# Polarization-division multiplexing

Polarization-division multiplexing (PDM) is a physical layer method for multiplexing signals carried on electromagnetic waves, allowing two channels of information to be transmitted on the same carrier frequency by using waves of two orthogonal polarization states. It is used in microwave links such as satellite television downlinks to double the bandwidth by using two orthogonally polarized feed antennas in satellite dishes. It is also used in fiber optic communication by transmitting separate left and right circularly polarized light beams through the same optical fiber.

Polarization techniques have long been used in radio transmission to reduce interference between channels, particularly at VHF frequencies and beyond.

Under some circumstances, the data rate of a radio link can be doubled by transmitting two separate channels of radio waves on the same frequency, using orthogonal polarization. For example, in point to point terrestrial microwave links, the transmitting antenna can have two feed antennas; a vertical feed antenna which transmits microwaves with their electric field vertical (vertical polarization), and a horizontal feed antenna which transmits microwaves on the same frequency with their electric field horizontal (horizontal polarization). These two separate channels can be received by vertical and horizontal feed antennas at the receiving station. For satellite communications, orthogonal circular polarization is often used instead, (i.e. right- and left-handed), as the sense of circular polarization is not changed by the relative orientation of the antenna in space.

A dual polarization system comprises usually two independent transmitters, each of which can be connected by means of waveguide or TEM lines (such as coaxial cables or stripline or quasi-TEM such as microstrip) to a single-polarization antenna for its standard operation. Although two separate single-polarization antennas can be used for PDM (or two adjacent feeds in a reflector antenna), radiating two independent polarization states can be often easily achieved by means of a single dual-polarization antenna.

When the transmitter has a waveguide interface, typically rectangular in order to be in single-mode region at the operating frequency, a dual-polarized antenna with a circular (or square) waveguide port is the radiating element chosen for modern communication systems. The circular or square waveguide port is needed so that at least two degenerate modes are supported. An ad-hoc component must be therefore introduced in such situations to merge two separate single-polarized signals into one dual-polarized physical interface, namely an ortho-mode transducer (OMT).

In case the transmitter has TEM or quasi-TEM output connections, instead, a dual-polarization antenna often presents separate connections (i.e. a printed square patch antenna with two feed points), and embeds the function of an OMT by means of intrinsically transferring the two excitation signals to the orthogonal polarization states.

A dual-polarized signal thus carries two independent data streams to a receiving antenna, which can itself be a single-polarized one, for receiving only one of the two streams at a time, or a dual-polarized model, again relaying its received signal to two single-polarization output connectors (via an OMT if in waveguide).

The ideal dual-polarization system lies its foundation onto the perfect orthogonality of the two polarization states, and any of the single-polarized interfaces at the receiver would theoretically contain only the signal meant to be transmitted by the desired polarization, thus introducing no interference and allowing the two data streams to be multiplexed and demultiplexed transparently without any degradation due to the coexistence with the other.

Companies working on commercial PDM technology include Siae Microelettronica, Huawei and Alcatel-Lucent.

Some types of outdoor microwave radios have integrated orthomode transducers and operate in both polarities from a single radio unit, performing cross-polarization interference cancellation (XPIC) within the radio unit itself. Alternatively, the orthomode transducer may be built into the antenna, and allow connection of separate radios, or separate ports of the same radio, to the antenna.

CableFree 2+0 XPIC Microwave Link showing OMT and two ODUs connected to H & V polarity ports

### Cross-Polarization Interference Cancellation (XPIC)

Practical systems, however, suffer from non-ideal behaviors which mix the signals and the polarization states together:

• the OMT at the transmitting side has a finite cross-polarization discrimination (XPD) and thus leaks part of the signals meant to be transmitted in one polarization to the other
• the transmitting antenna has a finite XPD and thus leaks part of its input polarizations to the other radiated polarization state
• propagation in presence of rain, snow, hail creates depolarization, as part of the two impinging polarizations is leaked to the other
• the finite XPD of the receiving antenna acts similarly to the transmitting side and the relative alignment of the two antennas contributes to a loss of system XPD
• the finite XPD of the receiving OMT likewise further mixes the signals from the dual-polarized port to the single-polarized ports

As a consequence, the signal at one of the received single-polarization terminals actually contains a dominant quantity of the desired signal (meant to be transmitted onto one polarization) and a minor amount of undesired signal (meant to be transported by the other polarization), which represents an interference over the former. As a consequence, each received signal must be cleared of the interference level in order to reach the required signal-to-noise-and-interference ratio (SNIR) needed by the receiving stages, which may be of the order of more than 30 dB for high-level M-QAM schemes. Such operation is carried out by a cross-polarization-interference cancellation (XPIC), typically implemented as a baseband digital stage.

