Patent Description:
Relevant prior art include <CIT> and <NPL>.

<CIT> discloses an approach for compensation for nonlinear distortion in multicarrier satellite systems. Source reflecting encoded and modulated sequences of source data symbols are received. Each source signal is predistorted, and a transmit filter is applied to each predistorted source signal. Each filtered signal is translated to a carrier frequency, and the translated signals are combined into a composite signal for transmission via a multicarrier transponder. The final predistorted version of each source signal is generated via an iterative process of a number of stages, wherein, for a given stage and for each source signal, the process comprises: receiving a prior predistorted version of each source signal from a preceding stage; processing each prior predistorted source signal based on all of the received prior predistorted source signals, wherein the processing is performed based on a characterization of one or more characteristics of the multicarrier satellite transponder.

Cominetti et al discloses a review of using various techniques for transmitting digital data over satellite networks, including OFDM-signals, in terms of data quality and power requirements.

According to a first aspect of the invention, there is provided a method of applying transmitter data predistortion to an orthogonal frequency-division multiplexing, OFDM,-like transmission channel of a satellite transmitter, as defined in claim <NUM>. Preferred and/or optional features are set in the dependent claims. The method compensates for nonlinear distortion in OFDM-like satellite networks.

Other features and aspects of the disclosure will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the features in accordance with various embodiments. The summary is not intended to limit the scope of the invention, which is defined solely by the claims attached hereto.

The technology disclosed herein, in accordance with one or more embodiments, is described in detail with reference to the following figures. The drawings are provided for purposes of illustration only and merely depict typical or example embodiments of the disclosed technology. These drawings are provided to facilitate the reader's understanding of the disclosed technology and shall not be considered limiting of the breadth, scope, or applicability thereof. It should be noted that for clarity and ease of illustration these drawings are not necessarily made to scale.

The figures are not intended to be exhaustive or to limit the invention to the precise form disclosed. It should be understood that the invention can be practiced with modification and alteration, and that the disclosed technology be limited only by the claims.

As noted above, OFDM is a cornerstone of a broad range of current standards, including <NUM> terrestrial wireless networks. OFDM may deliver wide-ranging benefits to broadband satellite systems, among them: <NUM>) integration with broadband terrestrial networks, due to greater commonality, for future-proofing satellite use cases; <NUM>) a dominant role in providing resilience and ubiquity to <NUM> services and extending their coverage to regions only satellites can penetrate; <NUM>) resistance to narrowband interference from terrestrial microwave signals as service providers are increasingly demanding a share of the radio frequency spectrum traditionally occupied by satellites, promoting co-existence; <NUM>) robustness to frequency-selective distortion from on-board transponder multiplexing filters, i.e., amplitude distortion appears flat over narrowband OFDM subcarriers; and <NUM>) flexible and highly efficient spectrum utilization by using adaptive loading of the best power allocation and modulation selection, in a location-dependent manner, when channel state information is exploited.

To this end, implementations of the technology described herein are directed to satellite transmitter and satellite receiver designs for applying OFDM-like signaling in broadband satellite transmissions. Particular implementations are directed to applying OFDM-like signaling in the outroute direction, namely, from the satellite gateway to user terminals. The technology disclosed herein may invoke two layers of multicarrier operation. The first layer allows for multiple independent signals to share a single on-board high-power amplifier (HPA) of a satellite transponder, maximizing payload mass efficiency. The second layer of multicarrier operation permits transmitted symbols from each individual signal to modulate multiple narrowband OFDM subcarriers.

Further implementations of the technology disclosed herein are directed to compensating for distortion in satellite communications systems that utilize OFDM-like signaling. A leading obstacle to adopting OFDM in satellite systems is OFDM's inherent sensitivity to nonlinear distortion, due to high peak-to-average power ratio (PAPR) levels, requiring inefficiently operating the on-board HPA of a satellite at a large output back-off (OBO). To this end, novel distortion compensation techniques are described herein for removing the resulting nonlinear distortion from the forward-error correction (FEC) decoder input of a receiver, thereby achieving superior performance and allowing a satellite HPA to operate close to saturation.

As further described below, a computationally efficient distortion construction may be used that incorporates not only input from all the narrowband OFDM subcarriers within a signal, but also those pertaining to other signals that share the same HPA. This distortion construction may subsequently be used at the transmitter in the form of successive data predistortion, and/or at the receiver, in the form of soft cancellation, successively exchanging frequency-domain soft information with decoders.

