Signal-to-Noise Ratio in Wireless Communications [Video 1] 

The variable "d" in the video is the distance to the receiver and, yes, it is the radius of the sphere. Was the word "diameter" used anywhere in the video? I couldn't find that.

he was just referring a distance from the antenna, not diameter nor radius

The description in the video is for omnidirectional antennas. If you have a directional antenna, then you need to multiply the SNR with the antenna gain in the direction of the signal.

If you want to compute data rate over the entire bandwidth, then you use the whole bandwidth. If you want to compute the data rate over one LTE resource block then you use 180 kHz. If you want to compute the data rate on one subcarrier then you use 15 kHz. The formulas applies for any type of point-to-point link.

@@WirelessFuture thank you

When working with noise and SNR, you should probably use proper SI units as KHz is literally decoded as kelvin hecto seconds, not kilo hertz as you likely intended. This is because K is the SI unit symbol for temperature in kelvin, and the SI unit for frequency is hertz (Hz). The SI unit prefix h is for the 10 to the second power and k is the 10 to the third power multiplier. Temperature is a component of the noise power equation kTB where k is Boltzmann's constant, T is temperature in kelvin, and B is the bandwidth in hertz or some multiple. With the SI unit errors above you would end up with a temperature factor left over in your kTB calculation. For example, at room temperature you would have 1.38 x 10^-23 J/K * 290 K * 15 K * Hz = 6 x 10^-20 K * Hz^-1. But in answer to your question, the concept of SNR works for all kinds of communications links including microwave and satellite communications, you just have to apply the appropriate necessary bandwidth (see ITU Radio Regulations Vol-1 for definition).

It works very well. You preferably estimate the multipath channels in the uplink and utilize the estimate in both uplink and downlink. The transmitted signal will not be look like a beam but exploit all the paths.

@@WirelessFuture Works very well in theory - in practice, not so much. Ask Verizon about their experience rolling out 28 GHz 5G roll. So far, not so good . . .

The effective area of an isotropic antenna is a hypothetical number, which is explained here: en.wikipedia.org/wiki/Isotropic_radiator For aperture antennas, the effective area is roughly the same as physical area of the antenna. But for a dipole, it is not as easy. If the length is lambda/2, the directivity gain is 2.15 dB, which means that is effective area is 2.15 dB ≈ 1.6 times larger than that of an Isotropic antenna.

1) The transmit power is the power of the transmitted signal. The received power is the transmit power multiplied with the channel gain. We consider unit antenna gain in this video, but otherwise I recommend including it in the channel gain. 2) The definition is based on the assumption of an isotropic antenna. Otherwise the numerator will change. 3) There is no strong far-field assumption in this video. As long as we are beyond the reactive near-field, it will be fine. That will be the case also indoors.

@@WirelessFuture thank you.

The SNR is used in 5G and other networks to determine what data rate the system supports.

Someone recently recommend the channel “Ian Explains Signals and Systems”. Maybe it can be of interest?

@@WirelessFuture Thanks a lot sir!!

It is a typo in the video and, unfortunately, I haven't found a way to correct it. -174 dBm/Hz is the correct number it becomes 10^(-20.4) Watt/Hz.

@@WirelessFuture No=KTo=4x10^-21 W/Hz. This is also -174 dBm/Hz

pulsatorius Yes, 0 dBi. Since I only consider isotropic antennas in this video, the effective and “physical” antenna area are the same. But you are right that this is not the case in practice.

The code associated with Chapter 1 in “Massive MIMO networks” might be what you are looking for: massivemimobook.com

@@WirelessFuture Thankyou so much again and I will refer on it.

@@WirelessFuture I tried to check but the link doesn't open is there another way to open the link? Thank you with regards

thewodros ayele The link works for us, try massivemimobook.com/wp/ The code is available on Github: github.com/emilbjornson/massivemimobook

@@WirelessFuture yes it works thankyou

Yes, it is the power of the noise in the receiver circuits. (There is also noise in the transmitter circuits, but it is usually neglected in communications because it is much weaker than the transmitted signals.)

Yes, that is one option. If you serve multiple users, then regularized zero-forcing is a better choice.

@@WirelessFuture Thank you

@@WirelessFuture Can I ask again please? Since Massive MIMO results in channel hardening , i.e. a channel with a condition number ~1 , so orthogonal, why is there still a need for zero-forcing?

I think you are referring to "favorable propagation" (channel hardening = the small-scale fading average out). The thing is that the orthogonality between the channels of different users only happens asymptotically, as we let the number of antennas go to infinity. In practice, when we have ~100 antenna, there will be some interference left and it can be suppressed using zero forcing. In the beginning of the Massive MIMO research, there was a hope that the difference would be small, but that hypothesis didn't hold. In many cases, one can double the data rate by using (regularized) zero-forcing.

@@WirelessFuture If I may again: So I simulated in Matlab a random wireless channel with 8 users and a large number of antennas (up to 1000) and I saw after doing a SVD that the singular values converge to a certain mean value as I was increasing the number of antennas, is this channel hardening?

I'm not sure if you are referring to isolation in the hardware or over the wireless channel, but precoding is the solution to the issue that you describe. If you know the propagation channel, you can use zero-forcing precoding to transmit two signals from the two antennas in such a way that each receive antenna observes one of the signals without any interference. You essentially make sure that the two antennas transmit copies of the same signal so that these copies add destructively at the undesired receiver. In this way, the interference disappear, at the price of an SNR reduction since the copies will not add fully constructively at the desired receiver. To mitigate this SNR loss, Massive MIMO is all about having more antennas than receivers to have sufficient degrees-of-freedom to suppress interference without affecting the SNR too much.

It should be -174 dBm/Hz and 10^(-20.4) W/Hz. The 1000 times difference has to with mW versus W.

@@WirelessFuture Makes sense to me now. Thank you so much for the quick reply!

You are right that there is noise also in the transmitter. However, since the propagation loss is normally -60 dB to -120 dB in wireless communications, the transmitter noise will be attenuated by such a huge factor before reaching the receiver. Hence, when computing the communication performance (which is measured at the receiver), it is normally the noise at the receiver that matters while the transmitter noise is negligible.

@@WirelessFuture As much as noise will be attenuated, so will the signal so Transmit SNR will not change because of path loss. Usually transmit SNR is much higher than receive SNR , that is why its impact can usually be ignored, but at mm wave for example, when PLL/VCO phase noise is not good enough, then transmit SNR could start having an impact in the overall SNR

​@@dreamerhavingfun2289 Yes, my point is that the transmit SNR typically is 60-120 dB higher than the receive SNR, so that is why it can be ignored. This argumentation is based on the noise being thermal noise. If you bring in phase noise or other types of hardware distortion into the game, then the situation could be different, but I wouldn't talk about SNR in that case but rather signal-to-distortion-and-noise ratio (SNDR).