If I understand correctly your layout, you have two (V, H) polarizations for transmitter channel and two polarization (V, H) of receiver channel. If so, you will have 2 co-polarization response channels: vertical (V, V), horizontal (H,H) and 2 cross-polarization channels (V, H) and (H, V). To process obtained data set you should use Malus low, applied to your object.

You don't provided information about even range of wavelength, frequencies of your radiation and your object, so it is difficult to add something more.

Thanks Valeriy for your response,

the frequency range is 0.5 GHz up to 100GHz (mm-waveband) which is used for 5G of mobile networks. you got scenario correctly, I used a 2*2 coupling matrix in my channel impulse response as it's used by 3GPP standard channel model for mm waveband. point is for each time delay I've got just a complex value for my channel impulse response because elements of radiated pattern of receiver antenna (V and H as a 1*2 vector) will multiply out by 2*2 coupling matrix and then multiply by a 2*1 vector which is included V and H components of transmitter antenna so at the end we will come up with a channel impulse response equal to a complex value (1*1Dimension) in each time delay, now my question is if dual polarization makes two V/H components merged then how receiver's antenna will understand that received complex value is V or H ?

Again, your information about your task is not complete. How do you provide radiation from your emitter? If I organize such experiment, I'll provide emitted polarization is H and measure H and V receiver components, then I'll emit V polarization and measure H and V receiver components. Do you work in such mode? If so, answer your quesion would be obvious, otherwise you need to provide clearer explanation of your time layout. And, again, what is your object of such study? What do you doing?

Question is clear, how receiver's antenna deal with channel impulse response for a dual polarized scenario? (Tx. and Rx are working in mm waveband frequency so Tx is emitting in two dimension V&H). based on 3GPP model answer for each time delay (each delay is related to a specific path in a multipath scenario-you can refer to Equation 7.5-22 in attached file) is a complex value, point is transmitter emits in two dimensions but channel impulse response is just one value so how receiver's antenna will recognize vertical and horizontal components?

OK, thank you. Sorry, this question is far from my area of activity. But scenario that I have proposed can answer your question, if you can realize it.

NP, the point that you didn't notice is the transmitter antenna has both components V and H at the same time...if it was emitting just vertically or Horizontally then it was easy to find the answer!

A dual-polarized system equipped with a single transmit antenna and a single receive antenna is typically modeled using the Two-Input Two-Output (TITO) system model [1] (some call it a dual polarized SISO system). That is why you see a matrix denoting the VH components rather than a single complex value. So you need to deal with the system as if its is a 2x2 MIMO.

[1] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4657346

thanks Ibrahim for your response,

this is so close to my scenario. Do you think can I write my received signal components as following and then find H components same as the paper that you share ? (root of idea I think is from 3GPP standard)

[Yv;Yh] = [Hvv Hvh ; Hhv Hhh]*[Xv Xh] + Noise

Hi Farah,

I'll try to explain this physically, rather than mathematically. Let's start very simply. Envision a line of sight (LOS) microwave link between two cell/radio towers. Traditionally I would have had two co-polarized elements (probably vertical) that communicate between these two points and, neglecting ground bounce (which is hopefully outside the beamwidth) the RX antenna receives the TX signal reduced by the Friis transmission equation. (More commonly, a circularly polarized antenna can be used to eliminate any impact of ground bounce, since the vertical polarization flips while the horizontal does not, resulting in an opposite circular polarization from the ground bounce.)

At any rate, somewhere along the line, someone realized that if you have a truly isolated link (no multipath) you can transmit two orthogonal polarizations ( e.g. V/H, LHCP/RHCP, left/right diagonal) along the same line of sight and receive those components completely independently, since both source and receiver are orthogonal. Of course, other than the LHCP/RHCP case, you have to have perfectly matched alignment or you get mixing of modes between the two transmitted signals on each receive antenna. Any mis-alignment angle alpha causes a given RX antenna to receive TXa * sin(alpha) + TXb * cos(alpha) and vice versa, simply due to geometry. Note here that there's nothing here about the phase of TXa or TXb, so the real/imaginary part are immaterial. The signals just sum geometrically.

Now, bringing in a bit of math, it should be apparent that it's possible to solve for TXa and TXb in terms of RXa and RXb simply by inverting the rotation matrix corresponding to angle alpha. For a LOS microwave link, this would be kind of stupid vs. just installing the antennas correctly, but it should give you insight into what you're attempting to accomplish with the H matrix in a multi-path environment. The equations become more complicated between TX and RX, but you're attempting to accomplish the same thing.

Now, let's step back to your original question for a moment. You mentioned "both of them will be excited by the identical complex value." What exactly do you mean by that? Are you proposing that you're sending the same signal through each element (e.g. splitting it and driving both) in which case you only have one linear (or circular/elliptical if there's an imbalance in phase) polarization and not two separate polarizations? Or are you indicating that you're using the same impulse response as your "source data" on each element?

