WO2022249033A1 - Method for embedded data modulation over pilot symbols in qam system - Google Patents

Abstract

The present application relates to a method for embedded data modulation over pilot symbols in a QAM system. Based on the concept of embedding data modulation, the CPE pilot symbols are also used to carry data, which is modulated in amplitude or in both amplitude and phase. Thus, it is proposed a better use of the necessary CPE-pilots overhead to enhance the Information rate of a transmitted signal. Based on the concept of embedding data modulation over CPE pilot symbols, it is also object of the present disclosure a method for transmitting embedded data modulation over pilot symbols in a QAM system and a method for receiving embedded data modulation over pilot symbols in a QAM system.

Description

DESCRIPTION

METHOD FOR EMBEDDED DATA MODULATION OVER PILOT SYMBOLS IN QAM

SYSTEM

FIELD OF THE DISCLOSURE

The present disclosure is enclosed in the field of QAM transmission systems. More particularly, the present disclosure relates to modulation and transmission schemes designed to optimize channel capacity utilization.

PRIOR ART

In modern coherent optical communication systems employing quadrature amplitude modulation (QAM), the use of pilot symbols is very common to aid on the estimation and compensation of carrier-phase noise. These pilot symbols are composed of sequences of QAM symbols with pre-defined amplitude and phase, which are known a priori both by the transmitter and receiver. Pilot symbols are time- multiplexed with regular data symbols - payload -, typically in a regularly distributed fashion, as shown by the example of Fig. 1, in which 1 pilot symbol is added after each 5 data symbols, defining a pilot-rate, R_PIL, of 5/6.

An example of the definition of pilot symbols for coherent optical communications can be found in the recent standardization of 400ZR communication systems for short reach - up to 120 km- optical systems by the Optical Internetworking Forum (OIF), where a pilot-rate of 31/32 with regularly spaced pilots mapped into a quaternary phase-shift keying (QPSK) constellation is recommended. Therein, the implementation agreement for the pilot sequence is that training symbols and pilot symbols shall be set at the outer 4 points of the 16QAM constellation. Additionally, the pilot sequence is a fixed PRBS10 sequence mapped to QPSK with different seed values for X/Y polarizations. A schematic representation of OIF's recommendation for pilot symbols generation and mapping is shown in Fig. 2.

On the one hand, these pilot symbols play a crucial role on a pilot-based carrier-phase estimation (CPE) subsystem, since they provide an absolute phase reference for the estimation of carrier-phase noise, resorting to pilot-based CPE. The performance of pilot-based CPE is improved as the pilot symbols are inserted more regularly, i.e., as the pilot-rate is lowered, or conversely, the pilot overhead is increased. However, on the other hand, the insertion of these pilot symbols imposes a reduction on the information rate (IR) of the transmission system, as it implies reducing the number of payload data symbols. In coded M-QAM modulation, the IR transported by the transmitted signal is proportional to the pilot-rate, as IR = log₂(M) R_FECR_PIL, where R_PIL is pilot-rate and R_FEC is the forward error correction (FEC) code-rate. In the aforementioned example of Fig. 1, the information rate is reduced by a factor of 5/6 due to the insertion of pilot symbols.

Therefore, the use of pilot symbols for CPE in modern coherent optical communication systems imposes a loss of IR that limits the practical achievable bit-rates in realistic transmission systems. PROBLEM TO BE SOLVED

The ever-increasing demand for high data-rate optical systems has led to the development of extremely efficient modulation formats and transmission schemes, in which the achievable IR is optimized close to the ultimate Shannon limit of spectral efficiency. In particular, it is quite common to allocate some non-negligible pilot overhead to aid on the carrier-phase estimation digital signal processing (DSP) subsystem, in order to guarantee a high-performance and cycle-slip-free DSP operation. However, the overhead allocated for CPE-pilots results in a waste of transmitted IR, leading to a suboptimal utilization of the channel capacity.

Thus, the development of improved techniques for the exploitation of the IR contained within the overhead required for pilot symbols is then of utmost importance.

The present solution intended to innovatively overcome such issues. In orderto maximize the transmitter IR in systems using pilot symbols for CPE, the present solution proposes to make a better use of the necessary CPE-pilots overhead to enhance the IR of the transmitted signal, which can then be utilized to increase the delivered bit- rate and/or reduce the required signal-to-noise ratio (SNR) for error-free operation.

SUMMARY OF THE DISCLOSURE

In order to minimize the IR loss imposed by the use of pilot symbols for CPE, it is proposed a method to embed data modulation over the CPE pilot symbols in QAM systems.

In a preferred embodiment, the method developed is comprised by the following steps: i. applying at least an amplitude modulation overthe carrier phase estimation pilot symbols of a M-level QAM signal with an information rate, IR = log ₂(M)R_FECR_PIL; wherein, R_FEC is a forward error correction code-rate and R_PIL is the pilot-rate; said amplitude modulation being restricted to a set of values that lie on a

diagonal of a M-QAM constellation; and the phase of the pilots is a multiple of (2 n — 1)π/4, with integer n; ii. carrying data on the amplitude of the pilot symbols and allocating an additional information rate, IR_PIL, into said pilot symbols, such that an overall information rate of the QAM system, IR_TOT is increased, being given by IR_TOT = log₂ (M)R_FECR_PIL + IR_PIL-

In one embodiment, the method applies amplitude modulation over CPE pilot symbols while keeping the original phase values that are pre-defined in the pilot sequence (A-PIL method). The amplitude modulation is restricted to the set of VM/2 values that lie on the diagonal of the M-QAM constellation, where the phase is a multiple of (2 n — 1)π/4, with integer n. Since the phase reference provided by the pilot sequence is unaltered, this allows to reuse the typical pilot-based CPE algorithm to track and mitigate phase noise at the receiver. Also, since the amplitude modulation is applied in such a way that the modulated pilot symbols coincide with the M-QAM symbols in the constellation diagonals, both the minimum Euclidean distance and mapping demapping space are preserved. In addition, since all amplitude levels are equally likely and evenly distributed between the minimum and maximum amplitudes of the QAM constellation, then the average transmitted power remains unaltered.

