Noise Modeling Guide
Because we don’t live in a perfect world, any time you send an optical signal, you will not receive 100% of the transmitted power at the receiver. This is because the signal doesn’t travel in a vacuum; it is affected by its enviroment as it travels from point A to point B. Moreover, there are defects within the equipment itself and human error which add interference. These interactions, known as noise, alter the strength of your signal. To deal with this, we create a link budget, which tracks how the strength of the signal changes during the transmission process, giving a measure of received power. This document will provide a guide on elementary noise analysis and link budget construction.
Understanding Noise
Signal-to-noise ratio
In signal processing, noise simply refers to any unwanted alteration or disturbance of a signal. Noise distorts your signal and makes the encoded data harder to decipher. In general, we want to maximize the system’s signal-to-noise ratio (SNR), which is defined as
where and are the signal and noise power in watts respectively. Since this quantity can grow very large very quickly, it is often helpful to convert to decibels by the relation
As one can see, the SNR quantifies how strong of a connection or link can be achieved between the transmitter and receiver. A standard minimum value for SNR is 5 dB, but it is best to aim for a higher value to allow some leeway.
Gains and losses
There are three main path losses as the laser travels from the transmitter to the receiver: space loss, atmospheric attenuation, and scintillation loss. Space loss results from the diverging wavefront of the optical energy as it traverses the link distance and is calculated as
where is the wavelength of the optical transmission and is the link distance.
Atmospheric attenuation results from the absorption and scattering of radiation by gases, water vapor, and aerosols. A general estimate can be obtained by simulating the conditions in which the optical transmission will take place (i.e., latitude, zenith, sensor height, visibility) using MODTRAN online: http://modtran.spectral.com/modtran_home#plot.
Scintillation is a fluctuation in the ampitude and phase of the signal due to variation in temperature, pressure, and refractive indices of Earth’s atmosphere. A generous (over)estimate is around 2 dB.
To compensate for the losses that are incurred during transmission, we often apply gains to boost the signal. This occurs both at the transmitter and the reciever. Beginning with the transmit gain, the gain of a transmitting antenna is defined as the ratio of radiated solid angles between an isotropic antenna and the transmitter, i.e.
where is the solid angle subtended by the source whose full angle divergence angle is , and we recall that the solid angle of a unit sphere is . For small , can be determined using a small angle approximation, yielding
where is the wavelength of the signal and is the aperature diameter.
Similarly, the effective collecting aperatre of the receiver constitutes the receiver antenna gain and is expressed as
where is the collecting area of the antenna.
Unfortunately, in addition to the path losses, the signal is subject to additional losses from the transmitter and receiver themselves. The optical transmission at the source wavelength needs to be estimated by the number and type of optical surfaces being traversed, as each optical surface contributes a multiplicative loss factor. Additionally, there are aberrations which result in imperfect optical wavefronts. A similar consideration must be taken for the receiver. We have estimated these errors using Zemax simulations. Lastly, an estimate of pointing error must be made. We have based our estimation off of CLICK-A, which measured an RMS pointing error of mrad.
Once all the gains and losses of the system have been considered, the resultant signal power at the receiver can be computed. First, the original power in W must be converted to decibel milliwatts (dBm) by the relation
Second, the gains and losses must be converted to decibels by the relation
where is any unitless quantity, in this case a gain or loss. Once this is done, the receiver signal power in dBm is simply the sum of all these quantities, i.e.
where is the set of all gains and losses in the system. This is the essence of constructing a link budget.
References: Lambert (1995) Laser Communications; Wikipedia.