Compared to spatial multiplexing, received signals for a PMD system have a much more favourable carrier-to-interference ratio, as the amount of leakage is often much smaller than the useful signal, whereas spatial multiplexing operates with an amount of interference equal to the amount of useful signal. This observation, valid for a good PMD design, allows the adaptive XPIC to be designed in a simpler manner than a general MIMO cancelling scheme, since the starting point (without cancellation) is typically already sufficient for establishing a low-capacity link by means of a reduced modulation.

An XPIC typically acts on one of the received signals "C" containing the desired signal as dominant term and uses the other received "X" signal too (containing the interfering signal as dominant term). The XPIC algorithm multiplies the "X" by a complex coefficient and then adds it to the received "C". The complex recombination coefficient is adjusted adaptively to maximize the MMSE as measured on the recombination. Once the MMSE is improved to the required level, the two terminals can switch to high-order modulations.

## Photonics

Polarization-division multiplexing is typically used together with phase modulation or optical QAM, allowing transmission speeds of 100 Gbit/s or more over a single wavelength. Sets of PDM wavelength signals can then be carried over wavelength-division multiplexing infrastructure, potentially substantially expanding its capacity. Multiple polarization signals can be combined to form new states of polarization, which is known as parallel polarization state generation.[1]

The major problem with the practical use of PDM over fiber-optic transmission systems are the drifts in polarization state that occur continuously over time due to physical changes in the fibre environment. Over a long-distance system, these drifts accumulate progressively without limit, resulting in rapid and erratic rotation of the polarized light's Jones vector over the entire Poincaré sphere. Polarization mode dispersion, polarization-dependent loss. and cross-polarization modulation are other phenomena that can cause problems in PDM systems.

For this reason, PDM is generally used in conjunction with advanced channel coding techniques, allowing the use of digital signal processing to decode the signal in a way that is resilient to polarization-related signal artifacts. Modulations used include PDM-QPSK and PDM-DQPSK.[2]

Companies working on commercial PDM technology include Alcatel-Lucent, Ciena, Cisco Systems, Huawei and Infinera.

## References

1. ^ She, Alan; Capasso, Federico (17 May 2016). "Parallel Polarization State Generation". Scientific Reports. Nature. arXiv:1602.04463. Bibcode:2016NatSR...626019S. doi:10.1038/srep26019. Retrieved 27 June 2016.
2. ^ "The Road to 100G Networking" (PDF). Ciena. 2008. Retrieved 2012-06-25.
Index of physics articles (P)

The index of physics articles is split into multiple pages due to its size.

Microwave transmission

Microwave transmission is the transmission of information by microwave radio waves. Although an experimental 40-mile (64 km) microwave telecommunication link across the English Channel was demonstrated in 1931, the development of radar in World War II provided the technology for practical exploitation of microwave communication. In the 1950s, large transcontinental microwave relay networks, consisting of chains of repeater stations linked by line-of-sight beams of microwaves were built in Europe and America to relay long distance telephone traffic and television programs between cities. Communication satellites which transferred data between ground stations by microwaves took over much long distance traffic in the 1960s. In recent years, there has been an explosive increase in use of the microwave spectrum by new telecommunication technologies such as wireless networks, and direct-broadcast satellites which broadcast television and radio directly into consumers' homes.

Multiplexing

In telecommunications and computer networks, multiplexing (sometimes contracted to muxing) is a method by which multiple analog or digital signals are combined into one signal over a shared medium. The aim is to share a scarce resource. For example, in telecommunications, several telephone calls may be carried using one wire. Multiplexing originated in telegraphy in the 1870s, and is now widely applied in communications. In telephony, George Owen Squier is credited with the development of telephone carrier multiplexing in 1910.

The multiplexed signal is transmitted over a communication channel such as a cable. The multiplexing divides the capacity of the communication channel into several logical channels, one for each message signal or data stream to be transferred. A reverse process, known as demultiplexing, extracts the original channels on the receiver end.

A device that performs the multiplexing is called a multiplexer (MUX), and a device that performs the reverse process is called a demultiplexer (DEMUX or DMX).

Inverse multiplexing (IMUX) has the opposite aim as multiplexing, namely to break one data stream into several streams, transfer them simultaneously over several communication channels, and recreate the original data stream.

