Method for receiving multiple digital signals in an optical digital communication system

Abstract

A method for receiving a plurality of digital signals in an optical digital communication system using a plurality of channels for transmitting the plurality of digital signals, the method comprising: - receiving the plurality of digital signals each after an analog-to-digital converter (ADC), wherein each of the plurality of received digital signals comprises a stream of zero-mean bipolar pulse-shaped baseband and oversampled digital complex-valued or real-valued samples, and wherein each of the plurality of received digital signals also includes a cross-channel interference (CCI) component, - jointly processing each pair of received digital signals from each pair of channels to provide an estimation and cancellation of the cross-channel interference (CCI) components,wherein each pair is defined as any combination without repetition of the received digital signals of two channels from the plurality of digital signals from the plurality of channels, - wherein the processing further comprises estimating a cross-factor for each pair of received digital signals, - wherein the processing further comprises estimating each interference component using the estimated cross-factor and subtracting each estimated interference component from the corresponding received signal.,

Description

[0001] The present invention relates to a method for receiving a plurality of digital signals comprising a plurality of independent streams of zero-mean bipolar pulse-shaped baseband and oversampled digital complex-valued or real-valued samples in an optical digital communication system using a plurality of channels for transmitting the plurality of digital signals.

[0002] The state of the art in optical digital communication systems with cross-channel interference (CCI) includes the following points that summarize their functionality.

[0003] The system has an optical multi-channel transmitter or alternatively several single-channel transmitters. - The system consists of a multi-channel receiver. - The system is a one-way connection. - The transmitter transmits data simultaneously over multiple optical channels. The multi-channel transmitter or multiple single-channel transmitters use independent processing chains for the different channels. - The receiver receives data on multiple channels simultaneously. The receiver uses independent processing chains for the multiple channels. - The receiver in the system introduces additive white Gaussian noise (AWGN). - The receiver performs adaptive coding and modulation (ACM) to adapt the transmission rates to the CCI and channel conditions. - The CCI and the AWGN reduce the probability of successful detection of the received signal, so that bit errors occur.

[0004] Existing solutions for CCI suppression in multi-channel optical digital communication systems in the digital electronics of the receiver are based on an adaptive filter architecture with access to the signals on the multiple channels. An example of such a solution is disclosed in [1], which describes a two-channel optical system. The adaptive filters for the intended and interfering channels are trained to generate signals for interference cancellation. The training of the filter coefficients of such solutions is either decision-driven or data-driven using known pilot signals.

[0005] An alternative approach to CCI cancellation in multi-channel optical digital communication systems is blind analog interference cancellation in the optical domain, accessing the signals on the multiple channels and combining the optical signals to mitigate the interference [2][3]. This approach is implemented by optical devices in front of the digital electronics of the receiver.

[0006] The CCI compensation method in this patent, referred to as CCI Correlation Learning Estimation and Adaptive Reduction (CCI-CLEAR), is implemented in the receiver's digital electronics and is applied to the oversampled samples of the signals of both polarizations directly after the analog-to-digital converter (ADC) stages. It exploits the correlation between the received signal pairs for adaptive estimation and suppression of the CCI and is therefore structurally different from approaches based on adaptive filtering or analog interference cancellation in the optical domain. The CCI-CLEAR method is completely blind, transparent, and signal-independent. It is non-decision-oriented and non-data-driven. It has low complexity and is therefore suitable for high-speed applications.A related approach to suppressing cross-polarization interference in radio frequency (RF) communications is described in [4] and implemented in a dual-polarization satellite receiver. In contrast, the present patent describes the CCI-CLEAR approach, which introduces the necessary modifications to make the method applicable to multi-channel optical communications.

[0007] Simultaneous transmission on multiple optical channels significantly increases the data throughput of optical communication systems. However, the increased CCI between channels reduces the signal-to-noise and interference ratio (SNIR) at the receiver and degrades decoder performance. State-of-the-art communication systems use ACM to adapt the modulation format to SNIR conditions. However, a high CCI is a limiting factor for the application of higher-order modulation formats and thus for data throughput.

[0008] Existing solutions for CCI cancellation are either implemented in the receiver's digital electronics and based on an adaptive filter architecture with access to the signals on the multiple channels, or they are based on analog interference cancellation in the optical domain, implemented in optical devices upstream of the receiver's digital electronics. While these approaches reduce CCI, they also increase receiver complexity. Adaptive filters are trained for multiple coefficients, which can be a limitation for implementation in high-speed hardware devices and applications. While analog interference cancellation in the optical domain has been proven to enable high data rates, the required additional optical devices increase receiver complexity and cost.

