Table of contents
1. Orthogonal frequency division multiplexing (OFDM)
2. Filter bank multi-carrier (FBMC)
OFDM (Orthogonal Frequency Division Multiplexing) and FBMC (Filter Bank Multi-Carrier) are two commonly used modulation technologies that are widely used in modern communication systems such as 5G. Below we will introduce the subcarrier spectrum performance under these two modulation methods in detail.
1. Orthogonal frequency division multiplexing (OFDM)
OFDM is a multi-carrier modulation technology. Its main idea is to divide a high-speed data stream into multiple lower-speed sub-data streams and transmit them in parallel on multiple orthogonal sub-carriers. This technology can effectively resist multipath effects and inter-symbol interference, improving the reliability and efficiency of data transmission.
In an OFDM system, the spectrum shape of each subcarrier is usually a rectangular wave, and orthogonal relationships are maintained between subcarriers. Therefore, under ideal circumstances, the spectrum performance of OFDM subcarriers is the spectrum of a single rectangular wave, that is, the main lobe width of the spectrum is narrow and there is no side lobe interference. However, due to the influence of various factors in actual systems, the orthogonality between subcarriers will be destroyed, resulting in inter-subcarrier interference and spectrum leakage. In order to optimize the performance of OFDM systems, complex technologies such as cyclic prefix and frequency domain equalization are usually required to control these interferences.
2. Filter bank multi-carrier (FBMC)
FBMC is a filter bank-based modulation technology. Its main idea is to split the data stream into multiple sub-streams and transmit them through a set of filters respectively. Unlike OFDM, the filters in FBMC systems have non-ideal characteristics, which causes the spectrum of each subcarrier to show different shapes and sizes. FBMC uses a set of parallel sub-band filters to filter multi-carrier signals. This set of filters is modulated from the same prototype low-pass filter. There are roughly two ways to implement FBMC systems: frequency domain and time domain. The frequency domain is implemented using extended FFT, and the time domain is implemented using a polyphase filter network. The FBMC system consists of a comprehensive filter bank at the transmitter and an analysis filter bank at the receiver. The analysis filter bank decomposes the input signal into multiple sub-band signals, and the synthesis filter bank synthesizes each sub-band signal and then reconstructs the output. It can be seen that the analysis filter bank and the synthesis filter bank are inverse structures of each other. Whether it is an analytical filter bank or a comprehensive filter bank, their core structure is the prototype filter. The other filters in the filter bank are obtained based on the frequency shift of the prototype filter. The analytical filter bank and the comprehensive filter bank The prototype functions of are mutually conjugate and time-reversed.
In FBMC systems, filter design and selection are key. Common filters include square root raised cosine filters, filter bank filters, etc. By rationally selecting filters, the spectrum performance of subcarriers can be optimized and side-lobe interference and inter-symbol interference can be reduced. Compared with OFDM, inter-symbol interference in FBMC systems is more complex, but the impact of interference can be effectively reduced by optimizing filter design.
In a real system, implementation complexity and hardware limitations also need to be considered. Since the design and implementation of filters are relatively complex, optimization algorithms and digital signal processing techniques are usually required to reduce computational complexity and hardware costs. In addition, the performance of the FBMC system is closely related to the selection of filters, so it is necessary to select appropriate filters based on actual application scenarios and system requirements.
OFDM and FBMC are two commonly used modulation technologies with their own characteristics and advantages. The OFDM system is simple, easy to implement, and has good anti-multipath effect and inter-symbol interference performance; while the FBMC system improves spectrum utilization and performance by optimizing filter design. In practical applications, the appropriate modulation method needs to be selected according to specific scenarios and requirements. In future communication systems, these two modulation technologies will still have important application value and may be further developed to support higher data transmission rates and more complex communication scenarios.
3.MATLAB core program
for m=0:u-1
r=m+1;% 原型滤波器方程K=4
% 如果需要，你可以根据需要打开以下两行代码，这是K=3和K=2的原型滤波器表达式
p1(m+1)=y(1,1)-2*y(1,2)*cos(r*s)+2*y(1,3)*cos(2*r*s)-2*y(1,4)*cos(3*r*s);
end
% 计算lp-1的值
for m=0:M-1
p2(m+1)=1;
end
% OFDM的原型滤波器
figure (1)
[H,w] = freqz(p1);% 使用freqz函数计算滤波器的频率响应H，w为频率向量
H=H./max(H);% 将H的幅度范围限制在[-1,1]之间，以更好地在图中显示
hold on
plot(w/pi,20*log10(abs(H)));% 在同一图形窗口中绘制多条曲线
plot(-w/pi,20*log10(abs(H))); % 绘制幅度为H的曲线，x轴为归一化频率w/pi，y轴为dB单位对数值20*log10(abs(H))
plot((w+.5)/pi,20*log10(abs(H)),'r');% 绘制幅度为H的曲线，x轴为归一化频率-w/pi，y轴为dB单位对数值20*log10(abs(H))，与上面一条线组成一个完整的振幅曲线图（虚线表示负频率）
plot((-w+.5)/pi,20*log10(abs(H)),'r'); %%% 绘制幅度为H的曲线，x轴为归一化频率(w+0.5)/pi，y轴为dB单位对数值20*log10(abs(H)),绘制红色的曲线为了与前面的曲线区分开
plot((w+1)/pi,20*log10(abs(H)),'m');%绘制幅度为H的曲线，x轴为归一化频率- (w+0.5)/pi，y轴为dB单位对数值20*log10(abs(H)),绘制红色的曲线为了与前面的曲线区分开
plot((-w+1)/pi,20*log10(abs(H)),'m'); %%% 绘制幅度为H的曲线，x轴为归一化频率(w+1)/pi，y轴为dB单位对数值20*log10(abs(H)),绘制紫色的曲线为了与前面的曲线区分开
up22214. Simulation results
The spectrum differences between OFDM and FBMC are mainly reflected in bandwidth efficiency, side lobe interference, spectrum leakage and multiplexing capabilities.
- Bandwidth efficiency: Under ideal circumstances, the frequency spacing of OFDM is 1/T, and there is no spectrum waste. However, in practical applications, the introduction of CP will reduce the frequency band utilization. In contrast, the frequency separation of FBMC is usually larger than 1/T, but due to the non-rectangular characteristics of the filter, it can utilize spectrum resources more effectively and improve bandwidth efficiency.
- Side lobe interference and spectrum leakage: OFDM has high synchronization requirements and is very sensitive to frequency offset, so CP needs to be used to overcome the destruction of orthogonal conditions caused by time expansion. But even with CP, its spectrum leakage is still large and side-lobe interference is strong. In contrast, FBMC can more effectively control side lobe interference and spectrum leakage due to the characteristics of the filter bank.
- Reuse capability: FBMC can efficiently utilize the allocated spectrum and can generate or occupy spectrum "holes" for spectrum sensing applications, thus having stronger spectrum reuse capabilities.