DE102019115473A1 - Systems and methods for polarization control using blind source separation - Google Patents

Abstract

Analog signal processing systems and methods manage the polarization in coherent optical receivers to eliminate the need for ultrafast, power-hungry ADCs and DSPs that require digitization of the full-bandwidth signal path, resulting in bulky and expensive circuit designs. Various embodiments of an analog polarization correction circuit that implements the equivalent of two matrix operations by combining variable and unity gain amplifiers to align polarizations of input signals to generate a polarization corrected output signal aligned with a receiver's polarization reference frame. Various embodiments use BSS to perform polarization control, including electro-optic polarization control, in a feedback loop and operate without the need for a pilot tone or start sequence in determining the polarization state.

Description

Cross-reference to related applications

This patent application is with the co-pending and commonly assigned provisional U.S. Patent Application No. 62 / 682,599 entitled "Systems and Methods for Polarization Control Using Blind Source Separation" and claims its priority under 35 USC § 119 (e). The inventor is Charles John Razzell, and the filing date was 8 June 2018 (Attorney Docket No. 20057-2215P2). This patent document is hereby incorporated by reference in its entirety and for all purposes in the present text.

Technical area

The present disclosure generally relates to the processing of electrical signals. More particularly, the present disclosure relates to systems and methods for controlling and restoring polarization and carrier phase in electro-optic communication systems.

background

In recent years, coherent optical communication links have been used commercially at rates of 100 Gbps / λ and higher. These systems rely heavily on power hungry (eg,> 10W) digital signal processing (DSP) devices even in the case of the very latest CMOS process technologies (for example, 16nm line widths in commercial products). The ability to support unreinforced interconnections of up to 80 km at such high rates justifies the cost of high-performance DSPs against the background of reducing other capital expenditures and operating costs. On the other hand, the ever-increasing demand for high-bandwidth data center communications is pushing the limits of the Four-Level Pulse Amplitude Modulation (PAM4) regime of direct detection and intensity modulation.

For example, IEEE P802.3cd as one of its PHY options, 100GBASE-DR, is expected to standardize 100 Gb / s serial transmission over a single wavelength using PAM4 over a single-mode fiber> 500 m. The results of contributors to the IEEE P802.3cd working group, in 1 (IEEE SMF Task Group Contribution by Marco Mazzini (Cisco), August 2014) suggest that 56 Gbaud / 112 Gbps PAM4 requires a feedforward equalizer to open the eye. While some approaches have proven their feasibility, numerous submissions suggest that meeting the budget margins for the interconnect sections is a challenge for this type of PHY option.

One type of distortion that is subjected to a polarized optical input beam passing through an optical fiber installation involves undesirable changes in the state of polarization (SOP) of the signal that occurs during transmission. In order to avoid having to manipulate the polarization states in the DSP domain, which would normally be expected for a DSP-based coherent receiver, some designers have proposed implementing polarization control using optical modulators. To facilitate this, a pilot or marker tone is added in the transmitter to designate and track one of the phases of the two polarizations (for example, the in-phase x-polarization signal branch) as a reference such that a control loop algorithm, the runs in a low power CPU that can monitor and adjust polarization states, to correct polarization rotations in two or three degrees of freedom.

The pilot tone (for example, 50 kHz) placed across the XI satellite in the transmitter is used to restore the polarization states in the receiver, which lowpass filters the XQ, YI, and YQ signals and places those signals in the four branches detected synchronously. In this way, the receiver monitors the amplitudes and signs of these signals while assuming that carrier phase lock has already been achieved. Then, slow signal processing can be used to adjust the polarization angles to reduce the unwanted pilot tone amplitudes, such that the receiver can compensate for polarization rotation in the fiber. However, this approach has drawbacks with respect to a bootstrap problem, namely, (1) that marker probe detection is possible only after carrier phase recovery, and (2) that carrier recovery is dependent on first restoring the polarization states, for example to ensure that a QPSK constellation is available for detection.

A proposed solution to overcoming these disadvantages involves a start of transmission protocol wherein the same data is sent in each of the two polarization branches simultaneously. This requirement allows the carrier recovery loop to "see" the QPSK modulation regardless of the polarization state such that carrier phase lock can be achieved. In a second step, the polarization recovery loop is activated, with the expectation that the 50 kHz marker tone will now be found at the expected frequency. However, such a solution is sub-optimal because (1) special boot sequences in a system context may not be feasible due to compatibility reasons (e.g., the lack of suitable protocols that may allow a particular boot sequence) and (2) if DQPSK is used, not phase locked System is such that the ability to synchronously detect the pilot tone, which is possible only with a phase-locked system is lost. As a result, for some reason, any timeout is lost and the connection section must be aborted and restarted, causing unwanted interruptions to the operation.

So what is needed are systems and procedures that work pilotless and start-sequence-free when determining the polarization state. This object is solved by the subject matter of the independent claims. Preferred embodiments are characterized by the features of the subclaims.

list of figures

• FIGUR („FIG.“) 1 veranschaulicht die Beschränkungen von im Stand der Technik vorgeschlagenen PAM4-Modulationsregimes, die einen Feedforward-Equalizer erfordern.
• 2 veranschaulicht ein beispielhaftes Blockschaubild einer Empfängerarchitektur, welche die Polarisation über digitales Subsampling abfühlt, gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 3 ist ein Flussdiagramm zum Anwenden einer Polarisationssteuerung auf der Basis einer Blindquellenschätzung gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 4 veranschaulicht ein beispielhaftes Blockschaubild einer Empfängerarchitektur, die eine elektronische Rückkopplungssteuerung verwendet, um eine Trägerphasenkorrektur auszuführen, gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 5 ist ein Flussdiagramm zum Anwenden einer Polarisations- und Trägerphasensteuerung auf der Basis einer Blindquellenschätzung gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 6 ist ein Flussdiagramm zum kohärenten Kombinieren zweier Empfängerabzweigungen mit zunächst unbekannter relativer Phase gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 7 ist ein Flussdiagramm zum kohärenten Kombinieren zweier Empfängerabzweigungen mit zunächst unbekannter relativer Phase zum Implementieren einer Polarisationsdiversität gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 8 ist ein veranschaulichendes Blockschaubild einer beispielhaften optischen Empfängerschaltung, die den Empfang eines Sendepolarisationsdiversitätsregimes implementiert, das unter Verwendung eines Space Time Block Coding (STBC)-Regimes organisiert wird, gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 9 ist ein Flussdiagramm eines veranschaulichenden Prozesses zur Kanalschätzung für STBC-codierte Diversitätssender gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.
• 10 zeigt ein 16-QAM-Sendermodulations-Vektordiagramm (mit hinzugefügtem Rauschen).
• 11 zeigt simulierte DP-16-QAM-Leistungsspektren.
• 12 zeigt Simulationsergebnisse, die ein Streudiagramm für einen 16-QAM-Empfänger zeigen, der keine Polarisationskorrektur verwendet.
• 13 - 15 zeigen allgemeine Simulationsergebnisse, die Streudiagramme für einen 16-QAM-Empfänger veranschaulichen, der EFICA, FicaCMPLX bzw. JADE verwendet, gemäß verschiedenen Ausführungsformen der vorliegenden Offenbarung.