In another embodiment, in addition to the amplitude modulation, the method also applies phase modulation over the CPE pilot-symbols (AP-PIL method). In this case, the pilot sequence is neglected, keeping only the "pilot slot" that is attributed to the symbols that are dedicated to aid on the CPE at the receiver. Similarly, to the A- PIL method described above, the amplitude modulation values are restricted to the values that coincide with the diagonals of the M-QAM template, where the phase is a multiple of (2n — 1) π/4. In turn, the phase modulation is restricted to phase values that are also a multiple of (2 n — 1)π/4, so that the carrier-phase estimation at the receiver- side can be optimally applied through a 4th-power CPE algorithm.

Based on the concept of embedding data modulation over CPE pilot symbols, it is also object of the present disclosure a method for transmitting embedded data modulation over pilot symbols in a QAM system and a method for receiving embedded data modulation over pilot symbols in a QAM system.

DESCRIPTION OF FIGURES

Figure 1 - representation of a time multiplexing between data symbols (1) - payload - and pilot symbols (2) for CPE. An exemplary case corresponding to a pilot-rate of 5/6 is depicted.

Figure 2 - representation of OIF's recommendation for the generation and constellation mapping of pilot symbols for carrier-phase estimation.

Figure 3 - extra information rate in bits-per-channel-use as a function of pilot rate/overhead enabled by the application of a) amplitude-only modulation (A-PIL) and b) amplitude and phase modulation of CPE pilot symbols (AP-PIL).

Figure 4 - an embodiment of a Transmitter-side implementation of the method developed. Particularly, it is illustrated the implementation of M-QAM modulation with embedded amplitude modulation of CPE pilot symbols (A-PIL). The graphical examples of the modulated constellations are based on the assumption of M = 64. Optional blocks are indicated by a dashed outline.

Figure 5 - an embodiment of a Receiver-side implementation of pilot symbols synchronization and extraction, followed by pilot-based CPE, for operation with the A- PIL technique. Optional blocks are indicated by a dashed outline.

Figure 6 - an embodiment of a Receiver-side implementation of signal demapping and decoding with embedded amplitude modulation of pilot symbols (A- PIL). Optional blocks are indicated by a dashed outline.

Figure 7 - an embodiment of a Transmitter-side implementation of the method developed. Particularly, it is illustrated the implementation of M-QAM modulation with embedded amplitude and phase modulation of CPE pilot symbols (AP-PIL). The graphical examples of the modulated constellations are based on the assumption of M = 64. Operations that are specific to the implementation of phase modulation are highlighted by a dotted framing box. Optional blocks are indicated by a dashed outline.

Figure 8 - an embodiment of a Receiver-side implementation of pilot symbols synchronization and extraction, followed by 4th-power CPE, for operation with the AP- PIL technique. Optional blocks are indicated by a dashed outline.

Figure 9 - an embodiment of a Receiver-side implementation of signal demapping and decoding with embedded amplitude and phase modulation of pilot symbols (AP-PIL). Operations that are specific to the implementation of phase modulation are highlighted by a dotted framing box. Optional blocks are indicated by a dashed outline.

Figure 10 - Overall implementation diagram of the proposed invention, including transmitter, channel and receiver functionalities. Optional blocks and signals are indicated by a dashed outline.

Figure 11 - an experimental setup utilized to validate the proposed concept of amplitude modulation of CPE pilots (A-PIL).

Figure 12 - Theoretical and experimental SNR gain enable by the application of the proposed invention to a coherent optical communication system, using the extra IR obtained from pilot modulation to increase the FEC overhead. DETAILED DESCRIPTION

Most commonly, the CPE pilots are in the form of "QPSK-like" symbols, typically inserted either at the outer QAM symbols or at the average QAM energy. Instead of following this convention, the present solution assumes that the CPE pilot symbols can take any value over the diagonals of the square QAM template, i.e., any QAM symbol with a phase component in the form (2 n — 1) π/4.

In an M-level QAM signal, it is well known that each data symbol carries an information rate of log₂(M) bits per channel use (bpcu). Instead, since pilot symbols are fully known by transmitter and receiver, they cannot transport any information, i.e., their associated information rate is 0 bpcu, which is a well-known limitation. However, the concept underlying the present solution relates to embedding data modulation over CPE pilot symbols so that an increase in the overall information rate of the QAM transmission system can be achieved.

More particularly, by applying amplitude modulation over the CPE pilots in an M- level QAM signal, it then becomes possible to allocate an additional information rate of log₂(√M/2) bpcu into the pilot symbols. It then becomes apparent that the amplitude of the CPE pilots offers an additional degree of freedom to carry information, providing an extra IR, IR_PIL, which is given by,

In addition, by also embedding modulation within the phase component of the pilot symbols, the corresponding information rate can be further increased by an additional 2(1 — R_PIL) bpcu, yielding

In practical terms, the CPE pilot symbols are modulated as a (2 n — 1) π/4-rotated amplitude-shift keying (ASK) signals with levels and an

Euclidean distance, d_PIL between levels of

d_PIL = √ 2d_QAM , where d_QAM is the minimum Euclidean distance of the M-QAM constellation template.

