How a diversity radio receiver works

Question

I need to know how a diversity radio receiver works and if it can mitigate fading then why most radio receivers are not having this technology?

Answer 1

most radio receivers are not having this technology

most radio receivers: arguable. In the amateur radio field, yes, but one could argue that most modern cellular phones and most modern Wifi access points do employ diversity technology (and they're by far not the only type of receivers that do) does.

There's billions of such devices! Anyway, whether they are in the majority or minority doesn't matter to your question.

why [do] radio receivers are not universally have this technology?

It costs extra money, and it requires a second, statistically independent receive path.

That means that while it can be a feasible way to increase throughput or reliability of a communications system, application of diversity reception is limited by physical and financial constraints.

Of course, this is an amateur radio site: it needs to be said that the hobby as a whole is very conservative, and the understanding of radio technology in the community is typically several decades behind professional and commercial understanding. So, if this question was asked in the context of ham radio receivers specifically: give it a couple of decades…

I need to know how a diversity radio receiver works

Consider the probability that a receiver experiences an outage due to being subject to fading that's deep enough to render the received signal worse than it needs to be for successful operation of the receiver. We call that probability the outage probability, and denote it as $p_{\text{outage}}$.

Let's now assume you have two of these receivers, receiver $1$ and receiver $2$. They both have their own outage probabilities, $p_{\text{outage},1} = P(\text{receiver 1 has outage})$ and $p_{\text{outage},2} = P(\text{receiver 2 has outage})$, respectively.

So here's my "potato diagram" of receiver 1: out of all possible reception scenarios, only a limited range lead to outages for receiver 1.

The probability of outage is hence basically the "size" of the set of scenarios where receiver 1 can't receive, divided by the total "size" of the set of all possible scenarios.

Same for receiver 2, but the "outage set" might be a different one:

Now, imagine you build a device with these two receivers integrated. And if one of them doesn't work, you just use the other.

That's a diversity receiver.

So, how likely is it that you get an outage when you use such a combined receiver?

Well, that combined receiver only fails if both receiver failed! So, we need to be in the set of receive scenarios that is in both "outage sets":

As you can see, that set is smaller. So, the outage probability of your diversity receiver is lower. Nice!

Also: the smaller the overlap between the outage scenarios, the better.

Of course, this is just an example illustration. The outage sets of receiver 1 or 2 might overlap more or less. Let's think about one special case:

Outage sets 1 and 2 are identical: Well, that means that if receiver 1 fails to receive, receiver 2 also fails. In that case, diversity reception brought us nothing.

So, since we don't want to have a second receiver for no advantage, that's a situation we do not want to end up in.

So, how would that happen? That would, for example, happen if you used the same antenna for both receivers. The same signal being received by both receivers would mean that there's no chance for the two receivers to see different scenarios, and thus ensure one works, while the other doesn't.

We hence take care to make the two antennas experience different reception scenarios: we give them different polarizations, we place them at different locations, if they have directivity, let them point in different directions.

And herein lies the problem:

1. You need a second receive antenna and receiver electronics. That simply costs money and potentially battery¹
2. You need to have "smarts" that tells you whether one of the receivers experiences an outage. By itself, that's not easy, especially not in the low-SNR regime
3. You need space for a second antenna. And that can be hard to find – the spatial separation needs to be in the order of half a wavelength, at least, to make the cases where an outage happens on each antenna not overlap fully.

The third point is why you won't have many antenna diversity schemes for private HF operation: HF has wavelengths between 10 and 100 m. Do you have enough space to put a second antenna, 50 m away from the first? Not many do!

Further remarks

• You can do the above with two antennas, or three, or four, or more antennas. Works!
• If you achieve completely independent outage behaviour, that's the best case you can hope for. Let's assume for a moment that all these independent receivers are independent, but have the same probability of outage, $p_{\text{outage},1}=p_{\text{outage},2}=p_{\text{outage},3}=\ldots=p_{\text{out}}$. Then, a single-antenna system would have $p_{\text{outage, total, single}}=p_{\text{outage},1 }=p_{\text{out}}$, a dual antenna system $p_{\text{outage, total, dual}}=p_{\text{outage},1 }\cdot p_{\text{outage},2}=p_{\text{out}}^2$. A three-antenna system would have $p_{\text{outage, total, triple}}=p_{\text{outage},1 }\cdot p_{\text{outage},2}\cdot p_{\text{outage},3}=p_{\text{out}}^3$.
  See the exponent? Because probabilities are smaller than one, $p_{\text{out}}< p_{\text{out}}^2 < p_{\text{out}}^3 < p_{\text{out}}^4 < \ldots$. So, higher exponent = better!
• That exponent is what we call the diversity order, as it tells us how many "practically indepenent" paths we use to make our reception better. In reality, it's impossible to make reception of different antennas completely independent. (For example, if you put your combination receiver in a salt mine, it will not receive much, no matter how many antennas it has. Luckily, that desire is rare)
  By calculating the power which you need to raise the outage probability of the single receiver to to get the outage probability of the whole system, you get a single number that tells you how much more robust you made your receiver.

Also:
Not every kind of diversity receiver uses antenna diversity. That's just one special case of diversity receiver. Another scheme that is somewhat commonly used are frequency diversity, where the transmitter sends the same signal on multiple carriers, and because fading is different for different frequencies, you get independent outage probabilities for each carrier. More commonly you get time diversity, where the same message is transmitted at multiple times, and the channel changes over time, so the different receptions are independent.

Footnotes

¹ Battery savings is a complicated argument to make. If you think about it, you can "invest" the safety margin you get for your receiver by having the second receiver into making the receivers noisier, but more power-efficient. Since power-efficiency vs noise figure is typically far from an easy relationship, statements of battery efficiency of diversity receivers usually require a bit more modelling than "two receive strings = twice the power"; it's not that simple!

Answer 2

A "diversity receiver" is nothing special: it's just two receivers, connected to two different antennas, receiving on the same frequency. Usually they're connected to left and right earphones, or stereo speakers.

The idea is that if the two antennas have different polarizations, or are simply spaced a decent fraction of a wavelength apart, it's less likely that both of them will encounter fading at a given moment than that either one of them will. Therefore, at least one receiver will have a decent signal for a greater part of the time, and the human brain does a pretty good job of paying attention to that one while ignoring the one that's just static.

The main reason for not doing it all the time is that it pretty much doubles the cost of a receiver, and it's only beneficial to those who can set up two sufficiently-diverse antennas.