Embodiments of the invention will be discussed, examples of which may be illustrated in the accompanying figures. These figures are intended to be illustrative and not restrictive. While the invention will be broadly described in the context of these embodiments, it will be understood that they are not intended to limit the scope of the invention to these particular embodiments.

• FIGURE ("FIG.") 1 illustrates the limitations of prior art proposed PAM4 modulation regimes that require a feedforward equalizer.
• 2 FIG. 12 illustrates an exemplary block diagram of a receiver architecture that senses polarization via digital subsampling, according to various embodiments of the present disclosure.
• 3 FIG. 10 is a flowchart for applying polarization control based on blind source estimation according to various embodiments of the present disclosure. FIG.
• 4 FIG. 12 illustrates an exemplary block diagram of a receiver architecture that uses electronic feedback control to perform carrier phase correction, in accordance with various embodiments of the present disclosure.
• 5 FIG. 10 is a flowchart for applying polarization and carrier phase control based on blind source estimation according to various embodiments of the present disclosure. FIG.
• 6 FIG. 10 is a flowchart for coherently combining two receiver branches with initially unknown relative phase according to various embodiments of the present disclosure. FIG.
• 7 FIG. 10 is a flowchart for coherently combining two receiver branches of initially unknown relative phase to implement polarization diversity according to various embodiments of the present disclosure. FIG.
• 8th FIG. 4 is an illustrative block diagram of an exemplary optical receiver circuit that implements the reception of a transmit polarization diversity regime organized using a Space Time Block Coding (STBC) regime, according to various embodiments of the present disclosure.
• 9 FIG. 10 is a flowchart of an illustrative channel estimation process for STBC encoded diversity transmitters according to various embodiments of the present disclosure.
• 10 shows a 16-QAM transmitter modulation vector diagram (with added noise).
• 11 shows simulated DP-16 QAM power spectra.
• 12 shows simulation results showing a scatter plot for a 16-QAM receiver that does not use polarization correction.
• 13 - 15 10 show general simulation results illustrating scatter plots for a 16-QAM receiver using EFICA, FicaCMPLX, and JADE, respectively, in accordance with various embodiments of the present disclosure.

Detailed description of the embodiments

In the following description, for purposes of explanation, specific details are set forth in order to provide an understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without these details. Further, those skilled in the art will recognize that embodiments of the present invention described below may be implemented in a variety of ways, such as a process, device, system, apparatus, or method on a tangible computer-readable medium.

Components or modules shown in diagrams are illustrative of exemplary embodiments of the invention and are intended to obscure the essential aspects of the invention. It is further understood that throughout the discussion, components may be described as separate functional units that may include subunits, but those skilled in the art will recognize that various components or portions thereof may be subdivided into or integrated with each other, including the Integrating in a single system or component. It should be noted that functions or operations discussed herein may be implemented as components. Components can be implemented in software, hardware or a combination thereof.

Furthermore, connections between components or systems within the figures are not intended to be limited to direct connections. Rather, data between these components may be modified, reformatted, or otherwise altered by intermediate components. In addition, additional or fewer connections can be used. It is also to be understood that the terms "coupled," "connected," or "communicatively coupled" are to be understood to include direct connections, indirect connections through one or more intermediate devices, and wireless connections.

When the specification speaks of a "particular embodiment," "preferred embodiment," "embodiment," or "embodiments," it means that a particular feature, structure, property, or function that may or may not function properly which is described in connection with the embodiment, is included in at least one embodiment of the invention and may be included in more than one embodiment. In addition, the mention of the above formulations at various points in the specification may not necessarily always refer to the same embodiment or embodiments.

The use of particular terms throughout the specification is illustrative and not to be construed in a limiting sense. A service, function, or resource is not limited to a single service, function, or resource; the use of these terms may refer to a grouping of related services, functions or resources that may be distributed or aggregated. Furthermore, the use of memory, databases, information banks, data stores, tables, hardware and the like may be used herein to refer to one or more system components into which information may be entered or in which information is otherwise recorded can.

It should be noted that: (1) certain steps may optionally be performed; (2) steps need not necessarily be limited to the order specifically set out in this text; (3) certain steps can be performed in other orders; and (4) certain steps can be performed simultaneously. For example, while examples are given in the context of blind source separation (BSS) methods that are applied to optical receivers, those skilled in the art will recognize that the teachings of the present disclosure are not limited to the BSS applications described herein and may equally be applied individually, collectively, or simultaneously in any combination and in other contexts, for example in applications that may or may not require carrier phase recovery.

Various embodiments advantageously use low-rate digital samples of the XI, XQ, YI, and YQ (for example, 10 MHz sampling rates) and estimate the unknown complex Jones 2x2 matrix describing the polarization transformation in the fiber installation using the Samples of XI, XQ, YI and YQ without prior information. In embodiments, the complex Jones matrix is estimated by treating it as a mixed matrix and applying a suitable BSS method to the resulting signal vectors, such as (1) Joint Approximate Diagonalization of Eigen Matrices (JADE); (2) Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals (cFAST-ICA); and (3) Efficient Variant of Algorithm FastICA for Independent Component Analysis (EFICA). In short, once the problem has been circled as a BSS problem, it can then be solved by selecting and employing a convenient method for solving the resulting BSS problem by using a BSS method based on complex matrices works to separate out the polarizations in the receiver, without having to resort to pilot tones, start sequences or other suboptimal techniques.

Since these methods rely solely on the statistical properties of data sets, for example, to optimize separation into independent components, estimating the Jones matrix using BSS is advantageously not tied to Nyquist sampling according to the baud rate of the communication signal to get satisfactory results. In embodiments, even massive undersampling (for example, several orders of magnitude) may be used, limited only by the update rate for the SOP changes in the fiber installation. In addition, undersampling advantageously reduces computational complexity and power consumption for calculations, such as updates to the polarization control state variable of a receiver (eg, φ and θ).