It is then shown that the minimum Euclidean distance of the modulated data within the pilot symbol positions is always higher (by a factor of √ 2) than the minimum Euclidean distance of the M-QAM signal, and therefore its detection performance does not pose any limitation to the overall system performance.

The extra IR obtained from the proposed pilot-modulation schemes can then be added to the baseline IR of the system, resulting in an effective increase of the overall information-rate of the QAM system, IR_tot, which is now given by,

IR_tot = log₂ (M)R_FECR_PIL + IR_PIL.

By these means, the transmission system experiences an increase in transmission rate by the addition of the IR_PIL term enabled by the embedded modulation of CPE pilots. The extra information rate resulting from the application of the method now developed with 16QAM, 64QAM and 256QAM modulation is shown in Fig. 3. For typical pilot rates of 31/32 (3.125% overhead), it can be seen that an extra 0.1 bits/symbol and 0.15 bits/symbol can be provided by the A-PILand AP-PIL methods with 256QAM modulation, respectively. Further IR gains can be obtained in systems that utilize lower pilot rates, achieving roughly 0.4 bits/symbol and 0.7 bits/symbol with the A-PIL and AP-PIL methods for a pilot-rate of 7/8 (12.5% overhead), respectively.

This additional IR, enabled by the technique developed, can then be utilized to improve the performance of the transmission system in various ways, namely: A direct increase of bit-rate for the same symbol-rate, modulation format, coding-rate and pilot-rate of the transmission system;

An improvement in terms of required SNR for operation, while keeping the same net bit-rate; In this case, several different ways of improving the required SNR can be exploited, namely, but not limited to: Use the obtained IR_PIL to decrease the overall pilot-rate of the system, while maintaining the same net bit-rate; By decreasing the overall pilot-rate, more CPE pilots can be inserted into the signal, thereby improving the performance of the CPE subsystem, which ultimately translates into a reduction of required SNR. This can be achieved by maintaining a single FEC decoder, while increasing its overhead, or by adding an outer FEC coding/decoding stage, whose overhead is fully provided by the IR_PIL obtained from pilot modulation.

In systems employing probabilistic constellation shaping, use the obtained IR_PIL to decrease the overall shaping rate of the system, while maintaining the same net bit-rate. By decreasing the overall shaping-rate, the shaping gain of the system can be improved, which ultimately translates into a reduction of required SNR.

Detailed proposals for possible realizations and implementations of the method developed are now presented. Note that, although the following implementation methodologies are recommended, many other alternative implementations might be considered, based on the same principle, in order to produce the same effect. The proposed implementations should then be interpreted as merely indicative and does bind the invention to its strict application.

A-PIL with Pilot-Based CPE

An implementation diagram of the operations required for the joint modulation of standard M-QAM signals interleaved with amplitude-modulated pilot symbols is depicted in Fig. 4. The transmission starts by taking a bitstream, b ∈ {0,1}, of payload binary information as input. Note that this input bitstream can optionally be encoded by a given error correction code within the Tx Encoder block, yielding a stream of encoded bits, b_enc. In case of uncoded modulation, the Tx Encoder block can be bypassed, yielding b = b_enc. Then, this binary data is divided into two parallel bitstreams, b_QAM,enc and b_{ASK, enc}, by the de-interleaver block, according to the established rate of pilot symbols, R_PIL, i.e. for each block of encoded bits,

the first sub-block of N_{bits, ASK} bits,

M_{bits, ASK} = log₂( √ M/2), are forwarded to the lower branch for ASK modulation, while the following sub-block of

M_{bits, QAM,}

are forwarded to the upper branch for QAM modulation. For instance, considering the example of Fig. 1 with R_PIL = 5/6 and M = 64, it results that for every 32 bits, the first 2 bits are fed to a 4-ASK mapping branch, while the following 30 bits are sent to the standard 64-QAM mapper. These sets of bits are then transformed into symbol indices by the respective bit2sym blocks, the upper one for M-QAM mapping and the lower one for √M/2 -ASK mapping, thereby giving rise to two sets of symbol indices, s_QAM ∈ {1, 2, ... , M} and s_ASK ∈ {1, 2, ... , √M/ 2} . Each of these sets of symbols is then applied at the input of a corresponding mapper block, for M-QAM and √M/ 2 -ASK constellation mapping, giving rise to the C_QAM and C_ASK constellation sets, respectively. One possible implementation for the QAM mapper is given by,

C_QAM(M ) = 2 ((S_QAM - 1) mod√M)

where j represents the imaginary unit.

Similarly, for the ASK mapper, one can apply the following real-valued symbol to constellation mapping, C_ASK = 2 . S_ASK — 1.

Note that, while many other implementations for the QAM and ASK mappers can be adopted, the main requirement of this invention is that the ASK constellation values must coincide with the in-phase (real part) or quadrature (imaginary part) of the QAM constellation. This will ensure that no novel constellation values are created in the process, thus maintaining the fundamental Euclidean distance of the ensemble constellation that will be created from the interleaving of standard QAM symbols and pilot-modulated symbols. Regarding the mapping from bits to symbols, it can be done in any desired order, most often resorting to Gray labeling for optimal performance. The pilot sequence, p, may take any of the following phase values, p ∈ In order to produce a "QPSK-like" constellation, this pilot sequence is

then introduced as the argument for the complex exponential block, yielding C_PIL = √ 2 exp (jp). The constellation corresponding to the amplitude-modulated pilots is then produced by multiplying C_ASK by C_PIL,

C_{PIL ,mod} = C_ASKC_{PIL .}

Finally, the C_QAM and C_PIL,mod constellations are properly interleaved according to the pilot-rate, R_PIL, in the interleaver block, giving rise to the transmitted constellation, C_TX. Still at the transmitter side, a set of digital signal processing (DSP) algorithms can yet be optionally applied in the Tx DSP block before generating the actual signal for transmission, S_Tx.

