vfund_C_dist/scaling;
这四个语句，分别是进行相位补偿和幅度归一化。
// EVMdecl evm = mag(vfund_C_dist[0::sn-1]-vfund_C_ideal[0::sn-1]);
这个呢，就是开始计算EVM呢，即理想矢量点和实测矢量点之间的误差的幅值。
(9)
// distorted compensated trajectory (phase compensation only)vfund_dist=vfund_dist*exp(-j*best_mean_phase_delta);decl dist_trajectory = vs(imag(vfund_dist),real(vfund_dist));decl distorted_constellation = vs(imag(best_vfund_C_dist), real(best_vfund_C_dist));set_attr(distorted_constellation,"TraceType","Scatter");return list(ideal_constellation, ideal_trajectory, distorted_constellation, dist_trajectory, best_evm, evm_percent);
最后，就是计算失真信号的星座图和变化轨迹啦！
(10)
终于讲完了！
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首次发布时间：2023-12-02
最近编辑：10月前
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