In embodiments, a sample rate much lower than the signal bandwidth Nyquist rate may be used, while sample-and-hold and ADW (eg in the front-end) circuits are configured to operate without excessive low-pass filtering, which would otherwise may cause the statistics to be moved to Gaussian statistics, for example, due to the central-limit theorem. Therefore, in embodiments, a high bandwidth sample and hold circuit is paired with a moderate sample rate ADW to acquire data, thereby avoiding the use of expensive ultra-high and multi-bit rate ADCs in the signal path.

2 FIG. 12 illustrates an exemplary block diagram of a receiver architecture that senses polarization via digital subsampling, according to various embodiments of the present disclosure. In 2 is the recipient 200 shown as a dual polarization M-QAM receiver; however, this is not to be considered as limiting the scope of the disclosure. The receiver circuit 200 is an optical receiver, which is an optical frontend 202 , an analog polarization correction circuit 204 and a differential modulator circuit 208 may include.

In embodiments, the optical front-end comprises 202 photodiodes 203 , PBS 250 , a 90 ° hybrid 256 and a local oscillator 260 , The optical frontend 202 can be any optical frontend known to those skilled in the art. In embodiments, the analog polarization correction circuit 204 amplifier 205 - 207 include and process the output of the photodiodes 203 to two polarization currents before the differential detection by the differential modulator circuit 208 to isolate. The differential modulator circuit 208 may include: low-pass filter 210 , ADWs 280 , Memory buffers (for example RAM), sample and hold circuits 282 , Timing Recovery and Bitslicing Modules 214 . 216 , and a polarization controller 212 (for example, a microcontroller), the angle 242 and 244 and perform a non-linear operation involving squaring of amplitudes.

In embodiments, the input signal is 240 from independent bitstreams in the x-polarization and the y-polarization present in the receiver 200 separated to access the independent bitstreams. In embodiments, this is done by reversing arbitrary, unknown rotations in at least two degrees of freedom to which the input signal 240 can be subjected in the fiber channel and otherwise can influence each other.

More specifically, the optical front end receives 202 for example via the PBS 250 an input signal 240 , for example from an optical channel. The PBS 250 separates the input signal 240 into two components, X and Y, which are orthogonal polarizations in two branches, ie an X polarization branch 252 and a Y branch 254 , In embodiments, the X-polarization branch becomes 252 into the 90 ° hybrid 256, for example, a six-port hybrid, and the Y polarization branch 254 is fed into the 90 ° hybrid 256.

In embodiments, the hybrid 256 . 258 a connection for the local oscillator 260 , such as a laser. It should be noted that the local oscillator 260 in an ideal homodyne receiver operates on the same wavelength as the signal to be decoded. In practice, drift and tolerances can lead to suboptimal conditions such that the wavelengths are not exactly the same.

In embodiments, the hybrid generates 256 different phases based on the summation of its input signals. In embodiments, in the uppermost branch, which is the hybrid 256 comprises the local oscillator signal with the X polarization signal 252 summed up, and the hybrid 256 outputs four phases, for example 0 °, 180 °, 90 ° and 270 °. Conversely, the Y polarization in the lowest branch is through the hybrid 258 For example, to process four signals having four phases and in the same order as the hybrid 254 issue.

The photodiodes 203 may be differential photodiodes that, in embodiments, process light that has a positive amplitude, ie, the photodiodes 203 even do not generate negative signals. In embodiments, the output signals of the adjacent photodiodes 203 electrical current signals which are 180 ° out of phase and which are the difference, for example, of the 0 ° output of the hybrid 256 and the 180 ° output, ie, a bipolar photocurrent that can take both positive and negative values. The difference of the photocurrents is a signal which is the in-phase component Xi of the X polarization signal 252 represents. Similarly, the photodiodes generate 203 at the 90 ° output and at the 270 ° output, a bipolar photocurrent which is the quadrature component Xq of the X polarization signal 252 represents, and so on. Overall, the hybrids can 256 . 258 each output two electrical signals in symmetrical pairs, for example Xi and Xq, which refer to in-phase polarization and quadrature polarization, respectively. It is understood that these four electrical signals throughout the remaining part of the receiver 200 amplified, filtered and processed further.

In embodiments, the in-phase signal Xi and the quadrature signal Xq become the analog polarization correction circuit 204 which rotates the phases of the signals in the X-polarization branch relative to the phase of the Y-polarization signal. In embodiments, the emphasis on the relative value of the phase difference allows the rotation of the X polarization values while not rotating the Y polarization values. As in 2 This can be accomplished by using the four amplifiers (for example, 202) in the X polarization branch to rotate the phase angles φ of the amplifier's input signals, while the phase angles of the input signals from amplifiers (e.g., 204) in the Y Polarization branch, which may have unity gain, can not be rotated.

The rotated signals can then be, for example, through the set of eight amplifiers 206 which, in embodiments, function as θ rotators that rotate the combination of the in-phase signals and the quadrature signals to match the X and Y coordinates of the receiver 200 aligned so that they are separated. As a result, the output of the θ rotators is polarization corrected, whereby clean separation of the polarization signals is achieved. It will be understood by those skilled in the art that in embodiments, a negative sign may be moved into the function of an amplifier itself, for example, by commutating differential signal pairs.

In embodiments, the separated polarization signals become the differential modulator circuit 208 fed, for example, to find the phase rotations. The phase angles θ of the output of the analog polarization correction circuit 204 represent phase differences that can be processed using conventional bit slicing and timing recovery to obtain the actual bitstream.

In embodiments, the polarization controller may be used to output two phase angles φ and θ which, in turn, may control the specific weights of the gains of the two sets of amplifiers to efficiently cancel the polarization rotation in the fiber channel, such that the outputs thereof Summation blocks in the analog polarization correction circuit 204 polarization corrected and are the same signals that were originally sent independently in two channels. In other words, the blocks of amplifiers may be controlled in a feedback loop by phase angles φ and θ to successfully accomplish this task and to separately resolve the two polarizations, ie the X and Y polarization branches of the receiver, to form orthogonal signals in the two branches before being processed into a subsequent block of mixers using differential detection, etc.

In embodiments, the polarization controller 212 are implemented as a hardware component of moderate complexity, such as an ARM core, by advantageously taking advantage of the subsampling of data received in four memory buffers (not shown) to reduce the signal processing computation rates to a manageable level. In embodiments, the polarization controller 212 , the ADWs 280 and the sample and hold circuits 282 in 2 configured to allow data collection through memory buffers that collect enough statistics to allow the controller 212 allow to execute a BSS method, such as JADE, FASTICA or EFICA, to manipulate a demixing matrix such that angles 242 . 244 which can then be derived and used to estimate polarization states in a continuous feedback loop. In embodiments, signals may be in the four branches of the receiver 200 after being polarization corrected but before a non-linear processing step that can be used for differential demodulation that demulses the polarization.