After propagation over a given transmission channel, which incurs an additional phase noise component to the signal, the received signal, S_Rx is detected and processed in a digital signal processing unit. Within this DSP unit, the implementation of pilot symbols synchronization and extraction, followed by pilot-based CPE, is depicted in the block diagram of Fig. 5. A first set of receiver-side DSP functions can be applied to the S_Rx signal within the Rx-DSPl block, including all the necessary DSP algorithms to correct for the distortion imposed by the channel and/or transceiver, namely including digital equalization of the channel response and compensation of the carrier frequency offset. Also note that the S_Rx signal might be oversampled (more than 1 sample per symbol), and in that case, the Rx -DSPl block should also perform the necessary downsampling operation, so that a noisy 1-sample-per-symbol received constellation, is obtained at its output. Afterwards, the synchronization between this noisy

constellation, and the known pilot sequence, p, is performed within the pilot sync

and extraction block. This synchronization is a well-known procedure that can be implemented by a plethora of different methods, namely through the analysis of the cross-correlation between the received signal and the transmitted pilot sequence, p. Once synchronization is achieved, the received symbols corresponding to the noisy pilot modulated sequence , can be extracted from the overall signal and sent for the

subsequent pilot-based carrier-phase estimation procedure. While other pilot-based CPE implementations can be considered, an exemplary implementation scheme is presented in the Pilot-Based CPE block in Fig. 5. Therein, the signal is first

complex conjugated and then multiplied by the synchronized pilot sequence, p, which, as previously highlighted, is pre-defined and known both by the transmitter and receiver. In order to reduce the impact of uncorrelated phase noise generated by other noise sources in the link (e.g. due to inline amplifier-induced noise), a moving average block of N taps is applied to partially filter out this noise component. The phase component is then calculated through the angle between the real and imaginary parts of the signal at the input of the arg(.) block. In order to remove ±π ambiguity of phase values within the range [— π, π], the unwrap phase block implements a phase unwrapping procedure that transforms phase jumps higher than π into their 2π complement, yielding the estimated phase at the pilot indices, . In order to retrieve

a phase estimation signal at all symbol times, an interpolation can be applied between the spaced values, thus yielding the final estimated phase noise signal,

. This phase noise is then inserted into a complex exponential operator in the exp (j(.)) block and multiplied by the noisy constellation obtained from the output of the Rx-DSP1 block, Finally, the output phase-corrected constellation (but still

potentially polluted with other sources of phase and amplitude noise), , can be

optionally forwarded to a second set of DSP functions implemented in the Rx- DSP2 block, which might include DSP algorithms for a refined equalization of channel impairments, or even additional stages of refined carrier-phase compensation, yielding the output constellation.

The noisy constellation finally enters the last processing stage, which

is depicted in Fig. 6, and includes the symbol demapping and bit decoding operations. First, the constellation is split into its QAM and pilot-modulated components,

and , respectively, within the de-interleaver block and according to the pilot-

rate, R_PIL. In order to remove the phase modulation from the constellation,

the absolute value of the constellation symbols is taken and a scale factor of is

applied within the block. The noisy constellation is then sent to the

K demapper block, which applies the reverse operation of the

ASK mapper block in Fig. 4, thus yielding the estimated symbols at its output. On

the upper branch, the M- QAM constellation is demapped within the M- QAM demapper block, which applies the reverse operation of the M- QAM mapper block in Fig. 4, providing the estimated s_QAM symbols. Both and symbol indices are finally

converted back into their assigned bits within the sym2bit M — QAM and sym2bit blocks, respectively, which apply the reverse operation of the bit2sym M-

QAM and bit2sym √M/ 2 -ASK blocks in Fig.4, respectively. The two streams of estimated encoded bits b_QAM,enc and b_{ASK enc}, are then fed to the interleaver block, which takes blocks of N_{bits ,QAM} bits from the upper branch and N_{bits, ASK} bits from the lower branch, producing at its output a block of N_bits estimated encoded bits, b_enc. Finally, an optional bit-decoder can be applied within the Rx Decoder block, to provide the estimated transmitted bits, b. Note that in the case of uncoded modulation, i.e., in the absence of a bit-decoder block, it simply turns out that

AP-PIL with 4^th-Power CPE

The proposed implementation schematic for the transmitter supporting amplitude and phase modulation of pilot symbols is depicted in Fig. 7. The only difference on the implementation proposed in Fig. 4 lies on the way the C_QPSK constellation is generated (highlighted by a dotted framing box), as opposed to the C_PIL constellation in Fig.4. While C_PIL was fully determined by the predefined pilot sequence, and hence no phase modulation was allowed, in Fig. 7 the C_QPSK constellation is freely obtained by phase modulating the payload data. To that end, an additional output is added to the de-interleaver block, yielding a set of N_bitS,QPSK= 2 bits, b_QPSK,enc, which are converted into corresponding QPSK (or equivalently, 4-QAM) symbol indices, s_QPSK ∈ {1, 2,3, 4} in the bit2sym 4-QAM block. Note that, while any bit-to-symbol assignment can be considered in the bit2sym 4-QAM block, Gray mapping is generally recommended to reduce the bit-error rate of the system. The symbol indices, s_QPSK, are then mapped into the corresponding QPSK constellation,

C_QPSK, within the 4-QAM mapper block. Although many implementations can be considered for the 4-QAM mapper block, it is recommended to follow the same approach as for the M-QAM mapper block, i.e.

but scaled by a factor of SO that the constellation values coincide with those of the

QAM template, thus yielding

Finally, the pilot-modulated constellation, C_PIL,mod, is obtained by directly multiplying the C_QPSK constellation signal by the C_ASK constellation signal, similarly to the apparatus previously described for Fig. 4.