[0009] DE 10 2022 104 457 A1 describes a method for receiving two digital signals in a digital dual polarization transmission system.

[0010] US 2018 / 0019905 A1 describes a method for interference cancellation, comprising: calculating a mean and a variance value of a received signal to obtain statistical information of the received signal; calculating an estimated log-likelihood ratio using the statistical information of the received signal; calculating a decoding log-likelihood ratio of the received signal using the estimated log-likelihood ratio of the received signal and performing calculations to update the statistical information of the received signal; repeating the above steps for a predetermined number of times, performing hard decisions on the decoding log-likelihood ratios of the received signal, and outputting data bits obtained from the hard decision.

[0011] It is an object of the present invention to provide a novel digital CCI compensation method, referred to as CCI-CLEAR, comprising an improved digital multi-channel receiver. This non-data-driven and non-decision-oriented method adaptively estimates the CCI and performs CCI suppression transparently, as it has access to the signals on the multiple channels. It has low complexity and is therefore suitable for high-speed applications. This increases the SNIR at the receiver decoder and improves the achievable data rates.

[0012] To achieve the object, the present invention provides a method for receiving a plurality of digital signals comprising a plurality of independent streams of zero-mean bipolar pulse-shaped baseband and oversampled digital complex-valued or real-valued samples in an optical digital communication system using a plurality of channels for transmitting the plurality of digital signals, the method comprising - Received digital signals of the plurality of each after an ADC, wherein each of the plurality of received digital signals comprises a stream of zero-mean bipolar pulse-shaped baseband and oversampled digital complex-valued or real-valued samples, and wherein each of the plurality of received digital signals also includes a CCI component, - jointly processing each pair of received digital signals from each pair of channels to provide an estimation and suppression of the CCI components, wherein each pair is defined as any combination without repetition of the received digital signals from two channels from the plurality of digital signals from the plurality of channels, - wherein the processing further comprises estimating a cross factor for each pair of received digital signals, - wherein the processing further comprises estimating each interference component using the estimated cross factor and subtracting each estimated interference component from the corresponding received signal, - wherein the processing further comprises buffering the received samples of the received digital signals of each pair of received digital signals to construct first and second vectors of consecutive samples of the received digital signals, respectively, the two vectors having the same even length (N), the length (N) being the number of consecutive samples, the consecutive samples being the elements of the vectors, - wherein the step of estimating the cross factor further comprises inputting the oversampling factor used during sampling of the plurality of received signals, and the cross factor is used to calculate the sampling correction factor by interpolation or extrapolation with a lookup table (LUT sampling) in Table 1 of the specification, and - wherein the step of estimating the cross factor further comprises the following steps: - generating D1+1 first vector variants from the elements of the first vector, where for each first vector variant d1 samples are removed at the beginning and d1 zeros are added at the end, where the number d1 is any number between 0 and D1, including 0 and D1, where D1 is a non-negative integer, - Calculating the arithmetic mean of the element-wise multiplication between the elements of the first vector variants and the complex conjugate of the elements of the second vector, - generating D2+1 second vector variants from the elements of the second vector, where for each second vector variant d2 samples are removed at the beginning and d2 zeros are added at the end, where the number d2 is any number between 0 and D2, including 0 and D2, where D2 is a non-negative integer, - Calculating the arithmetic mean of the element-wise multiplication between the elements of the second vector variants and the complex conjugate of the elements of the first vector, - Selecting the arithmetic mean with the maximum squared absolute value and determining the corresponding number d1 or d2 as the optimal number d1 or d2 at which the maximum occurs, - Using the first vector to calculate the arithmetic mean of the element-wise multiplication between its odd-index elements and the complex conjugate of its even-index elements, - Using the second vector to calculate the arithmetic mean of the element-wise multiplication between its odd-index elements and the complex conjugate of its even-index elements, - Taking the real value of the results of the last two arithmetic mean operations, including the odd and even elements of each vector, multiplying each of these elements by the sampling correction factor, and adding the results, - Calculating the inverse of the result of the latter addition using a lookup table (LUT inverse) of the inverse function, where the inverse function is defined as 1 divided by the argument of the function, and multiplying by the selected arithmetic mean with maximum squared absolute value, and - Taking the real and imaginary values ​​of the result of the latter multiplication, applying a lookup table (LUT function) for the function in equation (1) of the specification to each of these elements, and combining the two results to form a complex-valued number which is the estimate of the cross factor.

