Dr. Riki Morikawa, George Mason University

Updated: 29 May 2015

What is SNR?

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Transmitters are used to send signals to receivers.  The power that the transmitter puts out is measured in Watts.  Let’s refer to transmitted power as P_T.

However, RF noise in the environment reduces the distance that our transmitted signals can travel, thus interfering with our ability to receive the signal.

There are many sources of noise, but one of the biggest contributors is Thermal Noise.  Thermal Noise (N) is essentially the noise produced by the excitement of electrons.  The higher the temperature, the more excited/energetic the electrons become, the more noise they contribute.

So the goal is to make sure our transmitted power P_T, is high enough to overcome thermal noise power N.  The ratio of P_T to N is called the “Signal-to-Noise” ratio.

SNR = P_T/N (watts)

So when telecom engineers discuss transmitted power requirements to cover a distance or geographic area, they will use SNR.  This lets them know how much transmitted power is needed to sufficiently overcome any thermal noise that is contributed by the environment or communications system.

A couple of additional concepts to consider:

When considering if a signal will be received in free space, we use Friis’ equation.  The goal in any telecommunications link is to have sufficient signal power at the receiver (P_R).

Friis:  P_R = [P_TG_TG_R*lamda²]/[4*pi*R]² = P_TG_TG_R * FSPL

Essentially, Friis’ equation states that the power received is equal to the transmit power (P_T), plus transmitter and receiver antenna gains (G_T and G_R), minus attenuation (free space path loss).

FSPL = [lamda/(4*pi*R)]², where lamda is wavelength (note: frequency f = c/lamda; c=speed of light).

So we also know that FSPL (or attenuation) increases as frequency increases (see equation above).

Now attenuation is not noise.  It is the spreading of the signal as it propagates in space or through guided medium such as copper.  So transmit power decreases over distance (i.e., decrease in power density, watts/m²).  That means that the power received is already lower than what was transmitted.

Now add in noise.  Thermal noise is the most predictable, and in many case, the most troublesome source.  It exists across a wide frequency spectrum (N = ktB; k is Boltman’s constant, t is temp. in Kelvin, B is bandwidth).  This is also termed “noise floor”.

So you want your received power, P_R, to be sufficiently above the noise floor so that your receive equipment can pull the information out.  Thus you want high enough SNR at your receiver, but not too high that you overdrive your equipment.

A quick note regarding transmit power.  You can increase your transmit power to ensure high SNR, but engineers typically try to transmit just what is needed to close the link for many reasons.   These include the high cost of power amplifiers, desire to limit  power saturation, desire to enable frequency reuse, regulations which limit power levels (e.g., FCC, ITU,…), etc.  You can amplify a signal midway between the transmit and receive stations, but you also amplify the noise, so instead of simply increasing P_T, you end up increasing N as well.  If your signal is digital, you'll probably want to use repeaters instead of amplifiers, which will drastically reduce noise.

Lastly, the capacity for digital data throughput is proportional to SNR.  This is captured in another important formula referred to as the Shannon-Hartley equation which defines the theoretical maximum data rate for a given system:

C (capacity in BPS) = bandwidth * log₂(1 + SNR)

So SNR is critical.  It is used by communications engineers every day.