OFDM——PAPR减小（一）https://developer.aliyun.com/article/1473988
②、仿真结果
总的来说，当 N NN 增大时，PAPR 变得更加明显
从图中可以看出，x [ n ] x[n]x[n] 的实部和虚部服从高斯分布，而 ∣ x [ n ] ∣ |x[n]|∣x[n]∣ 或 ∣ x [ t ] ∣ |x[t]|∣x[t]∣ 服从瑞利分布
对于具有 N 个子载波的OFDM符号，当每个子载波分量具有相同的相位，且恰好出现最大幅度时， OFDM 信号具有最大功率。最大功率随着 N 的增大而增大，而且出现最大功率的概率随着 N 的增大而降低。
4、Chu 序列和 IEEE802.16e 前导的 PAPR
①、MATLAB 源码
PAPR_of_Chu.m
% PAPR_of_Chu.m % Plot Fig. 7.10(a) %MIMO-OFDM Wireless Communications with MATLAB㈢ Yong Soo Cho, Jaekwon Kim, Won Young Yang and Chung G. Kang %2010 John Wiley & Sons (Asia) Pte Ltd clear, clf N=16; L=4; i=[0:N-1]; k = 3; X = exp(j*k*pi/N*(i.*i)); [x,time] = IFFT_oversampling(X,N); PAPRdB = PAPR(x); [x_os,time_os] = IFFT_oversampling(X,N,L); %x_os=x_os*L; PAPRdB_os = PAPR(x_os); subplot(221), plot(x,'o'); hold on, plot(x_os,'k*'); legend('L=1','L=4'); axis([-0.4 0.4 -0.4 0.4]), axis('equal'); plot(0.25*exp(j*pi/180*[0:359])); % circle with radius 0.25 subplot(222), plot(time,abs(x),'o', time_os,abs(x_os),'k:*'); xlabel('时间（由符号间隔归一化）'); ylabel('|IFFT(u1(k))|'); title('IFFT(X1(k)),k=3,N=16,L=1,4'); legend('L=1','L=4'); PAPRdB_without_and_with_oversampling=[PAPRdB PAPRdB_os];
PAPR_of_preamble.m
% PAPR_of_preamble.m % Plot Fig. 7.10(b) (the PAPR of IEEE802.16e preamble) %MIMO-OFDM Wireless Communications with MATLAB㈢ Yong Soo Cho, Jaekwon Kim, Won Young Yang and Chung G. Kang %2010 John Wiley & Sons (Asia) Pte Ltd clear, clf N=1024; L=4; Npreamble=114; n=0:Npreamble-1; % Mod='BPSK'; %PAPR = zeros(N_preamble,1); PAPR_os = zeros(N_preamble,1); for i = 1:Npreamble X=load(['D:\Work\MIMO-OFDM无线通信技术及MATLAB实现\MIMO_OFDM-master\第7章 PAPR\Chu序列和IEEE802.16e前导的PAPR\Wibro-Preamble\Preamble_sym' num2str(i-1) '.dat']); X = X(:,1); X = sign(X); X = fftshift(X); x = IFFT_oversampling(X,N); PAPRdB(i) = PAPR(x); x_os = IFFT_oversampling(X,N,L); PAPRdB_os(i) = PAPR(x_os); end plot(n,PAPRdB,'-o', n,PAPRdB_os,':*'), xlabel('前导编码[0~113]'); ylabel('|IFFT(X1(k))|'); title('IEEE 802.16e前导，L=1,4'); legend('L=1','L=4');
②、仿真结果
1) Chu 序列经 IFFT 之后的幅度
该图显示了在没有采样和 L=4 过采样的情况下，Chu 序列经过 16 点 IFFT 之后的幅度，有过采样和没有过采样的 PAPR 分别为 0dB 和 4.27dB，这说明不同的采样速度会导致 PAPR 具有明显的差异
2) IEEE 802.16e 前导的 PAPR
该图显示了 IEEE802.16e 标准中定义的 114 个前导的 PAPR，有过采样的PAPR比没有过采样的 PAPR 大 0.4dB 左右。事实上，由于前导码存在放大功率的问题，因此最初设计的这些前导码具有低的 PAPR。这就是为什么不同的采样速率并没有使这些序列的 PAPR 明显不同。然而，对于 Chu 序列，采样速率的不同通常导致 PAPR 的明显变化。因此，为了在基带对 PAPR 进行精确的测量，需要过采样过程。
5、基于限幅和滤波的 OFDM 信号
①、MATLAB 源码
mapper.m
function [modulated_symbols,Mod] = mapper(b,N) % If N is given, it generates a block of N random 2^b-PSK/QAM modulated symbols. % Otherwise, it generates a block of 2^b-PSK/QAM modulated symbols for [0:2^b-1]. %MIMO-OFDM Wireless Communications with MATLAB㈢ Yong Soo Cho, Jaekwon Kim, Won Young Yang and Chung G. Kang %2010 John Wiley & Sons (Asia) Pte Ltd M=2^b; % Modulation order or Alphabet (Symbol) size if b==1, Mod='BPSK'; A=1; mod_object=comm.PSKModulator('ModulationOrder', M); elseif b==2, Mod='QPSK'; A=1; mod_object = comm.PSKModulator('ModulationOrder', M, 'PhaseOffset', pi/4); else Mod=[num2str(2^b) 'QAM']; Es=1; A=sqrt(3/2/(M-1)*Es); mod_object = comm.RectangularQAMModulator('ModulationOrder', M, 'SymbolMapping', 'Gray'); end if nargin==2 % generates a block of N random 2^b-PSK/QAM modulated symbols modulated_symbols = A * mod_object(randi([0 M-1], N, 1)); else modulated_symbols = A * mod_object((0:M-1)'); end
IFFT_oversampling.m
function [xt, time] = IFFT_oversampling(X,N,L) %MIMO-OFDM Wireless Communications with MATLAB㈢ Yong Soo Cho, Jaekwon Kim, Won Young Yang and Chung G. Kang %2010 John Wiley & Sons (Asia) Pte Ltd if nargin<3, L=1; end NL=N*L; T=1/NL; time = [0:T:1-T]; X = X(:).'; xt = L*ifft([X(1:N/2) zeros(1,NL-N) X(N/2+1:end)], NL);
add_CP.m
function y=add_CP(x,Ncp) % Add cyclic prefix %MIMO-OFDM Wireless Communications with MATLAB㈢ Yong Soo Cho, Jaekwon Kim, Won Young Yang and Chung G. Kang %2010 John Wiley & Sons (Asia) Pte Ltd y = [x(:,end-Ncp+1:end) x]; % CP 循环前缀
clipping.m
function [x_clipped,sigma]=clipping(x,CL,sigma) % CL : Clipping Level % sigma: sqrt(variance of x) %MIMO-OFDM Wireless Communications with MATLAB㈢ Yong Soo Cho, Jaekwon Kim, Won Young Yang and Chung G. Kang %2010 John Wiley & Sons (Asia) Pte Ltd if nargin<3 x_mean=mean(x); x_dev=x-x_mean; sigma=sqrt(x_dev*x_dev'/length(x)); % 计算标准差 end CL = CL*sigma; % 限幅比 = 输入限幅比 × 标准差 x_clipped = x; ind = find(abs(x)>CL); % Indices to clip % 找到大于限幅比的索引 x_clipped(ind) = x(ind)./abs(x(ind))*CL; % 进行限幅
OFDM——PAPR减小（三）https://developer.aliyun.com/article/1473990