The corresponding implementation of the receiver-side DSP for carrier- phase estimation and compensation with embedded amplitude and phase modulation of pilot symbols is presented in Fig. 8. Note that, since pilot symbols can now take any phase value multiple of π/4, there is no pre-defined pilot sequence, but only a pre- defined positioning for the pilot symbols. Therefore, the synchronization with the pilot symbols cannot be done resorting to a cross-correlation with the pilot sequence, as proposed in Fig.5. Nevertheless, other training sequences and/or protocol overheads can be easily applied to perform this task. By implementing a given synchronization procedure within the pilot sync and extraction block, the noisy constellation

values corresponding to the amplitude and phase modulated pilot symbols can be retrieved. Then, the remaining processing only differs from that proposed for the amplitude only pilot modulation scheme in Fig. 5 on what regards the implementation of the 4th-power CPE subsystem, implemented by the 4th-Power CPE block in Fig. 8. Therein, the signal is first raised to the 4th power, thereby removing the phase modulation from the data, owing to the (2 n — 1)π/4 restriction that is imposed on the valid phase values that can be modulated over the pilot symbols. The following operations are similar to those that were previously described in Fig. 5 for the amplitude-only pilot modulation scheme, finally returning the noisy phase compensated and optionally post-processed constellation, . The final step for the implementation of the transmission system with embedded amplitude and phase modulation of pilot symbols involves the constellation demapping and optional decoding, which is shown in Fig. 9. It can be quickly observed that the implementation scheme of Fig. 9 is very similar to that of Fig. 6, with the only difference lying on the inclusion of an additional parallel demapping branch (highlighted by a dotted yellow-framing box) to retrieve the information that was QPSK-modulated over the phase of the pilot symbols. Therein, the phase component from the noisy pilot- modulated constellation, , is firstly retrieved by calculating the angle between

the I and Q(real and imaginary) components of the signal within the arg(·) block. Then, to recover a QPSK-like constellation, these phase values are transformed back into a complex signal and scaled by a factor of within the block to fit to the

scale of the 4-QAM demapper block, which will apply the exact inverse operation of the 4-QAM mapper block in Fig. 7, thereby yielding the estimated QPSK symbols,

Finally, a symbol-to-bit operation is applied within the sym2bit 4-QAM block, which applies the exact inverse operation of the bit2sym 4-QAM block in Fig. 7, generating the estimated encoded bits that were originally modulated over the phase of the pilot symbols, . These bits, organized in blocks of N_bits,QPSK = 2, are finally

interleaved back into the overall bitstream in the interleaver block, and the remaining operations are similar to those previously described for the amplitude-only pilot modulation in Fig. 6.

End-to-End Application Scenario

A schematic representation of the application of the proposed invention in an end-to-end communications system is depicted in Fig. 10. The transmitted bits, b, can be optionally encoded in the Tx Encoder block, yielding the encoded transmitted bits, b_enc. Then, the encoded bits, b_enc, are applied at the input of the Tx Mapper block as in Figs. 4 and 7, which will return the transmitted constellation symbols, C_TX, at its output. Note that the pilot symbols sequence, p, is only required for the A-PIL variant, whereas in the AP-PIL implementation there is no pilot sequence definition, but only a pilot slot allocation, in which the pilot symbols are periodically introduced. An optional transmitter side DSP unit can also be applied over these constellation symbols within the Tx DSP block, yielding the digital transmitted signal, S_TX. This concludes the digital component of the transmitter. Then, for an actual transmission over a practical communications system, a given transmitter hardware (Tx HW block) must be utilized, including the necessary digital-to-analog conversion of the S_TX signal and all the additional hardware for transmission of the signal according to the requisites of a given transmission system. For instance, in an optical communications system, this would include the light emitting source (typically a laser or a light emitting diode) and the devices required for direct or external modulation of the optical waveform. Afterwards, the transmitted signal might be propagated over a given channel, depending on the actual transmission system that is being considered. For instance, in an optical fiber communications system, this channel is typically composed of a set of fiber spans and optical amplifiers, possibly also with intermediate optical filters for wavelength routing.

At the receiver-side, the signal is first detected by a given receiver hardware, within the Rx HW block. For instance, in an optical communications system, this receiver hardware might include a given optical frontend (e.g. in the case of coherent reception) followed by a set of photodetectors. Then, the necessary analog- to-digital conversion is performed, providing the S_RX digital signal at the output. This digital signal can then be subject of a set of digital signal processing routines, within the Rx DSP block, as in Figs. 5 and 8, namely including digital equalization of the channel- induced distortions, carrier-frequency offset compensation and digital resampling to one sample per symbol, thus yielding the noisy constellation of received symbols,

These noisy constellation symbols are then sent to the Rx Demapper block, as in Figs. 6 and 9, where the constellation symbols are demapped and the estimated transmitted encoded bits, are retrieved. Finally, an optional bit decoder can be applied within

the Rx Decoder block, as in Fig. 6, providing the final estimated transmitted bits, b. EMBODIMENTS