The above discussion centers around the concept of correlation. In the ideal orthogonal case, the channels are completely uncorrelated. They could be replaced with a pair of (lossy) cables. Nothing I transmit on one gets on the other or vice versa. Thus, it doesn't make any difference to one of I'm transmitting the same information (i.e. sending the same text string) on each channel simultaneously or not, we treat them completely independently. Even for the multi-path case, the coupling between the antennas can be evaluated completely independently by simply transmitting the impulse on one at a time. You can get the coupling between them and once you have all combinations, you can calculate the correlation between the two channels that are created in the multipath environment.

Now, extending this to actual communication, in a typical MIMO channel, the modulated data is random between the two channels and thus the signals themselves are uncorrelated and do not impact the correlation between the antennas. Note however that if the signals are 100% correlated, now your back to the discussion above where the phase DOES matter. Essentially you're beamforming, whether that's circular polarization for orthogonal elements or actual beam steering with two co-polarized elements. At some points in space the signals are in phase and others they're out of phase, and you get a gain over a single antenna or the sum of the powers in each. On the other hand, if we take an example from the "one after the other" impulse response test I suggested above, we get the concept of transmit diversity used in LTE transmission mode 2 (TM2). There, the same information is sent on both antennas, but with a delay between them. The signals are no longer temporally correlated and the result is a power gain (3 dB instead of 6 dB) at all points in the pattern. Basically the H matrix is inverted and the original equivalent TX signals can be extracted, time shifted, and summed back together.

Well, that's plenty to absorb for now, so hopefully this will help.

Thanks,

Michael

Thanks Michael for your explanation, by " exciting by identical complex value" I meant "using the same impulse response as "source data" on each element".

I used equation (7.5-27) in attached pdf which is 3GPP document to calculate channel impulse response in a multipath high frequency scenario. my expectation was having 2-dimentional answer for the channel impulse response (Eq. 7.5.27) but as you may know at each specific time, channel impulse response is just one complex value, so I was wonder then how the receiver should recognize its vertical and horizontal component?

Hi Farah:

Ok, so that equation is multi-dimensional, since H is a matrix. In the simple LOS example I'd given above for the cross polarized antenna H would be something like:

cos(alpha), sin(alpha)

-sin(alpha), cos(alpha)

for the 2x2 system produced. H can of course have any number of channels, but generally the more you add, the harder it becomes to get completely decorrelated channels. The point is that there are four completely different channels in that 2x2 matrix above (V-V, V-H, H-V, and H-H). For the LOS case, the channel definitions aren't significantly different, so separation of mixed signals may not be easy, but they are different channels.

Re-reading your last question, I'm wondering if you're not getting stuck thinking instantaneously. MIMO works through space-time coding, so if you're trying to understand decorrelation by looking at a single instant in time, you probably won't get there. You have to look at the entire impulse response (or in the case of a modulated signal, how the signals progress over the period of the symbol) in order to evaluate the correlation and the ability to separate signals. In the LOS case, that's problematic because the output impulse response for each channel is just a delayed input impulse. However, in the NLOS case with multiple scattered reflections, the single input impulse is spread across multiple delayed impulses with different delays and magnitude/phase relationships. In an uncorrelated case, each channel has a different set of delayed impulses (taps) that result in a unique received signal through that channel.

Note too that I'm not talking about temporal fading here, where the channel changes over time. The impulse response of the channel IS instantaneous, if you think of it as the time domain transform of the instantaneous frequency response of the channel. In a dynamic fading model, that will progress over time, but at any given instant, the receiver is still receiving the sum of all of those taps, whatever they may be. Some of what it's seeing is just from further back in time (possibly even the previous symbol) than other components of the received signal.

I'm really not sure if this is what you're asking, but hopefully that helps.

Thanks,

Michael

Hi Michael,

Thank you so much for your time and response. Yes, you answer my question, so in your opinion I cannot separate vertical and horizontal elements by looking at the channel impulse response in one specific time and instead I need to check whole channel impulse response and use correlation to see which part is for vertical/horizontal element.

BR//

Farah

Hi Farah,

You're quite welcome. Your last statement confuses me a bit so I want to go back and make sure we're both on the same page. Going back to the equation you reference in the 3GPP channel model, the result is Hu,s, where u, s is the receiver and transmitter element pair. Thus, the H matrix gives you the impulse response (coupling) between each transmit and receive antenna. From that, there are various pieces of information you can extract that will tell you different things about the system. Obviously you can evaluate how much of each signal from each antenna transmit antenna, s, reaches each receive antenna, u. That's what the H matrix is. However, one of the most common quantities of interest is the correlation of the received signals (u), which will indicate whether or not a receiver can easily separate out the transmit signals (s). If this is the quantity you're looking for, then yes, you'd check the correlation of the resultant impulse responses determined by summing the inputs to each u.

Note however that the correlation determined from the H matrix is a system level correlation, and doesn't necessarily indicate if the antennas on the transmit and/or receive side are themselves uncorrelated (unless both are). Highly correlated antennas on either end will result in a high correlation in the H matrix. For example, an ideal cross polarized antenna inherently has zero correlation because the elements are orthogonal, but if the TX antenna pair were two co-polarized, co-located (or just separated by a small fraction of a wavelength) antennas, they are highly correlated due to the co-location in space, and regardless of the environment or the quality of the RX antenna, the H-matrix will provide highly correlated signals. Note too that correlation is a function of environment, but I don't have time to go into that now.