In embodiments, the ADWs 280 are implemented as low complexity ADWs that use a relatively low sampling rate, for example, on the order of a few MHz, which may be sufficient to match the rate of change or rotation of the polarization in the fiber installation based on the Nyquist rate Frequency for the polarization or phase rotation to keep up, form no obstacle to the BSS. In embodiments, the bandwidths of the sample and hold circuits become 282 chosen so that they are compatible with the sampled signals.

3 FIG. 10 is a flowchart for applying polarization control based on blind source estimation according to various embodiments of the present disclosure. FIG. For example, in embodiments, the method may be implemented by a receiver whose architecture is similar to that found in FIG 2 is shown. The process 300 in 3 can at step 302 begin when polarization control state variables are initialized, for example, such that θ ₀ = 0 and φ ₀ = 0.

At step 304 Using a set of sample-and-hold and ADC circuits in a receiver, a number of samples are obtained from the XI, XQ, YI and YQ branches of the receiver and the samples are accumulated in a set of memory buffers. It will be understood by those skilled in the art that scans may be detected simultaneously.

At step 306 For example, a BSS may be executed, for example, by applying a complex ICA to the samples in the memory buffers indicated at step 304 accumulated.

At step 308 For example, the segregation matrix (eg 2x2) can be adjusted to become one. In embodiments, this can be accomplished using one of the methods described below.

At step 310 For example, the resulting demixing matrix may be factored to include incremental angles, for example Δφ and θΔ.

At step 312 For example, the incremental angles may be added to the previous state variables θ _{k + 1} = θ _k + Δθ and φ _{k + 1} = φ _k + Δφ to obtain updated polarization state variables {θ _{k + 1} , φ _{k + 1} }.

At step 314 For example, the updated polarization state variables {θ _{k + 1} , φ _{k + 1} } may be written to the receiver hardware; the process 300 can with step 304 be resumed.

In embodiments, the systems and methods described herein may, in addition to polarization control applications, be extended to carrier phase estimation or recovery applications, for example, for coherent modulation regimes, as described in the following paragraphs.

Simultaneous, joint restoration of polarization and carrier phase

In embodiments, the complex Jones matrix may be factored into individual rotations according to four degrees of freedom. In this way, the inverse of the Jones matrix, ie the segregation matrix J ^-1 , can be expressed as: $$J^{-1}=e^{-\frac{j\psi }{2}}\left[\begin{array}{cc}{e}^{-\frac{\mathrm{<figure-callout\; id="0"\; label="j\; \phi "\; filenames="DE102019115473A1\_0015.png,DE102019115473A1\_0024.png"\; state="\{\{state\}\}">j\; </figure-callout>}{\phi }_{}{}_0}{2}}& 0\\ 0& {\mathrm{<figure-callout\; id="0"\; label="e\; j\; \phi "\; filenames="DE102019115473A1\_0015.png,DE102019115473A1\_0024.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^{\frac{j{\phi }_{}}{}}\end{array}\right]\left[\begin{array}{cc}\text{cos}\theta & -\text{sin}\theta \\ \text{sin}\theta & \text{cos}\theta \end{array}\right]\left[\begin{array}{cc}{e}^{-\frac{\mathrm{<figure-callout\; id="1"\; label="j\; \phi "\; filenames="DE102019115473A1\_0015.png"\; state="\{\{state\}\}">j\; </figure-callout>}{\phi }_{}{}_1}{2}}& 0\\ 0& {\mathrm{<figure-callout\; id="1"\; label="e\; j\; \phi "\; filenames="DE102019115473A1\_0015.png"\; state="\{\{state\}\}">e\; </figure-callout>}}^{\frac{j{\phi }_{}}{}}\end{array}\right]$$

In embodiments, instead of resolving the values of φ ₀ and ψ representing the absolute carrier phases in the X and Y polarization branches, using means such as differential demodulation or a Costas analog loop, the complete segregation matrix J ^-1 using BSS to also perform carrier phase recovery, ie, in addition to restoring in-phase and quadrature components for the X and Y polarization modes.

4 FIG. 12 illustrates an exemplary block diagram of a receiver architecture that uses electronic feedback control to perform carrier phase correction, in accordance with various embodiments of the present disclosure. As in 4 shown is the recipient 400 a dual polarization M-QAM receiver. But that should not be a limitation. For the sake of brevity, a description of similar components, previously with reference to 2 and their function is not repeated here.

Recipient 400 includes a carrier phase correction 410 , the vehicle live information into the receiver 400 feeds. 4 FIG. 4 is an exemplary implementation illustrating where an absolute carrier phase control in the analog domain may be applied in accordance with updates calculated using BSS calculated in a suitable microcontroller. For the sake of simplicity φ ₀ and ψ have been reformulated in the diagram as phase angles δ and ∈.

In theory, it is expected that preventing mixing of I and Q components for square or rectangular signal constellations, such as 4-QAM and 16-QAM, works well, but less well for circular constellations, such as 8- PSK or higher because, in order for the carrier phase estimates to be adequately estimated, the degree of independence of the information resolved into the in-phase and quadrature channels of the receiver should be highly dependent on the rotation of the signal constellation.

5 FIG. 10 is a flowchart for applying polarization and carrier phase control based on blind source estimation according to various embodiments of the present disclosure. FIG. For example, in embodiments, the method may be implemented by a receiver whose architecture is similar to that found in FIG 4 is shown. The process 500 can at step 502 begin when polarization control state variables and carrier phase state variables are initialized, for example, such that θ ₀ = 0, φ ₀ = 0, and δ ₀ = 0, ∈ ₀ = 0.

At step 504 Using a set of sample-and-hold and ADC circuits in a receiver, a number of samples are obtained from the XI, XQ, YI and YQ branches of the receiver and the samples are accumulated in a set of memory buffers. It will be apparent to those skilled in the art that the scans should be detected simultaneously.

At step 506 For example, a BSS may be executed, for example, by applying a complex ICA to the samples in the memory buffers indicated at step 504 accumulated.

At step 508 For example, the segregation matrix (eg 2x2) can be adjusted to become one. In embodiments, this can be accomplished using one of the methods described below.

At step 510 For example, the resulting demixing matrix may be factored to include incremental angles, for example, Δφ, θΔ, Δδ, and Δ∈.