[0013] In a preferred variant of the present invention, the method is applicable in a multi-channel receiving device for any digital communication system for both forward and return links.

[0014] According to yet another aspect of the invention, the step of estimating each cross-channel interference component and subtracting it from the corresponding received signal comprises the following steps: - if the optimal number d1 is greater than or equal to 0, multiplying the estimate of the cross factor by the samples of the second vector, in which d1 samples are removed at the beginning and d1 zeros are added at the end, and subtracting the result element-wise from the samples of the first vector, thereby generating the improved received samples of the first channel of the current pair of processed channels, - if the optimal number d1 is greater than or equal to 0, multiplying the conjugate estimate of the cross factor by the samples of the first vector, with d1 samples removed at the end and d1 zeros added at the beginning, and subtracting the result element-wise from the samples of the second vector, thereby generating the improved received samples of the second channel of the current pair of processed channels, - if the optimal number d2 is greater than or equal to 0, multiplying the estimate of the cross factor by the samples of the second vector, in which d2 samples are removed at the end and d2 zeros are added at the beginning, and subtracting the result element-wise from the samples of the first vector, thereby generating the improved received samples of the first channel of the current pair of processed channels, - if the optimal number d2 is greater than or equal to 0, multiplying the conjugate estimate of the cross factor by the samples of the first vector, removing d2 samples at the beginning and adding d2 zeros at the end, and subtracting the result element-wise from the samples of the second vector, thereby generating the improved received samples of the second channel of the current pair of processed channels, and - Repeating this step of estimating each cross-channel interference component and subtracting it from the corresponding received signal for each pair of received digital signals from each pair of channels.

[0015] In the following, the present invention will be described in detail with reference to the drawings, in which: Fig.1 shows a block diagram of a multi-channel optical digital communication system with cross-channel interference, Fig. Figure 2 shows a block diagram of the multi-channel optical digital receiver device implementing the CCI-CLEAR method, Fig. 3 shows a block diagram of the CCI-CLEAR process, Fig. 4 shows the sampling correlation factor as a function of the oversampling factor, Fig. Figure 5 shows a comparison of standard and enhanced receivers for cross-channel discrimination (CCD) values ​​of 10, 15 and 20 dB, and Fig. Figure 6 shows a comparison of standard and improved receivers for a CCD of 10 dB and phase angles of 15, 30 and 45 degrees.

[0016] The block diagram of a multi-channel optical digital communication system with CCI is shown in Fig.1. This block diagram can be considered representative of optical commercial digital communication systems in which data is transmitted over multiple channels. Illustrative examples of such communication systems are fiber optic communication, free-space optical communication (FSO), and wireless optical communication (OWC), which use multiple optical polarizations with coherent demodulation or multiple wavelengths with intensity modulation and direct detection (IM / DD). In addition, Fig. 1 describes both the forward and return connections.

[0017] At the transmitter, the data bits on the multiple channels are encoded using a forward error correction (FEC) code to provide protection against channel impairments in the system. The encoded bits are mapped to symbols of a given constellation according to a modulation format such as quadrature amplitude modulation (QAM) with coherent demodulation or multilevel pulse amplitude modulation (PAM) with IM / DD. The symbols are framed according to a given transmission standard. Each signal is then pulse-shaped using a filter such as a square root raised cosine filter (SRRCF). Each signal is then passed through a digital-to-analog converter (DAC), and after electrical-to-optical (E / O) conversion via a light-emitting diode (LED) or a laser diode (LD), the signals are transmitted over the optical channel.

[0018] Each transmitted signal is routed through an optical channel with CCI. The received digital signal after optical-to-electrical (O / E) conversion may therefore contain interference from other channels that can cross each other and cause amplitude, phase, frequency, timing, and memory effects.

[0019] At the receiver, the signals on each optical channel are received by a photodiode (PD), where they are O / E converted, any direct current (DC) bias is removed, and AWGN is introduced. Next, each signal is passed through an ADC, where each signal is oversampled. After synchronization, a matched SRRCF is applied. After downsampling to the symbol rate, the received symbols are generated, which are then demapped and decoded to obtain the received bits.

