A waveguide MIMO 

Until now we have considered a number of different transmission lines. In this case it is quite obvious that the channel capacity dramatically increases with the number of the transmission lines used. However, the use of several transmission lines is quite expensive. A much more convenient solution would consist in adopting MIMO communication system using a single guiding device.

Let us consider for example a waveguide. It is well known that the field in the waveguide can be expanded in  Transverse Electric (TE) and Transverse Magnetic (TM) modes. For sake of simplicity we suppose that the structure does not support Transverse ElectroMagnetic (TEM) modes. Furthermore, it is also supposed that the waveguide is sufficiently short to neglect the intermodal and intramodal dispersion. 

The TE and TM modes represent an orthonormal basis for the field in the waveguide. After fixing the operating frequency only a finite number of modes, let M be, are propagative.

The propagation associated with each of these modes is modelled by means of an equivalent transmission line. Accordingly, we have M channels, each of them can be used to send one of the M substreams of the data stream. A waveguide operating on more than one mode is a simple example of a MIMO channel. Of course, such a MIMO system can be modelled as M equivalent transmission lines.

For example, let us consider a waveguide having a square section, operating on the TE_01 and TE_10  modes. Let us suppose we are able to excite and to receive the two modes independently, for example by means of two orthogonal electric monopoles at the TX and RX sections. If the waveguide is straight, there are no discontinuities and no losses, then there is no mutual coupling between the modes. Consequently, we have two orthogonal channels, and the propagation can be modelled as a set of parallel equivalent transmission lines. In practical instances, there is some degree of coupling between the two modes. However, by a training sequence the receiver can estimate the channel matrix, and can obtain two equivalent orthogonal channels by means of a proper processing algorithm as outlined in the coupling section.

Let us suppose that the waveguide supports the TE_10 and TE_20 modes. In this case, good positions of the two monopoles are on the maximum of the transverse electric field pattern of the modes . The first monopole, placed in the centre of the transverse section, excites only the TE_10, while the second one excites both the modes. The energy of the data substream associated to the second monopole is consequently split between the two modes. If the energy coupled in the TE_20 by the second monopole is almost equal to the energy globally coupled in the TE_10 by the two monopoles, both the modes contribute to the communication channel.

However, if the position of the second antenna is very close to the first one, the TE_20 is weakly coupled, and only the TE_10 is excited. In this case the channel matrix H is practically rank deficient and we have only one orthogonal channel. The same result is valid also when the two RX antennas are positioned very close each other.

Finally, we consider a rectangular waveguide supporting the modes TE_10, TE_20 and TE_30, and two TX and two RX monopoles. Note that the energy of the two data substreams is generally divided among the three modes and the number of subchannels is limited by the number of antennas. 

Starting from the above simple MIMO system, we can make a number of interesting observations:

• the maximum number of MIMO orthogonal channels is limited by the number of TX-RX antennas, and is two in spite of the presence of three orthogonal modes;

• if the monopoles are incorrectly posed (f.i. very close each other) the number of MIMO orthogonal channels can be smaller than the number of TX-RX antennas;

• we can increase the channel capacity by adopting three TX and three RX antennas, that allows us to use all the three orthogonal modes;

• a number of monopoles greater than the number of orthogonal modes is useless, since the number of orthogonal modes fixes also the maximum number of SISO subchannels available.