At step 512 the incremental angles can be added to the previous state variables θ _{k + 1} = θ _k + Δθ, φ _{k + 1} = φ _k + Δφ, δ _{k + 1} = δ _k + Δδ and ∈ _{k + 1} = ∈ _k + Δ∈, to obtain updated polarization state variables {θ _{k + 1} , φ _{k + 1} } and carrier phase state variables {δ _{k + 1} , ∈ _{k + 1} } that can be written to the receiver hardware; and the process 500 can with step 504 be resumed.

Use of complex or real versions of the ICA

In embodiments, instead of treating the mixed matrix as a 2x2 Jones complex matrix J equivalently and using complex versions of the ICA algorithms to estimate J, the two complex data streams output by the (four) branches of the receiver can are treated as four real data streams that generate signals that can be demixed using, for example, a real 4x4 matrix instead of a complex 2x2 matrix. Therefore, in embodiments, each output may be considered the product of four unknown mix coefficients and four input signals, respectively. $$\left[\begin{array}{c}{e}_{rxi}\\ e_{rxq}\\ e_{ryi}\\ e_{ryq}\end{array}\right]=\left[\begin{array}{cccc}\Re \left\{J_{11}\right\}& -\Im \left\{J_{11}\right\}& \Re \left\{J_{12}\right\}& -\Im \left\{J_{12}\right\}\\ \Im \left\{J_{11}\right\}& \Re \left\{J_{11}\right\}& \Im \left\{J_{12}\right\}& \Re \left\{J_{12}\right\}\\ \Re \left\{J_{21}\right\}& -\Im \left\{J_{21}\right\}& \Re \left\{J_{22}\right\}& -\Im \left\{J_{22}\right\}\\ \Im \left\{J_{21}\right\}& \Re \left\{J_{21}\right\}& \Im \left\{J_{22}\right\}& \Re \left\{J_{22}\right\}\end{array}\right]\left[\begin{array}{c}{e}_{txi}\\ e_{txq}\\ e_{tyi}\\ e_{tyq}\end{array}\right]$$

By writing J as a real matrix in this way, the real and imaginary parts of each of the four elements of J are used twice. However, if a real ICA algorithm is used to estimate the 16-element blend matrix, there would be 16 degrees of freedom in the estimate, and the pairs of coefficients that should be numerically equal to each other need only be approximately equal to each other, for example due to additional noise. Therefore, in embodiments, when a matrix, such as the 4x4 matrix discussed above, is interpreted as a Jones matrix that has less, in this case four, degrees of freedom, two averaging steps may be performed to obtain the benefits of averaging , For example, the first step may yield a complex 2x2 matrix based on the 16 values in the 4x4 matrix; and the second step may result in a complex unitary matrix based on the complex - eg 2x2 - matrix.

In embodiments, the first step may provide an estimate of J given by the following expression: $$\widehat{J}=\frac{1}{2}\left[\begin{array}{cc}\left(M_{11}+M_{22}\right)+j\left(M_{21}-M_{12}\right)& \left(M_{13}+M_{24}\right)+j\left(M_{23}-M_{14}\right)\\ \left(M_{31}+M_{42}\right)+j\left(M_{41}-M_{32}\right)& \left(M_{33}+M_{44}\right)+j\left(M_{43}-M_{34}\right)\end{array}\right]$$

However, this expression may only be valid if the 4x4 blending matrix has not permuted the imaginary part of the Y polarization with the imaginary part of the X polarization or the real part of the Y polarization with the imaginary part of the X polarization.

In other words, the rows 1 and 2 should belong to the same complex number before doing this kind of averaging. In embodiments, a maximum of one pair of rows may need to be exchanged to meet this criterion. The row leading to row 1 may, using a permuted and selectively negated version of the first row as a predicted value for the second row and finding the most exact match of the candidate rows 2 . 3 and 4 being found.

wobei der hochgestellte Strich eine Konjugiert-transponierte anzeigt und ${(\cdot )}^{-\frac{1}{2}}$

das Invers der Quadratwurzel der Matrix anzeigt.In embodiments, the second step involves forcing the matrix to be unitary. If Ĵ is invertible, then the nearest unitary matrix is J $$\widehat{J_u}={\left(\widehat{J},\widehat{J}\text{'}\right)}^{-\frac{1}{2}}\widehat{J}$$

wherein the superscript indicates a conjugate transposed and ${(\cdot )}^{-\frac{1}{2}}$

the inverse indicates the square root of the matrix.

zu einer unitären Matrix, die vorteilhafterweise die Anzahl von Freiheitsgraden auf - in diesem Fall - vier reduziert, was die Rauschminderung unterstützt.In embodiments, the expression for $\widehat{J_u}$

to a unitary matrix that advantageously reduces the number of degrees of freedom to-in this case-four, which supports noise reduction.

It should be noted that although the polarization rotation of the fiber installation can be expressed as a unitary matrix, some implementation impairments in the optical front-end may not be unitary. For example, finite extinction ratios in a polarization beam splitter or polarization dependent losses can lead to a nonunit transfer matrix. Depending on the magnitude of these impairments, forcing the demixing matrix to be unitary may make the estimation worse than if this step were omitted. Consequently, this step should be applied in systems where the unitary approximation remains within acceptable fault tolerance.

6 FIG. 10 is a flowchart for coherently combining two receiver branches with initially unknown relative phase according to various embodiments of the present disclosure. FIG. For example, in embodiments, the method may be implemented by a receiver whose architecture is similar to that found in FIG 4 is shown. The process 600 can at step 602 when four series vectors representing XI, XQ, YI and YQ receiver branch signals are vertically interlaced to form a 4xN matrix.

At step 604 a real-valued BSS is executed to obtain a 4x4 demixing matrix.

At step 606 will undo all row permutations that might have separated complex variables into non-contiguous rows (for example, using the correlation coefficient as a comparative measure after permuting and inverting the correct columns).

At step 608 a first estimate of the complex 2x2 demixing matrix is obtained, for example using the following averaging method: $$\widehat{J}=\frac{1}{2}\left[\begin{array}{cc}\left(M_{11}+M_{22}\right)+j\left(M_{21}-M_{12}\right)& \left(M_{13}+M_{24}\right)+j\left(M_{23}-M_{14}\right)\\ \left(M_{31}+M_{42}\right)+j\left(M_{41}-M_{32}\right)& \left(M_{33}+M_{44}\right)+j\left(M_{43}-M_{34}\right)\end{array}\right]$$

was eindeutig die nächstgelegene unitäre Matrix J bestimmt, wodurch die Qualität der Schätzung in Fällen verbessert wird, in denen die Beeinträchtigungen in der Faserinstallation und dem Empfänger nicht signifikant von unitären abweichen.At step 610 For example, a method may be used to force J to be unitary, for example, using $$\widehat{J_u}={\left(\widehat{J},\widehat{J}\text{'}\right)}^{-\frac{1}{2}}\widehat{J},$$

which uniquely determines the closest unitary matrix J, thereby improving the quality of the estimate in cases where the degradations in the fiber installation and the receiver do not differ significantly from unitary ones.