In a first embodiment, the concept of embedding data modulation over CPE pilot symbols, is applied for transmitting embedded data modulation in a QAM system. Said method is comprised by the following steps: i. inputting a bitstream of payload binary data, b, with a number of bits N_bits wherein, N and wherein, R_PIL is a predefined

rate of pilot symbols per data symbols; ii. dividing the bitstream b into at least two bitstreams b_ASK and b_QAM, by a de- interleaver block; the first bitstream b_ASK being forward for ASK modulation and the second bitstream b_QAM being forward for QAM modulation; wherein the b_ASK corresponds to a portion of b, defined by the first N_bits,ASK number of bits of b, wherein and the b_QAM corresponds to a

remaining portion of b, defined by N_bits,QAM number of bits of b, wherein

iii. transforming the bitstreams b_ASK and b_QAM into and

..,M} symbol indices, respectively;

iv. feeding a constellation mapper with the set of symbol indices s_ASK

to create a C_ASK constellation set; and feeding a M — QAM constellation mapper with the set of symbol indices s_QAM to create a C_QAM constellation set; wherein, the constellation values coincide with the in-phase or

with the quadrature of the M — QAM constellation values; v. producing a constellation of amplitude-modulated pilots, C_PIL,mod, based on at least the C_ASK constellation set; vi. generating a transmitted constellation, C_TX, by interleaving C_QAM constellation and C_PIL,mod constellation, according to the R_PIL; vii. generating a transmission signal, S_TX, based on the C_TX constellation, to be transmitted via a transmission channel. In connection with the first embodiment, In a second embodiment the concept of embedding data modulation over CPE pilot symbols is applied for receiving embedded data modulation in a QAM system. Said method is comprised by the following steps: i. detecting a received signal S_RX; S_RX being a signal transmitted over a transmission channel by a transmitter operating according to the data modulation principle; said signal having an additional phase noise component introduced by the transmission channel; ii. obtaining a received signal noisy constellation ;

iii. synchronizing the and a pilot sequence p; p being the same as defined in

the transmission method described in the first embodiment; iv. extracting from the constellation, received symbols corresponding to

noisy pilot modulated sequences ,

v. retrieving a phase estimation noise signal,

from each of the extracted symbols by implementing a pilot-based carrier-phase estimation procedure; vi. inserting the phase estimation noise signal

of each received symbol into a complex exponential operator and multiplying it by the noisy constellation

in order to generate an output phase-corrected constellation, ;

vii. de-interleaving the constellation into QAM components, , and into

pilot-modulated components, , according a R_PIL; the R_PIL being the

same as defined in the transmission method described in the first embodiment; viii. de-mapping the constellation within M — QAM constellation demapper,

by applying a reverse operation of the M — QAM constellation mapper implemented in the transmission method described in the first embodiment, in order to estimate e {1, 2, ... , M} symbols;

ix. from the constellation, at least remove the phase modulation by

applying a scale factor of to the absolute value of the constellation

symbols, in order to retrieve noisy constellation which is then applied to a

constellation demapper, by applying a reverse operation of the

constellation mapper implemented in the transmission method

described in the first embodiment, for estimating symbols;

x. estimating at least streams of bits , by respectively converting the

symbols and the symbols into bitstreams; the conversion being

executed by applying a reverse operation of the operation of transforming bitstreams into symbol indices executed in the transmission method described in the first embodiment; xi. feeding an interleaver block with at least the stream , having N_bits,QAM

number of bits, and with the stream , having N_{bits, ASK} number of bits, in

order to estimate a stream of bits with N_bits.

In a preferred embodiment, the concept of embedding data modulation over CPE pilot symbols, is applied to a communication system comprising:

— a transmitter unit comprising processing and transmission means adapted to transmit a bitstream b of data, according to the transmission method described in the first embodiment;

— a communication channel through which b is transmitted; and

— a receiver unit comprising detecting and processing means adapted to estimate the bitstream

, according to the method described in the second embodiment.

APPLICATION SCENARIOS

The solution described in this disclosure can be applied to improve the performance of QAM transmission systems that rely on the use of pilot symbols for CPE. Within the broad range of systems that can be framed in this category, it is highlighted the potential application to modern coherent optical communication systems with intradyne detection, both for short-range and long-range applications.

Practical application scenarios include high-capacity transmission for inter/intra-datacenter communications, optical transport networks and submarine inter-continental fiber-optic communications. From the point of view of practical implementation in a commercial transceiver, the proposed technique does not require any additional hardware functionalities. Instead, it only requires to reconfigure the digital modulation and demodulation subsystems at the software/firmware level.

A-PIL TECHNIQUE - APPLICATION EXAMPLE

The possibility of increasing the system performance in terms of spectral efficiency (or conversely, delivered bitrate at fixed bandwidth) and/or required SNR, without the need for any hardware upgrades, is a major advantage that might attract a strong industrial interest. Its applicability is currently foreseen, but not limited to, for high-capacity coherent optical transmission systems.

In the following, it is presented an implementation example of the A-PIL technique of the developed transmission technique, in which its application is exploited to achieve an improvement in the required SNR to operate the system, by utilizing the extra information-rate, IR_PIL, to accommodate an additional FEC overhead that improves the net coding gain of the system.

The experimental setup utilized for the validation of the proposed solution in a commercially-ready prototype is presented in Fig. 11. The optical carrier and local oscillator are generated by external cavity lasers (ECL) operating at 1550nm with roughly 100 kHz linewidth. The electrical signal is synthesized by an arbitrary waveform generator (AWG) with 120Gsa/s and 45GHz bandwidth. A dual-polarization (DP) IQ modulator with 35GHz bandwidth followed by a booster EDFA is utilized at the optical transmitter. The operating OSNR is measured by an optical spectrum analyzer (OSA) and set through EDFA-generated noise loading, whose power is controlled by an electronically-actuated variable optical attenuator (VOA). Out-of-band noise is filtered by 200 GHz optical band-pass filters (OBPF). A coherent receiver with 40 GHz bandwidth performs the optical-to-electrical conversion and sends the I and Q components to a real-time oscilloscope operating at 100 Gsa/s on 4 ports, with 33 GHz bandwidth.