[0020] The present invention relates to a novel digital CCI compensation method, referred to as CCI-CLEAR, and is described as part of an improved digital multi-channel receiver that simultaneously processes the data transmitted in the various channels. With access to the signals in the channels, the CCI-CLEAR method adaptively estimates the CCI and performs CCI suppression. This increases the SNIR at the receiver decoder and improves the achievable data rates.

[0021] The following describes a new optical digital multi-channel receiver that implements the new CCI-CLEAR compensation method. The block diagram of this receiver is shown in Fig.2. The signals on each channel are received by a PD, any DC bias is removed, and AWGN is introduced during the O / E conversion. Each signal is passed through an ADC, where each signal is oversampled. Since the CCI-CLEAR block has local access to the signals on the multiple channels, the oversampled signals are input after the ADC stages. The ADCs are assumed to be driven by synchronous sampling clocks, which is readily possible due to the colocation of the digital processing electronics, and sampling rates greater than or equal to the Nyquist rate are required, which is a common premise in communications systems. The CCI-CLEAR block performs CCI estimation and cancellation transparently by simultaneously using the signal samples on each pair of optical channels.The processed signal samples are output and fed to the subsequent receiver stages, each preserving all structural signal properties. In the following blocks, the signals from the multiple channels undergo synchronization, matched filtering, subsampling, demapping, and decoding to generate the received data bits.

[0022] The block diagram of the CCI-CLEAR process is shown in Fig.3. The CCI-CLEAR block takes as input the samples of the oversampled signals from the multiple channels. Without loss of generality, zero-mean bipolar complex-valued signals are implied throughout the description, unless otherwise stated, and the separation into in-phase (I) and quadrature (Q) components is considered straightforward. This applies to a setup with multi-laser polarization transmission and coherent demodulation. For a setup with multi-optical wavelength transmission and IM / DD, zero-mean bipolar real-valued signals are implied. No prior knowledge of the power level or step scaling for the various signals is required. In addition, the oversampling factor used in all ADCs is also provided as input. It is a real-valued number greater than or equal to 2 and is used to calculate a sampling correction factor.For a TDM transmission with SRRCF pulse shaping with roll-off factors between 5% and 35%, the sampling correction factor depends on the oversampling factor in . Fig.4, and the values ​​for the corresponding sampling lookup table (LUT) are listed in Table 1. The sampling correction factor is a real-valued number greater than or equal to 1 and converges to 1 for very large oversampling factors. In general, a LUT can be used in digital electronics to achieve a high-speed implementation of a function. The pairs of values ​​in the LUT can be used to calculate the output for a given input according to the nearest input-output pair or by interpolation and extrapolation, e.g., linear, quadratic, etc. The size of the LUT and the granularity of the quantization, as well as the use of interpolation / extrapolation, determine the trade-off between numerical accuracy and processing speed. Table 1 - LUT for the values ​​of the sampling correction factor depending on the oversampling factor. Oversampling factor Sampling correction factor Oversampling factor Sampling correction factor Oversampling factor Sampling correction factor 2 1,5885 4 1,1138 6 1,0488 2,1 1,5153 4,1 1,1079 6,1 1,0469 2,2 1,4562 4,2 1,1025 6,2 1,0453 2,3 1,4068 4,3 1,0975 6,3 1,0438 2,4 1,3667 4,4 1,0928 6,4 1,0425 2,5 1,3309 4,5 1,0885 6,5 1,0411 2,6 1,3009 4,6 1,0845 6,6 1,0399 2,7 1,2750 4,7 1,0807 6,7 1,0386 2,8 1,2525 4,8 1,0774 6,8 1,0375 2,9 1,2328 4,9 1,0739 6,9 1,0364 3 1,2153 5 1,0709 7 1,0353 3,1 1,1997 5,1 1,0680 7,1 1,0343 3,2 1,1858 5,2 1,0653 7,2 1,0334 3,3 1,1734 5,3 1,0627 7,3 1,0324 3,4 1,1624 5,4 1,0603 7,4 1,0315 3,5 1,1522 5,5 1,0581 7,5 1,0307 3,6 1,1434 5,6 1,0559 7,6 1,0298 3,7 1,1349 5,7 1,0539 7,7 1,0291 3,8 1,1272 5,8 1,0520 7,8 1,0283 3,9 1,1202 5,9 1,0502 7,9 1,0276 8 1,0269