Application of a real FICA to a carrier phase estimation reconstruction for polarization diversity combining

As discussed above, in embodiments, various information may be sent in two orthogonal polarization modes of a fiber, and a BSS separation may be used to determine a blend matrix for the four branches of a receiver, for example, by looking at four real or two complex signal streams become.

In embodiments, if the same information is encoded on two orthogonal polarizations, coherently combining the orthogonal polarization branches of the receiver to implement polarization diversity may be used. In such cases, the only rotations that may need to be restored to allow a successful polarization diversity combination are the carrier phases. If we assume that the receiver's I and Q channels include independent information, in embodiments, an ICA on each pair of I and Q channels may be used to estimate rotations that substantially encode the real and imaginary components or completely independent. In embodiments, such carrier recovery techniques may be more suitable than other decision-directed methods for carrier recovery of 16-QAM or higher-order modulations that generally operate effectively only when the plurality of tentative decisions are correct.

7 FIG. 10 is a flowchart for coherently combining two receiver branches of initially unknown relative phase to implement polarization diversity according to various embodiments of the present disclosure. FIG. In embodiments, polarization diversity may be implemented, for example, by a receiver whose architecture resembles that found in US Pat 4 is shown. The process 700 can at step 702 begin when a real ICA is executed on a pair of signal buffers representing XI and XQ branches of a receiver.

At step 704 For example, a resulting 2x2 demixing matrix can be made orthogonal, for example, by adding or subtracting the conjugate, for example, according to the sign of the real part of its determinant.

At step 706 For example, the resulting demixing (ie phase-decrement) matrix can be applied to the XI and XQ branch signal buffers, for example, by matrix-multiplying the 2x2 demixing matrix with a 2xN matrix comprising XI and XQ signal buffers as respective matrix rows ,

At step 708 can the process 700 using another pair of signal buffers representing Yl and Yq branches of the receiver to step 702 to return. At this point, the two X and Y branches may have been carrier phase corrected if there is a relative 90 degree phase ambiguity.

At step 710 the argument of the complex dot product of the phase corrected X and Y signals can be calculated; and the resulting angle may be quantized to the nearest multiple of 90 degrees, for example, to resolve the remaining 90 degree phase ambiguity.

At step 712 can the step in 712 calculated 0, 90, 180, or 270 degree rotation, the Y polarization signal buffer can be applied to phase align it with the X polarization signal buffer.

At step 714 the phase-corrected X signal (at step 706 calculated) with the phase-corrected Y signal (at step 712 calculated).

At step 716 For example, the weights found by the standards of the mixed matrices for the X and Q branches can be used to adjust the gain of the two receiver branches to approximate a maximum ratio combination, thereby increasing the gain Signal-to-noise ratio (SNR) of the combined signal is optimized.

Application of Complex FICA to Blind Channel Estimation for Space Time Block Code (STBC) Encoded Diversity Transmitters

In embodiments, polarization diversity is obtained using an orthogonal block code in the transmitter. This allows the receiver block to be simplified to a single branch, making the optical front end much less cumbersome to implement. The resulting polarization specificity in the receiver can be compensated for by the ability of the transmitter to transmit in two orthogonal polarizations simultaneously, while ensuring that signals remain independent due to an orthogonal coding regime. 8th FIG. 4 is an illustrative block diagram of an exemplary optical receiver circuit that implements the reception of a transmit polarization diversity regime organized using a Space Time Block Coding (STBC) regime, according to various embodiments of the present disclosure.

As in 8th shown is the digital homodyne receiver 800 a dual polarization DQPSK receiver comprising a DSP based STBC transmit polarization diversity M-QAM receiver 860. Recipient 800 comprises a single polarization branch, for example the upper half of 8th which requires in embodiments a channel estimation given by h ₁ and h ₂ .

In embodiments, a conventional Orthogonal Frequency Division Multiplexing (OFDM) approach may be used. For simplicity, for a single-carrier approach, pairs of adjacent QAM symbols may be sent in a pair of orthogonal polarizations, followed by a conjugate and negated conjugate copy of the same pair of transposed symbols. An example of a coded block can be symbolically expressed as: $$\begin{array}{l}\begin{array}{ccc}X:& x_1& -x_1^{*}\\ Y:& x_2& x_1^{*}\end{array}\\ \begin{array}{cccc}& & \to & \\ & & \text{Time}& \end{array}\end{array}$$

wodurch die originalen Symbole unter Verwendung dieses Ausdrucks wiederhergestellt werden können. $$\left[\begin{array}{c}\widehat{x_1}\\ x_2\end{array}\right]={\left(H^{H}H\right)}^{-1}{H}^H\left[\begin{array}{c}{y}_1\\ y_2^{\ast }\end{array}\right]$$

wobei (H^HH)^-1H^H als das Pseudoinvers der Matrix H bekannt ist.In embodiments, complex channel tap estimates may be used in the receiver to determine a relationship between the transmitter's X-polarization reference frame and the receiver's polarization reference frame (h ₁ ) and the transmitter's Y-polarization reference frame to the receiver's polarization reference frame (h ₂ ) express. The coefficients h ₁ and h ₂ can be formed into a 2x2 matrix. $$H=\left[\begin{array}{cc}{H}_1& H_2\\ -H_2^{*}& -{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102019115473A1\_0015.png"\; state="\{\{state\}\}">H</figure-callout>}}_1^{*}\end{array}\right]$$

whereby the original symbols can be restored using this expression. $$\left[\begin{array}{c}\widehat{x_1}\\ x_2\end{array}\right]={\left(H^{H}H\right)}^{-1}{H}^H\left[\begin{array}{c}{y}_1\\ y_2^{*}\end{array}\right]$$

where (H ^H H) ^-1 H ^{H is known} as the pseudoinverse of the matrix H.