Receiver-side DSP includes a 5-taps CMA followed by frequency estimation and pilot-based CPE. Finally, after a 51 taps LMS equalizer, the signal is demapped and the NGMI is evaluated. The obtained experimental results, in terms of SNR gain (or conversely, reduction of required SNR), are depicted in Fig. 12 for three different use cases: i) 16QAM at 60 Gbaud; ii) 64QAM at 30 Gbaud and iii) 64QAM at 60 Gbaud.

The SNR gain depicted in Fig. 12 is obtained through the allocation of an extra FEC overhead enabled by the additional IR provided by amplitude modulation of CPE pilots. The increased overhead allows to improve the net coding gain of the FEC subsystem, thereby reducing the required SNR for error-free operation. It can be seen that the experimental results obtained for 16QAM modulation at 60 Gbaud and 64QAM at 30 Gbaud are in good agreement with the theoretical predictions.

Nevertheless, in the case of very high-capacity systems that push the capabilities of the optical transceiver to their physical limits, as in the 64QAM at 60 Gbaud scenario, a substantially increased gain is observed. This happens due to the stronger dependence of system performance on required SNR associated with these systems. This is a typical behavior in systems that are operating close to the Generalized Mutual Information (GMI) saturation point, which might happen in practical transceivers when the target bit-rates are pushed to the limits. The logical consequence of such behavior is that a significant SNR gain can be obtained by increasing the FEC overhead and thus lowering the threshold GMI. However, in traditional transmission systems this cannot be done without reducing the net bit-rate. By utilizing the proposed feature of CPE-pilots modulation, the extra IR allocated within the pilot symbols can be transferred to an additional FEC overhead, thus lowering the operating GMI threshold without compromising the net bit-rate. Consequently, substantial gains can be achieved in these systems, as shown in Fig. 12, where 0.6 dB gain is observed at a typical pilot-rate of 31/32 and 1.7 dB gain is achieved at a pilot-rate of 15/16.

As will be clear to one skilled in the art, the present solution should not be limited to the embodiments described herein, and a number of changes are possible which remain within the scope of the present disclosure.

Claims

1. Method for embedding data modulation over carrier phase estimation pilot symbols in a QAM system; the method comprising the following steps: iii. applying at least an amplitude modulation overthe carrier phase estimation pilot symbols of a M-level QAM signal with an information rate, IR = log ₂(M^')R_FECR_PIL; wherein, R_FEC is a forward error correction code-rate and R_PIL is the pilot-rate; said amplitude modulation being restricted to a set of values that lie on a

diagonal of a M-QAM constellation; and the phase of the pilots is a multiple of

(2 n — 1)π/4, with integer n; iv. carrying data on the amplitude of the pilot symbols and allocating an additional information rate, IR_PIL, into said pilot symbols, such that an overall information rate of the QAM system, IR_TOT is increased, being given by IR_TOT = log₂ (M)R_FECR_PIL + IR_PIL.

2. Method according to claim 1, wherein the additional information rate,

IRpii, is given by:

3. Method according to claim 1, wherein a further phase modulation is applied over the carrier phase estimation pilot symbols; the phase modulation being restricted to phase values that are multiple of (2 n — 1)π/4.

4. Method according to claim 3, wherein the additional information rate, IRpii, is given by:

5. Method for transmitting embedded data modulation over pilot symbols in a QAM system, comprising the following steps: i. inputting a bitstream of payload binary data, b, with a number of bits N_bits wherein, N_bits = log₂(M) — 1, and wherein, R_PIL is a predefined

rate of pilot symbols per data symbols; ii. dividing the bitstream b into at least two bitstreams b_ASK and b_QAM, by a de- interleaver block; the first bitstream b_ASK being forward for ASK modulation and the second bitstream b_QAM being forward for QAM modulation; wherein the b_ASK corresponds to a portion of b, defined by the first N_{bits, ASK} number of bits of b, wherein N_{bits ,ASK} = log₂ ; and the b_QAM corresponds to a

remaining portion of b, defined by N_bits,QAM number of bits of b, wherein

iii. transforming the bitstreams b_ASK and b_QAM into s_ASK ∈ and

^SQAM ∈ {1_/ 2, .

..,M} symbol indices, respectively; iv. feeding a constellation mapper with the set of symbol indices s_ASK

to create a C_ASK constellation set; and feeding a M — QAM constellation mapper with the set of symbol indices s_QAM to create a C_QAM constellation set; wherein, the constellation values coincide with the in-phase or

with the quadrature of the M — QAM constellation values; v. producing a constellation of amplitude-modulated pilots, C_{PIL mod}, based on at least the C_ASK constellation set; vi. generating a transmitted constellation, C_TX, by interleaving C_QAM constellation and C_{PIL mod} constellation, according to the R_PIL; vii. generating a transmission signal, S_TX, based on the C_TX constellation, to be transmitted via a transmission channel.

6. Method according to claim 5, wherein the bitstream, b, is encoded by an error correction code within a transmitter encoder block, yielding a stream of encoded bits b_enc.

