Mysterious pCell, or DIDO under the microscope

So, today, after reading the translation article about pCell , I hit my face in the face a couple of times. Because anyone who deals with the physical level of mobile communication networks will have no difficulty in understanding what the “mysterious motimatika (! Sic)” of DIDO is.

Let's start from afar. From where the legs grow.

Orthogonal Sets

An orthogonal set in mathematics is a set or a subset of elements, where for any x and y from this set the following conditions are true:

1) f (x, y) = 0 , if x! = Y
2) f (x, x) = 1
')
Where the operation f is a scalar product that fulfills all three properties of the scalar product

Moreover, the operation f and the elements of the set can be anything. So f can be either a banal scalar product of vectors, or an integral. And the elements of a set can be either vectors or even functions. For example, when approximating functions, systems of orthogonal polynomials are often used. But that's another topic.

Let's return to our sheep. Suppose we have two numbers (scalars) a and b and an orthogonal subset B of set A. Take 2 elements x and y from B and make up such an element (a * x + b * y) that will belong to A but not belong B. We get the implementation of the following chains of operations:

1) f ((a * x + b * y), x) = a * f (x, x) + b * f (y, x) = a * 1 + b * 0 = a ,
2) f ((a * x + b * y), y) = a * f (x, y) + b * f (x, x) = a * 0 + b * 1 = b

Thus, in order to obtain the initial scalar from a composite element, it is sufficient to take the scalar product from this element and the original element of the orthogonal set.

If it is not yet clear how this relates to the topic, I will rephrase the previous sentence.

Thus, in order to obtain the original signal from the composite signal , it is sufficient to take the scalar product from the received signal and the original element of the orthogonal set.

Is starting to clear, is not it?

Orthogonal Codes

Orthogonal codes are the usual set of orthogonal vectors. In telecommunication systems, they are used everywhere. For example, their application can be found in CDMA and W-CDMA technologies. The idea is that each bit that is transmitted through the physical medium must be encoded with a specific orthogonal code. Here, the "encoded" refers to the banal operation of multiplying a number by a vector. And so, after coding through the physical medium, it is not the bit that is transmitted, but the whole vector multiplied by the value of the bit. And each element of such a vector is called a chip . The multiplication operation itself is called channelization, and the orthogonal code is the channelization code.

What this gives is shown in the 2 properties of the orthogonal sets in the previous section. Using signal coding by orthogonal codes, it becomes possible to transmit several different signals simultaneously on the same physical frequency. Of course, the maximum number of signals is still limited by the length of the code. For a code with a length of 2 elements - a maximum of 2 signals can be transmitted, for 3 elements - 3 signals, etc. I want to emphasize that it is used now . The base station equipment encodes the signal and the receivers in mobile phones receive the signal intended for them using the assigned orthogonal code.

In reality, there are a lot of nuances, such as generating orthogonal codes for transmission on the fly, but these are details.

So what can be innovative in receiving a signal from several radio points simultaneously, what is declared in pCell? That's right - nothing. The only difference is that by creating several separate transmitting points, system developers received additional haemorrhoids associated with the time synchronization of signals (transmitters must send the beginning of the frame synchronously, otherwise an offset will appear between orthogonal codes and the magic will stop working).

The rest of the filling and the theory has been used for a long time, and I cannot call it all but a marketing blurring of the eyes.