However, because the matrix H is unknown, H is estimated in embodiments using BSS techniques, for example, by forming, in a buffer, a complex 2xN matrix of mixed symbols, as follows: $$\left[\begin{array}{ccccc}{y}_1& y_3& y_5& & y_{2N-1}\\ & & & \cdots & \\ y_2^{*}& {\mathrm{<figure-callout\; id="4"\; label="y"\; filenames="DE102019115473A1\_0020.png"\; state="\{\{state\}\}">y</figure-callout>}}_4^{*}& y_6^{*}& & y_{2N}^{*}\end{array}\right]$$

In embodiments, an algorithm, for example an ICA algorithm, may then be used which uses the 2xN matrix as input data to find a segregation matrix D, for example a 2x2 matrix. In embodiments, the estimation quality of D can be improved by forcing D to be unitary, for example, by any suitable method previously described.

In embodiments, it is assumed that the segregation matrix D is a useful approximation of the pseudoinverse of the matrix H (ie D ≅ (H ^H H) ^-1 H ^H ), such that D is in the place of (H ^H H) ^-1 H ^H can be set to estimate the separated symbols in their original state, for example according to the expression $$\left[\begin{array}{ccccc}{x}_1& x_3& \widehat{x_5}& & x_{2N-1}\\ & & & \cdots & \\ x_2& x_4& x_6& & x_{2N}\end{array}\right]=D\left[\begin{array}{ccccc}{y}_1& y_3& y_5& & y_{2N-1}\\ & & & \cdots & \\ y_2^{*}& {\mathrm{<figure-callout\; id="4"\; label="y"\; filenames="DE102019115473A1\_0020.png"\; state="\{\{state\}\}">y</figure-callout>}}_4^{*}& y_6^{*}& & y_{2N}^{*}\end{array}\right]$$

Since the resulting symbols may be subject to a rotation multiple uncertainty of an integer multiple of 90 degrees (ie 90, 180, 270), in embodiments such uncertainty may be resolved using any method known to those skilled in the art, such as continuous pilot tones or a preamble which can form a convenient external reference, for example to a zero phase.

9 FIG. 10 is a flowchart of an illustrative channel estimation process for STBC encoded diversity transmitters according to various embodiments of the present disclosure. In embodiments, a process 900 that supports getting estimates of original symbols, implemented, for example, by a receiver whose architecture resembles that in 8th is shown. The process 900 in 9 can at step 902 when using a set of sample-and-hold and ADC circuits in a receiver, for example at the Nyquist rate (one sample per symbol), start a number of samples from the XI and XQ branches of a receiver and the samples are accumulated in a set of memory buffers. It will be understood by those skilled in the art that scans may be detected simultaneously.

At step 904 it can be determined if the XI and XQ buffers are filled with valid symbols. If so, so can the process 900 with step 906 when the odd-numbered symbols in the first row of a 2xN matrix of mixed symbols can be arranged and the conjugate values of the even-numbered symbols in the second row can be arranged.

At step 908 For example, an ICA method using the 2xN matrix of mixed symbols as input data may be used to estimate a demixing matrix D. In embodiments, a real or complex valued ICA may be used according to preference using any of the methods previously described.

zu bilden.At step 910 For example, the estimated demixing matrix D may be applied to the 2xN matrix of mixed symbols, for example, using matrix multiplication $$\left[\begin{array}{ccccc}{x}_1& x_3& \widehat{x_5}& & x_{2N-1}\\ & & & \cdots & \\ x_2& x_4& x_6& & x_{2N}\end{array}\right]=D\left[\begin{array}{ccccc}{y}_1& y_3& y_5& & y_{2N-1}\\ & & & \cdots & \\ y_2^{*}& {\mathrm{<figure-callout\; id="4"\; label="y"\; filenames="DE102019115473A1\_0020.png"\; state="\{\{state\}\}">y</figure-callout>}}_4^{*}& y_6^{*}& & y_{2N}^{*}\end{array}\right]$$

to build.

At step 912 For example, {x ₁ , x ₂ , x ₃ ..., x _2N } may be taken as the estimated transmitted symbols, and symbol slicing, forward error correction, etc. may be used according to the modulation type used. At this point, the process can 900 with step 904 be resumed.

It will be understood by those skilled in the art that the performance of the disclosed embodiments for carrier recovery and / or polarization correction may depend on the particular ICA method used.

Simulation of 16-QAM polarization correction and carrier recovery

10 - 15 show simulation results for various embodiments of the present disclosure. Implementations were simulated using two independent 16-QAM modulation streams, which were used with 12 Samples per symbol are sampled and use Bessel low pass filtering to perform 5th order Bessel pulse shaping. The results suggest that a baud rate of 50 Gbaud 400 Gbps / λ can provide.

10 shows a 16-QAM transmitter modulation vector diagram (with added noise).

11 shows simulated DP-16 QAM power spectra.

12 shows simulation results showing a scatter plot for a 16-QAM receiver that does not use polarization correction.

13 FIG. 12 shows simulation results illustrating a scattergram for a 16-QAM receiver using EFICA according to various embodiments of the present disclosure. FIG.

14 FIG. 10 shows simulation results illustrating a scattergram for a 16-QAM receiver using FicaCMPLX according to various embodiments of the present disclosure. FIG.

15 FIG. 12 shows simulation results illustrating a scattergram for a 16-QAM receiver using JADE according to various embodiments of the present disclosure. FIG.

All three methods, EFICA, FicaCMPLX and JADE, have been shown to resolve the polarization rotations. Like the scatterplots in 13 and 14 EFICA and FicaCMPLX correctly resolved the carrier phases while JADE did not, as did the simulation results in 15 can be seen. A comparison of 13 and 14 illustrates that EFICA delivered superior results compared to FicaCMPLX.

It should be noted that the general simulation results presented herein are by way of illustration only and have been carried out under specific conditions using specific embodiments. Accordingly, neither these simulations nor their results may be used to limit the scope of the disclosure of the present patent document.

System embodiments

Aspects of the present invention may be encoded on one or more non-transitory computer readable media having instructions for one or more processors or processing units to cause the execution of steps. It should be noted that the one or more non-transitory computer-readable media include both volatile and non-volatile memory. It should be noted that alternative implementations are possible, including hardware implementation or software / hardware implementation. Hardware-implemented functions may be implemented using one or more ASICs, programmable arrays, digital signal processing circuits, or the like. Accordingly, the "middle" terms in the claims are intended to encompass both software and hardware implementations. Similarly, the term "computer-readable medium or media" as used herein includes software and / or hardware on which a program is embodied with instructions, or a combination thereof. In light of these implementation alternatives, it should be understood that the figures and the related description provide the functional information necessary for a person skilled in the art to write program code (i.e., software) and / or make circuits (i.e., hardware) to perform the necessary processing.