[0023] The estimation and suppression of the CCI is performed for each pair i of received signals, where i = 1, ..., K! / (2*(K-2)!), where K is the total number of channels. Each signal of the two channels of each pair i is respectively buffered to form two vectors of consecutive samples, y1 and y2, of length N, an even number indexed from 1 to N. The elements of the two vectors are used to calculate the arithmetic mean of the element-wise multiplication between the elements of the first vector, y1, and the complex conjugate of the elements of the second vector, conj(y2), for a number of delayed variants of the first vector by d1 samples, where d1 = 0, ..., D1.The elements of the two vectors are also used to calculate the arithmetic mean of the element-wise multiplication between the elements of the second vector, y2, and the complex conjugate of the elements of the first vector, conj(y1), for a number of delayed variants of the first vector by d2 samples, where d2 = 0, ..., D2. From all resulting arithmetic means, the arithmetic mean with the maximum squared absolute value is selected, also determining the corresponding optimal delays d1 or d2 for which the maximum occurs.

[0024] In addition, the elements of the first vector, y1, are also used to calculate the arithmetic mean of the element-wise multiplication between its elements with odd index, y 1,odd , and the complex conjugate of its elements with even index, conj(y 1,even), is used. The elements of the second vector, y2, are also used to calculate the arithmetic mean of the element-wise multiplication between its odd-index elements, y 2,odd , and the complex conjugate of its elements with even index, conj(y 2,even ). The real parts of these two arithmetic means, which include the odd and even elements of each vector, are taken, then multiplied by the sampling correction factor and added. The result of the addition is passed through a LUT for the inverse function f(x) = 1 / x and then multiplied by the selected arithmetic mean with maximum squared absolute value. The real and imaginary parts of the result are passed separately through a LUT for the function: f(x)=Real{1−1−4x22x}.

[0025] The two results are then combined to form a complex-valued number, which represents the estimate of the cross factor of the CCI.

[0026] Next, the CCI is estimated and suppressed. If d1 is greater than or equal to 0, the cross factor is multiplied by the samples of the second vector, y2, removing d1 samples at the beginning and adding d1 zeros at the end, and the result is subtracted element by element from the samples in the first vector, y1. The factor is also conjugated, then multiplied by the samples of the first vector, y1, removing d1 samples at the end and adding d1 zeros at the beginning, and the result is subtracted element by element from the samples of the second vector, y2.

[0027] If d2 is greater than or equal to 0, the cross factor is multiplied by the samples of the second vector, y2, removing d2 samples at the end and adding d2 zeros at the beginning, and the result is subtracted element by element from the samples in the first vector, y1. The factor is also conjugated, then multiplied by the samples of the first vector, y1, removing d2 samples at the beginning and adding d2 zeros at the end, and the result is subtracted element by element from the samples of the second vector, y2.

[0028] As a result, the two enhanced channels of pair i are generated. The process is repeated for all pairs of channels, and all enhanced channels are provided as the output of the CCI-CLEAR block.

[0029] The performance advantages of the CCI-CLEAR method and the improved receiver in this invention were evaluated using a Monte Carlo simulation of a two-channel optical transmission on two polarizations of a laser diode with coherent demodulation. A signal waveform consisting of 1,000,000 16-QAM symbols using TDM with a signal rolloff of 20% and an oversampling factor of 4 is transmitted over each of the two channels. For the application of the CCI-CLEAR method, the vector length is set to N = 500.

