In my previous post, I talked about how to calculate the range of a wireless system and the importance of receiver sensitivity in optimizing that range. One of the key takeaways was the physical law that says that the range of a signal decreases with an increase in operating frequency. While this is true, several readers responded indicating that this loss was often offset by the fact that, at the higher frequencies, smaller gain antennas could be used. Good point—I should have mentioned that.

High-gain antennas like Yagis, parabolic dishes, horns, or even phased arrays are considerably smaller at the higher frequencies, allowing them to boost the effective radiated power (ERP) of the signal to make it travel as far (or even farther) than lower-frequency signals. A great example of this is the tiny phased used in WiGig 802.11ad radios that operate at 60 GHz. These super-high-frequency signals travel just as far as some other technologies at a frequency that is less than a tenth of 60 GHz.

Of course, this is not always true where the high-frequency radios are embedded into a product and hindered by a low-efficiency PCB loop, random wire, or other compromised antenna. In these cases, the range is even more restricted. Anyway, remember the antenna gain solution when you are designing your higher-frequency wireless link. Now you know how the forthcoming 5G New Radio cellular systems will be useful at millimeter-wave frequencies.

### Noise and Receiver Sensitivity

In this post I discuss the impact of noise on receiver sensitivity and reliability of a wireless link. Since most wireless systems are digital these days, it is the bit error rate (BER) that suffers if there is too much noise involved.

Remember that receiver sensitivity is the minimum received signal power that will result in full demodulation and recovery of the sent data. You will sometimes hear of this referred to as the minimum detectable signal (MDS). The calculation of the sensitivity based upon range, transmit power, and antenna gains is a good estimate of performance, but it ignores the reality of noise.

Noise is that random variation of voltage that exists in all electronic circuits. If that noise level is too high, it can mask the desired signal, making recovery impossible. In other instances, the noise may not completely block the signal, but it could be high enough to introduce bit errors. A desirable design factor to know is that noise level and the receiver sensitivity needed to overcome the noise.

### The Characteristics of Noise

Most of the noise we need to worry about is caused by thermal agitation in resistors and transistors used in the front-end of the receiver. It is mostly a product of the RF preamplifier between antenna and mixer. The mixer is another noise source, but it is not always a major factor if an RF amplifier is used. Yes, there are external sources of noise, such as atmospheric conditions (e.g., lightning and space) or extraterrestrial noise from the sun, distant stars, and cosmic rays. At operating frequencies below about 30 MHz, this noise is a problem. It is far less of a problem at VHF, UHF, and microwave frequencies and usually neglected.

The general formula for calculating noise power is:

P_{N} = kTB

The k is Boltzmann’s constant of 1.38 x 10^{−23} J/K. T is the surrounding temperature in Kelvin units and B is the bandwidth of the circuit or system. Bandwidth is important as it controls the amount of noise. Noise is a random mix of a wide range of frequencies and amplitudes. So as you narrow the bandwidth, you filter out some of the noise. T is generally the room temperature of 25°C, or 290 Kelvin.

The most useful figure is the noise floor of the receiver. Without going through the derivation, the noise floor is:

P_{N} = −174 dBm/Hz

This is the noise power in a bandwidth of 1 Hz and minimum noise level at the input to the receiver.

### Receiver Sensitivity and Noise

The receiver sensitivity is the minimum input power level necessary to recover the signal.

P_{N }(min) = −174 + 10logB + NF + SNR

SNR, or S/N, is the signal to noise ratio. It is the ratio of the signal power to the noise power stated in dB. This is the pre-detection SNR. SNR varies with the application but is usually better than 5 to 10 dB.

NF is noise figure, the noise ratio stated in dB. Noise ratio (NR) is the ratio of the SNR at the input to the receiver and the SNR at the output.

NR = SNRinput/SNRoutput

NR can be stated for one stage such as the RF preamp or the whole receiver. Obviously, the SNR at the output of an RF preamp will be less than the SNR at the input because of the noise contributed by the amplifier. The noise figure is:

NF = 10log(NR)

The ultimate best NF is 0 dB which is impossible. In the real world it is rare to see an NF of less than 2 dB. In any case, the lower the NF the better.

### Calculating Sensitivity

Now let’s compute receiver sensitivity P_{N }(min).

P_{N }(min) = −174 + 10logB + NF + SNR

Assume a bandwidth of 6 MHz, an SNR of 10 dB, and a noise figure of 4 dB.

P_{N }(min) = −174 + 10logB + NF + SNR = −174 + 10log (6,000,000) + 4 + 5 = −174 + 68 + 4 + 5 = −97 dBm

One other thing: A variation of this sensitivity calculation uses the carrier to noise ratio (C/N) instead of the SNR. The C/N ratio factors in the type of modulation you are using. Ordinary types of modulation like FSK or BPSK give a good C/N. The higher the level of modulation, like 8PSK or 16QAM, the C/N is less—meaning you need better sensitivity to achieve a desired BER.

Anyway, that’s how you do it. With sensitivity figures based on range, power, and antenna gains, and those based on noise, you can get a good sense of what kind of receiver sensitivity you need to get the results you want.