7. Method according to claims 5 or 6, wherein the C_ASK constellation set is defined by C_ASK = 2 ^. S_ASK — 1 ; and the C_QAM constellation set is defined by

8. Method according to any of the previous claims 5 to 7, wherein the constellation of amplitude-modulated pilots, C_PIL,mod, is generated by multiplying the C_ASK constellation set by a constellation of pilot sequences C_PIL; wherein the constellation of pilot sequences C_PIL is defined by , being generated by inputting a pilot sequence p, wherein p into a complex exponential

block defined by .

9. Method according to any of the previous claims 5 to 7, wherein bitstream b is further divided into a third bitstream, b_QPSK of N_bits,QPSK = 2 bits; said bitstream being converted into QPSK symbol indices s_QPSK ∈ ; the

symbols s_QPSK being mapped into the corresponding QPSK constellation C_QPSK, wherein,

l), being M = 4.

10. Method according to claim 9, wherein the constellation of amplitude- modulated pilots, C_PIL,mod, is generated by multiplying the C_ASK constellation set with the C_QPSK constellation set.

11. Method according to any of the previous claims 5 to 10, wherein the transformation from bits to symbols is executed using Gray-labeling.

12. Method for receiving embedded data modulation over pilot symbols in a QAM system, comprising the following steps: i. detecting a received signal S_RX; S_RX being a signal transmitted over a transmission channel by a transmitter operating according to the method of claims 5 to 11; said signal having an additional phase noise component introduced by the transmission channel; ii. obtaining a received signal noisy constellation

iii. synchronizing the and a pilot sequence p; p being the same as defined in

the transmission method of any of the claims 5 to 11; iv. extracting from the constellation, received symbols corresponding to

noisy pilot modulated sequences

v. retrieving a phase estimation noise signal, from each of the extracted

symbols by implementing a pilot-based carrier-phase estimation procedure; vi. inserting the phase estimation noise signal of each received symbol into a

complex exponential operator and multiplying it by the noisy constellation

in order to generate an output phase-corrected constellation,

vii. de-interleaving the constellation into QAM components, and into

pilot-modulated components, according a R_PIL; the R_PIL being the

same as defined in the transmission method of any of the claims 5 to 11; viii. de-mapping the constellation within M — QAM constellation demapper,

by applying a reverse operation of the M — QAM constellation mapper implemented in the transmission method of any of the claims 5 to 11, in order to estimate symbols;

ix. from the constellation, at least remove the phase modulation by

applying a scale factor of to the absolute value of the constellation

symbols, in order to retrieve noisy constellation which is then applied to a

constellation demapper, by applying a reverse operation of the constellation mapper implemented in the transmission method of

any of the claims 5 to 11, for estimating symbols;

x. estimating at least streams of bits by respectively converting the

symbols and the symbols into bitstreams; the conversion being

executed by applying a reverse operation of the operation of transforming bitstreams into symbol indices executed in the transmission method of any of the claims 5 to 11; xi. feeding an interleaver block with at least the stream , having N_bits,QAM

number of bits, and with the stream having N_{bits, ASK} number of bits, in

order to estimate a stream of bits with N_bits.

13. Method according to claim 12, wherein the synchronization o

and the pilot sequence p is performed by analysing the cross correlation between the received signal S_RX and the pilot sequence p.

14. Method according to claim 13, wherein the pilot-based carrier-phase estimation procedure includes the following steps:

— complex conjugating the signal and multiplying it by the synchronized

pilot sequence p;

— applying to the resulting signal, a moving average block of N taps;

— calculating the phase component of the signal through the angle between the real and the imaginary parts of said signal;

— transforming the phase jumps higher than π into their 2π complement, yielding an estimated phase at the pilot indices, ;

— retrieving a phase estimation noise signal, , at all symbol times by performing

an interpolation between spaced values.

15. Method according to claim 12, wherein the synchronization of

and the pilot sequence p is performed by analysing the cross correlation between the received signal S_RX and training sequences and/or protocol overheads.

16. Method according to claim 15, wherein the pilot-based carrier-phase estimation procedure includes the following steps:

— raising the signal to the 4^th power;

— applying to the resulting signal, a moving average block of N taps; — calculating the phase component of the signal through the angle between the real and the imaginary parts of said signal;

— transforming the phase jumps higher than π into their 2π complement, yielding an estimated phase at the pilot indices, ;

— retrieving a phase estimation noise signal, , at all symbol times by performing an interpolation between spaced values.

17. Method according to claims 15 and 16, further comprising the step of retrieving from the constellation set, the information that is QPSK-modulated

over the phase of pilot symbols; said step comprising:

— calculating the angle between the real and the imaginary components of the constellation set;

— transforming the angle values into a complex signal and scaling it by a factor of

— applying the resulting signal to a M — QAM constellation demapper, by applying a reverse operation of the M — QAM constellation mapper implemented in the transmission method of any of the claims 5 to 11, in order to estimate

{1, 2, ..., M} symbols;

— estimating a stream of bits by converting symbols into a bitstream;

the conversion being executed by applying a reverse operation of the operation of transforming bitstreams into symbol indices executed in the transmission method of any of the claims 5 to 11.

18. Method according to claim 17, wherein the estimation of the stream of bits is obtained by interleaving the streams _M having N_bits,QAM number of bits,

the stream having N_{bits, ASK} number of bits and the stream having N_{bits, QPSK}

number of bits.

19. A communication system comprising: — a transmitter unit comprising processing and transmission means adapted to transmit a bitstream b of data, according to the transmission method of any of the claims 5 to 11;

— a communication channel through which b is transmitted; and — a receiver unit comprising detecting and processing means adapted to estimate the bitstream b, according to the method of any of the claims 12 to 18.