[0030] The performance of the improved receiver with the CCI-CLEAR technique is compared with a standard receiver without CCI-CLEAR for real-valued cross factors with CCD values ​​of 10, 15, and 20 dB. The carrier-to-interference ratio C / I and the carrier-to-noise-to-interference ratio C / (N+I) for the received constellation are shown in Fig.5 depending on the ratio between the energy per symbol and the spectral noise power density E s / N0. It should be noted that tests with higher-order modulations up to 64-QAM resulted in very similar performance curves, as the CCI-CLEAR method is agnostic to the modulation format used. In the presented scenario, similar performance is observed on both channels. The deterioration of the C / I for E s / N0 values ​​below about 6 dB lead to only a slight deterioration of the C / (N+I), while the improvement of the C / I for E s / N0 values ​​above approximately 6 dB lead to a significant improvement in C / (N+I). Since C / (N+I) is the metric that determines the receiver's bit error rate (BER) for the received constellation, the resulting degradation for C / (N+I) values ​​below 5 dB is less than 1 dB for a very low CCD of 10 dB and negligible for practical CCD values ​​above 15 dB, while the improvements for C / (N+I) values ​​above 5 dB are substantial, amounting to up to 12.7 dB in the presented scenario. The results justify the suitability of the CCI-CLEAR method for application with ACM and higher-order modulation. The C / I gains in the mid-range E s / N0 of 14 dB are 7.8, 7.1, and 4.5 dB for XPD values ​​of 10, 15, and 20 dB, respectively. These increase to 15.3, 11.4, and 6.7 dB at higher E s / N0 of 26 dB. The C / (N+I) gains in the mid-range E s / N0 of 14 dB are 3.9, 1.9 and 0.6 dB. These increase to 12.7, 8.5 and 4.3 dB at higher Es / N0 of 26 dB.

[0031] The performance of the improved receiver with the CCI-CLEAR technique is compared to a standard receiver without CCI-CLEAR for complex-valued cross factors with a practical CCD of 15 dB and phase angles of 15, 30, and 45 degrees to evaluate the impact of phase rotation effects. A phase angle of 45 degrees represents the worst case. The C / I ratio and the C / (N+I) ratio at the received constellation are shown in Fig. 6 depending on the E s / N0 ratio. In the presented scenario, similar performance is observed on both channels. While this setup has no effect on the standard receiver, it does show a dependence of the performance of the CCI-CLEAR method on the phase angle of the cross factor. The C / I gains in the mid-range E s / N0 of 14 dB are 5.8, 3.7, and 1.8 dB for a CDD of 15 dB and phase angles of 15, 30, and 45 degrees, respectively. These increase to 8.4, 4.8, and 2.3 dB at higher E s / N0 of 26 dB. The C / (N+I) gains in the mid-range E s / N0 of 14 dB are 1.7, 1.3 and 0.7 dB. These increase to 6.8, 4.2 and 2.1 dB at higher E s / N0 of 26 dB.

[0032] The CCI-CLEAR method and improved receiving apparatus described in this patent can be used in commercial optical digital communication systems where data is transmitted over multiple channels. Illustrative examples of such communication systems are fiber optic communication, FSO communication, and OWC, which use multiple optical polarizations with coherent demodulation or multiple wavelengths with IM / DD. Furthermore, it can be applied in both the forward and reverse links. This non-data-driven and non-decision-oriented method adaptively estimates the CCI and performs CCI suppression transparently, as it has access to the signals on the multiple channels. It has low complexity and is therefore suitable for high-speed applications. As shown, the CCI-CLEAR method reduces the CCI and increases the SNIR at the receiver decoder.This improves the achievable data rates, resulting in higher throughput and lower costs per transmitted bit. REFERENCES [1] J. Mitra, M. Jana, H.-JL Lampe, J. Wang, C. Li, System and Method for Interference Cancellation in Optical Transmission, WO 2023 / 284617 A1, 2023. [2] M. Lu, M. Chang, Y. Deng, PR Prucnal, Performance Comparison of Optical Interference Cancellation System Architectures, Applied Optics, Vol. 52, No. 11, pp. 2484-2493, April 2013. [3] JC Lederman, W Zhang, TF de Lima, EC Blow, S Bilodeau, BJ Shastri, PR Prucnal, Real-Time Photonic Blind Interference Cancellation, Nature Communications, Vol. 14, No. 8197, December 2023. [4] S. Dimitrov, Method for Receiving Two Digital Signals in a Dual-Polarization Digital Communication System, WO 2023 / 161084 A1, 2023.