Orbital angular momentum multiplexing

Orbital angular momentum (OAM) multiplexing is a physical layer method for multiplexing signals carried on electromagnetic waves using the orbital angular momentum of the electromagnetic waves to distinguish between the different orthogonal signals.Orbital angular momentum is one of two forms of angular momentum of light. OAM is distinct from, and should not be confused with, light spin angular momentum. The spin angular momentum of light offers only two orthogonal quantum states corresponding to the two states of circular polarization, and can be demonstrated to be equivalent to a combination of polarization multiplexing and phase shifting. OAM on the other hand relies on an extended beam of light, and the higher quantum degrees of freedom which come with the extension. OAM multiplexing can thus access a potentially unbounded set of states, and as such offer a much larger number of channels, subject only to the constraints of real-world optics.

As of 2013, although OAM multiplexing promises very significant improvements in bandwidth when used in concert with other existing modulation and multiplexing schemes, it is still an experimental technique, and has so far only been demonstrated in the laboratory. Following the early claim that OAM exploits a new quantum mode of information propagation, the technique has become controversial; however nowadays it can be understood to be a particular form of tightly modulated MIMO multiplexing strategy, obeying classical information theoretic bounds.

Polarization scrambling

Polarization scrambling is the process of rapidly varying the polarization of light within a system using a polarization controller so that the average polarization over time is effectively randomized. Polarization scrambling can be used in scientific experiments to cancel out errors caused by polarization effects. Polarization scrambling is also used on long-distance fibre optic transmission systems with optical amplifiers, in order to avoid polarization hole-burning. Polarization scrambling, also for the variation of polarization mode dispersion, is a mandatory test procedure for fiber optic data transmission systems based on polarization-division multiplexing.

Polarization scramblers usually vary the normalized Stokes vector of the polarization state over the entire Poincaré sphere. They are commercially available with speeds of 20 Mrad/s on the Poincaré sphere (see external link). Various speed distributions such as peaked and quasi-Rayleigh can be generated.

Recent experiments implemented ultrafast polarization scrambling on a polaritonic platform with speeds in the order of the Trad/s on the Poincaré sphere.

XPIC

XPIC, or cross-polarization interference cancelling technology, is an algorithm to suppress mutual interference between two received streams in a Polarization-division multiplexing communication system.

The cross-polarization interference canceller (known as XPIC) is a signal processing technique implemented on the demodulated received signals at the baseband level. It is typically necessary in Polarization Division Multiplexing systems: the data sources to be transmitted are coded and mapped into QAM modulating symbols at the system's symbol rate and upconverted to a carrier frequency, generating two radio streams radiated by a single dual-polarized antenna (see feed pattern of Parabolic antenna). A corresponding dual-polarized antenna is located at the remote site and connected to two receivers, which downconvert the radio streams into baseband signals (BB H, BB V).

This multiplexing/demultiplexing technique is based on the expected discrimination between the two orthogonal polarizations (XPD):

As a practical consequence, at the receiving site the two streams are received with a residual mutual interference. In many practical cases, especially for high-level M-QAM modulations, the communication system cannot tolerate the experienced levels of cross-polarization interference and an improved suppression is necessary. The two received polarizations at the antenna outputs, normally linear horizontal H and vertical V, are routed each to a receiver whose baseband output is further processed by an ad-hoc cross-polarization cancelling scheme, commonly implemented as a digital stage. The XPIC algorithm attains the correct reconstruction of H by summing V to H to cancel any residual interference, and vice versa.

The cancelling process is typically implemented using two blocks: a baseband equalizer and the baseband XPIC. The output from the latter is subtracted from the former and then sent to the decision stage, responsible for yielding the estimation of the data stream. The equalization and XPIC blocks are normally adaptive for a correct tracking of the time-variant channel transfer function: XPIC must provide a shaping of the received cross signal equal to the portion of the cross interference affecting the main one. The feedback control to drive the adapting criteria comes from the measure of the residual error across the decision block.

In the example, both blocks are based on the typical structure of the Finite Impulse Response digital filter and whose the coefficients are not fixed, but adapted to minimize a suitable functional ${\displaystyle J}$ while multiple delays ${\displaystyle D}$ act on the input signal.

Given:

if the function to minimize is for example the mean power the residual error, ${\displaystyle J=E[|\epsilon _{k}|^{2}]}$, the adapting gradient algorithm prescribes that the coefficients are updated after every time step ${\displaystyle k}$ as:

where the asterisk denotes complex-conjugation. No a-priori knowledge on the transmitted symbols is required with this basic scheme (blind or zero-knowledge).

When the delay ${\displaystyle D}$ is equal to the symbol period, the blocks are denoted as symbol-spaced, while if ${\displaystyle D}$ is a fraction of the symbol period the blocks are said to be fractionally-spaced. Other minimizing functions are least mean square LMS or zero forcing ZF while the architecture can be a Decision Feedback or further improved by means of known signals (Pilot signal).

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