It should be noted that embodiments of the present invention may further relate to computer products having a non-transitory, tangible computer-readable medium on which computer code resides to perform various computer-implemented operations. The media and computer code may be those that have been specifically designed and constructed for the purposes of the present invention, or they may be of the type known or available to those of ordinary skill in the art. Examples of tangible computer-readable media include, for example: magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROMs and holographic devices; magneto-optical media; and hardware devices that are specifically configured to store or store and execute program code, such as application specific integrated circuits (ASICs), programmable logic devices (PLDs), flash memory devices, and ROM and RAM devices. Examples of computer code include machine code, such as that created by a compiler, and files containing higher code that are executed by a computer using an interpreter. Embodiments of the present invention may be implemented in whole or in part as machine-executable instructions that may reside in program modules executed by a processing device. Examples of program modules include libraries, programs, routines, objects, components, and data structures. In distributed computing configurations, program modules may be physically located in environments that are local, remote, or both.

Those skilled in the art will recognize that no computing system and programming language are critical to the practice of the present invention. Those skilled in the art will also recognize that a number of the elements described above may be physically and / or functionally separated into submodules or combined with each other.

Those skilled in the art will appreciate that the foregoing examples and embodiments are exemplary and do not limit the scope of the present disclosure. It is intended that all permutations, extensions, equivalents, combinations, and improvements thereto that will become apparent to those skilled in the art upon reading the specification and the study of the drawings, be included within the true spirit and scope of the present disclosure. It should also be noted that elements of claims may be rearranged, including multiple dependencies, configurations, and combinations.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 62682599 [0001]

Claims (20)

Method for analog polarization control using blind source separation (BSS), the method comprising: Initializing a set of polarization control state variables; Using a set of sample-and-hold and ADC circuits in a receiver to obtain a number of samples of XI, XQ, YI and YQ branches of the receiver; Accumulating the samples in a set of memory buffers; Applying to the samples in the set of memory buffers, a complex ICA, to execute a BSS; Factoring a demixing matrix to obtain incremental angles; Adding the incremental angles to the set of polarization control state variables to obtain updated polarization control state variables; and Use the updated polarization control state variable to perform a polarization control. Method according to Claim 1 further comprising adjusting a segregation matrix to become unitary. Method according to Claim 1 or 2 wherein obtaining updated polarization state variables comprises obtaining updated carrier phase state variables. Method according to one of Claims 1 - 3 , further comprising: in response to receiving a first set of output signals having a first phase and a second set of output signals having a second phase, rotating to a first phase angle, the first phase of one or a plurality of signals in the first set of output signals relative to the second phase of one or more signals in the second set of output signals to generate a set of rotated signals; and rotating the set of rotated signals by a second phase angle to align the set of rotated signals with a polarization reference frame. Method according to Claim 4 wherein rotating the set of rotated signals reduces at least one component of the second set of output signals from the first set of output signals. Method according to Claim 4 or 5 wherein rotating the first phase comprises adjusting a gain defined by a set of trigonometric weights corresponding to the first and second phase angles. Method according to Claim 6 further comprising adjusting a polarity of the gain by adjusting relative transconductances of parallel differential amplifiers coupled in opposite polarities. Method according to Claim 6 or 7 further comprising adjusting gains of one or more amplifiers or dampers in a plurality of signal paths representing a complex number representation of the amplitude and phase of each polarization component. A dummy source separation (BSS) based analog polarization and carrier phase control system, the control system comprising: a polarization controller in a receiver; ADW circuits coupled to the polarization controller; Sample-and-hold circuits coupled to the ADC circuits, the sample-and-hold and ADC circuits simultaneously detecting a number of samples of XI, XQ, YI, and YQ branches of the receiver ; a set of memory buffers coupled to the sample and hold circuits for accumulating samples, the polarization controller performing steps including: initializing a set of polarization control state variables and a set of carrier phase state variables; Applying to the samples in the set of memory buffers, a complex ICA, to execute a BSS; Factoring a demixing matrix to obtain incremental angles; Adding the incremental angles to the set of polarization control state variables to obtain updated polarization control state variables; and using the updated polarization control state variable to perform a polarization control. Control system after Claim 9 further comprising adjusting a segregation matrix to become unitary. Control system after Claim 9 or 10 , which further comprises an analog polarization control circuit using amplifiers having variable gain using trigonometric weights. Control system after Claim 11 wherein the analog polarization control circuit executes in response to receiving a first set of polarization signals having a first phase and a second set of polarization signals having a second phase: rotating, by a first phase angle, the first phase of one or a plurality of signals in the first set of polarization signals relative to the second phase of one or more signals in the second set of polarization signals to generate a set of rotated signals; and rotating the set of rotated signals by a second phase angle to align the set of rotated signals with a polarization reference frame. Control system after Claim 12 wherein the analog polarization control circuit rotates the set of rotated signals about the second phase angle to align the set of rotated signals with a polarization reference frame. Control system after Claim 12 or 13 wherein the set of rotated signals compensates for polarization rotation of at least one component of the first set of polarization signals relative to the second set of polarization signals. A method of coherently combining two receiver branches of initially unknown relative phase, the method comprising: vertically concatenating four row vectors representing XI, XQ, YI and YQ receiver branch signals to form a 4xN matrix; Performing a real-valued blind source separation (BSS) to obtain a 4x4 demixing matrix; Inverting row permutations that separate complex variables into non-adjacent rows; and Obtain a first estimate of a complex 2x2 segregation matrix. Method according to Claim 15 further comprising adjusting a segregation matrix to become unitary. Method according to Claim 15 or 16 in which the first estimate of the complex 2x2 demixing matrix is obtained using an averaging method. Method according to one of Claims 15 - 17 wherein executing the real-valued BSS comprises: initializing a set of polarization control state variables; Using a set of sample-and-hold and ADC circuits in a receiver to obtain a number of samples of XI, XQ, YI and YQ branches of the receiver; Accumulating the samples in a set of memory buffers; Applying to the samples in the set of memory buffers, a complex ICA, to execute a BSS; Factoring a demixing matrix to obtain incremental angles; Adding the incremental angles to the set of polarization control state variables to obtain updated polarization control state variables; and using the updated polarization control state variable to perform a polarization control. Method according to Claim 18 wherein obtaining updated polarization state variables comprises obtaining updated carrier phase state variables. Method according to Claim 18 or 19 , further comprising: in response to receiving a first set of output signals having a first phase and a second set of output signals having a second phase, rotating to a first phase angle, the first phase of one or a plurality of signals in the first set of output signals relative to the second phase of one or more signals in the second set of output signals to generate a set of rotated signals; and rotating the set of rotated signals by a second phase angle to align the set of rotated signals with a polarization reference frame.

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