Claims

[1] A method for receiving a plurality of digital signals comprising a plurality of independent streams of zero-mean bipolar pulse-shaped baseband and oversampled digital complex-valued or real-valued samples in an optical digital communication system using a plurality of channels for transmitting the plurality of digital signals, the method comprising - receiving the plurality of digital signals each after an analog-to-digital converter (ADC), wherein each of the plurality of received digital signals comprises a stream of zero-mean bipolar pulse-shaped baseband and oversampled digital complex-valued or real-valued samples, and wherein each of the plurality of received digital signals also includes a cross-channel interference (CCI) component, - jointly processing each pair of received digital signals from each pair of channels to provide an estimation and cancellation of the cross-channel interference (CCI) components, wherein each pair is defined as any combination without repetition of the received digital signals from two channels from the plurality of digital signals from the plurality of channels, - wherein the processing further comprises estimating a cross factor for each pair of received digital signals, - wherein the processing further comprises estimating each interference component using the estimated cross factor and subtracting each estimated interference component from the corresponding received signal, - wherein the processing further comprises buffering the received samples of the received digital signals of each pair of received digital signals to construct first and second vectors of consecutive samples of the received digital signals, respectively, the two vectors having the same even length (N), the length (N) being the number of consecutive samples, the consecutive samples being the elements of the vectors, - wherein the step of estimating the cross factor further comprises inputting the oversampling factor used during sampling of the plurality of received signals, and the oversampling factor is used to calculate the sampling correction factor by interpolation or extrapolation with a lookup table (LUT sampling) in Table 1 of the specification, and - wherein the step of estimating the cross factor further comprises the following steps: - generating D1+1 first vector variants from the elements of the first vector, where for each first vector variant d1 samples are removed at the beginning and d1 zeros are added at the end, where the number d1 is any number between 0 and D2, including 0 and D2, where D1 is a non-negative integer, - Calculating the arithmetic mean of the element-wise multiplication between the elements of the first vector variants and the complex conjugate of the elements of the second vector, - generating D2+1 second vector variants from the elements of the second vector, where for each second vector variant d2 samples are removed at the beginning and d2 zeros are added at the end, where the number d2 is any number between 0 and D2, including 0 and D2, where D2 is a non-negative integer, - Calculating the arithmetic mean of the element-wise multiplication between the elements of the second vector variants and the complex conjugate of the elements of the first vector, - Selecting the arithmetic mean with the maximum squared absolute value and determining the corresponding number d1 or d2 as the optimal number d1 or d2 at which the maximum occurs, - Using the first vector to calculate the arithmetic mean of the element-wise multiplication between its odd-index elements and the complex conjugate of its even-index elements, - Using the second vector to calculate the arithmetic mean of the element-wise multiplication between its odd-index elements and the complex conjugate of its even-index elements, - Taking the real value of the results of the last two arithmetic mean operations, including the odd and even elements of each vector, multiplying each of these elements by the sampling correction factor, and adding the results, - calculating the inverse of the result of the latter addition using a lookup table (LUT inverse) of the inverse function, where the inverse function is defined as 1 divided by the argument of the function, and multiplying by the selected arithmetic mean with maximum squared absolute value, and - Taking the real and imaginary values of the result of the latter multiplication, applying a lookup table (LUT function) for the function in equation (1) of the specification to each of these elements, and combining the two results to form a complex-valued number which is the estimate of the cross factor. [2] A method according to claim 1, wherein the method is applicable in a multi-channel receiving device for any digital communication system for both forward and return links. [3] Method according to claim 1 or 2, wherein - the step of estimating each cross-channel interference component and subtracting it from the corresponding received signal comprises the following steps: - if the optimal number d1 is greater than or equal to 0, multiplying the estimate of the cross factor by the samples of the second vector, in which d1 samples have been removed at the beginning and d1 zeros have been added at the end, and subtracting the result element-wise from the samples of the first vector, thereby generating the improved received samples of the first channel of the current pair of processed channels, - if the optimal number d1 is greater than or equal to 0, multiplying the conjugate estimate of the cross factor by the samples of the first vector, with d1 samples removed at the end and d1 zeros added at the beginning, and subtracting the result element-wise from the samples of the second vector, thereby generating the improved received samples of the second channel of the current pair of processed channels, - if the optimal number d2 is greater than or equal to 0, multiplying the estimate of the cross factor by the samples of the second vector, with d2 samples removed at the end and d2 zeros added at the beginning, and subtracting the result element-wise from the samples of the first vector, thereby generating the improved received samples of the first channel of the current pair of processed channels, - if the optimal number d2 is greater than or equal to 0, multiplying the conjugate estimate of the cross factor by the samples of the first vector, with d2 samples removed at the beginning and d2 zeros added at the end, and subtracting the result element-wise from the samples of the second vector, thereby generating the improved received samples of the second channel of the current pair of processed channels, and - Repeating this step of estimating each cross-channel interference component and subtracting it from the corresponding received signal for each pair of received digital signals from each pair of channels.

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