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Estimating Noise Figure (NF) of the RF-over-Fiber (RoF) Link
Tool Used: Synopsys OptSim
Overview
The field of microwave photonics cover wide-ranging, analog and digital data communication and sensing applications for the civilian, and aerospace & defense sectors. The linear convolution-based time-domain split-step (TDSS) simulation engine of Synopsys OptSim is ideally suited for simulation-assisted design of RF-over-Fiber (RoF) systems. Unlike frequency-domain split-step (FDSS) approaches, the TDSS engine of Synopsys OptSim requires no assumptions on periodicity of the signal, noise or simulation time window. As a results, arbitrary RF signals can be modulated over optical carriers without the burden of ensuring periodicity.
The design trade-offs in RoF systems involve noise, sensitivity, bandwidth, dynamic range and linearity of the link. From the perspective of the transmit side, link linearity and high RF output power over wide bandwidth are more important than noise. On the other hand, from the perspective of the receiving end, low noise and high dynamic range are of utmost importance.
Noise in RF-over-Fiber Systems
The most common sources of noise that dominate in microwave photonics include output thermal noise, photodetector shot noise, relative intensity noise of the laser, and noise originated from the beating of a carrier with the optical noise floor caused via optical amplification. In this application note, we will describe a method to estimate noise figure of an analog radio-over-fiber link with Mach-Zehnder modulator (MZM) and erbium-doped fiber amplifiers (EDFA).
The RF noise figure of the RoF link is usually defined with respect to the weak input signals, mostly out of concern for dynamic range rather than sensitivity, and is given by [1]:
![The RF noise figure of the RoF link is usually defined with respect to the weak input signals, mostly out of concern for dynamic range rather than sensitivity, and is given by [1]: ¡¼NF¡½_RF= N_out/(G_RF k_B T) [A] where Nout is the total RF noise-power spectral density (PSD) at the output of the link, GRF is small-signal gain of the RF link, kB is Boltzmann¡¯s constant (1.380649E-23 Joules/K) and T is operating temperature (say, 290K).](/photonic-solutions/product-applications/pon-catv-rof/estimating-noise-figure-of-rf-over-fiber-link/_jcr_content/root/synopsyscontainer/column/colLeft/image.coreimg.svg/1701788095316/nf-rf-formula1.svg)
where Nout is the total RF noise-power spectral density (PSD) at the output of the link, GRF is small-signal gain of the RF link, kB is Boltzmann¡¯s constant (1.380649E-23 Joules/K) and T is operating temperature (say, 290K).
In dB units:
![In dB units: NFRF (dB) = 174 + Nout (dBm/Hz) - GRF (dB) [B] where dBm/Hz is dB-scale representation of PSD with respect to 1mW, and thermal noise PSD is 10*log10(kB*standard noise temperature 290K).](/photonic-solutions/product-applications/pon-catv-rof/estimating-noise-figure-of-rf-over-fiber-link/_jcr_content/root/synopsyscontainer/column/colLeft/image_1368414506.coreimg.svg/1701788095533/nf-rf-formula2.svg)
where dBm/Hz is dB-scale representation of PSD with respect to 1mW, and thermal noise PSD is 10*log10(kB*standard noise temperature 290K). Per Hz in the unit of Nout is because Haus [2] uses ¡°total noise power per unit bandwidth¡± in the definition of noise figure.
Simulation Setup in Synopsys OptSim
The simulation setup for the NF measurement of an analog RoF link is shown in Figure 1.
Figure 1: Schematic of the NF measurement setup for an analog RoF link
The link consists of two RF tones at 9.1-Ghz and 9.5-GHz frequencies. A continuous-wave (CW) laser at 1550.5-nm emits optical power of 10-mW. An MZM outputs RF-modulated optical signal, which passes through an EDFA with gain and noise figure of 5- and 4.5-dB respectively. The amplified signal travels through a 50-km of standard single-mode fiber (SSMF) followed by another EDFA with gain and noise figure of 10- and 4.5-dB respectively. At the receiving end, a photodetector discards optical carrier and measurements are carried out on the detected RF.
Analysis and Discussion of Results
The simulation steps for the noise figure measurement are:
1. Estimation of RF link gain
Turn-off noise, measure small-signal link gain.
2. Noise measurement
(a) Turn noise on, turn RF tones off, and measure total noise power at the receiver output. This measurement is done over the entire simulation bandwidth.
(b) Divide noise power by measurement bandwidth to get dBm/Hz
3. Calculate the NF of the analog RF link using Eq. [B]
Click on the ¡°GO¡± button to run the simulation. When simulation is over, observe measured power and output waveforms in the visualizers. The NF calculations for the schematic of this application note are as below:
Step 1: Measure RF Link Gain in dB units
Turn noise off (set include noise to ¡°no¡± in the simulation dialog window). Measure P_in (RF input power) and P_out (RF_out power). The (small-signal) RF link gain is P_out/P_in.
Link Gain (dB) = 10*log10(P_out/P_in) = -75.78dB - (-13.98dB) = -61.8dB
Step 2: Measure Noise, and calculate noise density in dBm/Hz units
Turn off RF (i.e., set their amplitudes to 0), include noise in simulation and measure noise power at the output. The parameter window of the power meter tells range over which power was evaluated; or one could also convert optical simulation bandwidth in the simulation parameters to half its Hz equivalent (RF power is over positive frequencies). The former is more convenient.
Noise_out=0.19e-11 W = 0.19e-8 mW
Noise Bandwidth = 128GHz
(see power meter's upper range; or calculate it from the simulation bandwidth)
Noise density mW/Hz = (0.19e-8)/(128e9) = 1.484375e-20 mW/Hz = -198.2845 dBm/Hz
Step 3: Use formula NF (dB) = 174 + N_out (dBm/Hz) - G (dB)
NF (dB) = 174 + Nout (dBm/Hz) - G (dB) = 174 + (-198.2845) - (-61.8) = 174-198.2845+61.8 = 37.52dB
In this application note, we discussed a method to estimate noise figure of an analog RF-over-fiber link. In the process, we also measured the link gain. Synopsys OptSim, with its rich library of models and simulation methods, is an ideal tool for simulation of analog and digital microwave photonic links and estimation of performance metrics of common interest to RF designers, such as, inter-modulation distortion (IMD), composite second order (CSO), composite triple beat (CTB), carrier-to-noise ratio (CNR), spurious-free dynamic range (SFDR), input- and output intercept points (IIP, OIP), 1-dB compression point, and so on.
References
- Vincent J. Urick Jr, Jason D. Mckinney, and Keith J. Williams, Fundamentals of Microwave Photonics, John Wiley & Sons, Inc, ISBN: 9781118293201, 2015.
- Hermann A. Haus, ¡°The proper definition of noise figure of optical amplifiers,¡± Proceedings of the Optical Fiver Communication Conference (OFC), Session ThU3, 1999.