<FIG> illustrates an exemplary satellite communication system that utilizes OFDM-like signaling in accordance with implementations. In the system of <FIG>, one or more OFDM-like data signals (s<NUM>(t). sMc(t)) are shaped and composited into a composite data signal sc(t) at an OFDM-like transmitter <NUM> (e.g., a transmitting base station of a satellite gateway) using OFDM-like signaling. The one or more data signals that are carried over the satellite channel by the composited signal may have (m) independent carriers (<NUM>,. , Mc) where each carrier corresponds to a respective data signal. Additionally, each data signal may carry multiple OFDM subcarriers. In various implementations, the OFDM-like data signals may carry image, video, audio, and other information. A nonlinear satellite transponder <NUM> receives composite signal sc(t) from transmitter <NUM>, and amplifies and rebroadcasts the OFDM-like signal for reception by one or more OFDM-like receivers <NUM> (e.g., a satellite user terminal such as a very small aperture terminal).

<FIG> illustrates one example implementation of an OFDM-like transmitter <NUM> that may generate a composite signal sc(t) of Mc frequency-multiplexed independent signals sm(t), where each signal is modulated with multiple OFDM subcarriers. As illustrated, for each frequency carrier (<NUM>,. , Mc), OFDM-like transmitter <NUM> includes, a forward error correction (FEC) encoder <NUM> that receives information from a bit source <NUM>, an interleaver <NUM> (represented by Π), a modulator <NUM>, an OFDM modulator <NUM>, a transmit pulse-shaping filter <NUM>, and a mixer <NUM>. Additionally, transmitter <NUM> includes an optional transmitter-based correction module <NUM> that may apply data predistortion to correct for any distortion that would appear in the signal received by a receiver <NUM>. Although the components of transmitter <NUM> are shown in a particular order in this example, one of ordinary skill in the art reading this description will understand that the order of components can be varied and some components may be excluded. One of ordinary skill in the art will understand how other transmitter configurations can be implemented, and that one or more of these components can be implemented in either digital form (e.g., as software running on a DSP or other processing device, with the addition of a DAC ) or as analog components. Additionally, although bit sources <NUM> are illustrated in this example implementation as being separate from transmitter <NUM>, in some implementations bit sources <NUM> may be incorporated into transmitter <NUM>. Further, although transmitter <NUM> is described with respect to exemplary mathematical implementations and constructions, it is not limited to these precise implementations and constructions.

Bit source <NUM> provides information bits to be transmitted to FEC encoder <NUM>. The information can include, for example, images, video, audio, text and other data. FEC encoder <NUM> performs forward error correction by adding redundancy to information data bits signal <NUM>. Forward error correction improves the capacity of a channel by adding redundant information to the data being transmitted through the channel. Examples of forward error correction codes that can be applied by FEC encoder <NUM> can include block codes (e.g., turbo codes, low-density parity check codes (LDPC), Reed-Solomon codes, Hamming codes, Hadamard codes, BCH codes, and so on), and convolutional codes.

Interleaver <NUM> scrambles the encoded data bits by rearranging the bit sequence order to make distortion at receiver <NUM> more independent from bit to bit. In other words, interleaver <NUM> rearranges the ordering of the data sequence in a one to one deterministic format. Interleaving may be used to enhance the performance of the FEC codes. Modulator <NUM> is a bit-to-symbol modulator that modulates the interleaved bits using a bit-to-symbol modulation scheme to form complex-valued data symbols Xm. The interleaved bits may be modulated using any of a number of different modulation techniques. Examples of modulation schemes that can be implemented include Amplitude Phase Shift Keying (APSK), Quadrature Phase Shift Keying (QPSK), π/M-MPSK, other orders of Multiple Phase Shift Keying MPSK, Quadrature Amplitude Modulation (QAM), and so on.

For each signal, an OFDM modulator <NUM> is applied such that transmitted symbols from each signal modulate a plurality of narrowband OFDM subcarriers. The number of modulated OFDM subcarriers or size N, can be different (e.g., two more OFDM subcarriers) for each signal to allow different OFDM numerology amongst them. As such, the disclosed transmitter may modulate different numbers of narrowband OFDM subcarriers onto each signal to provide flexibility and efficiency in the satellite communication system. In alternative implementations, only a subset of the signals may be modulated with OFDM subcarriers.

In implementations, OFDM modulator <NUM> is an inverse fast Fourier transform (IFFT) modulator (e.g., an N -point IFFT) that modulates N narrowband OFDM subcarriers onto the complex-valued data symbols output by modulator <NUM>, where the number N may be different or the same for each signal output by transmitter <NUM>. The use of an IFFT may provide for a computationally efficient modulation with OFDM subcarriers.

In implementations, no guard tones are inserted at the input of the OFDM modulator <NUM> to avoid reduction in throughput.

An optional transmitter-based correction <NUM> may be included to apply data predistortion to correct for any distortion that would appear in the signal received by a receiver <NUM>. This distortion correction may take into account the linear and nonlinear distortion caused by the interaction amongst the other OFDM-like signals at the transmitter and any linear and non-linear distortion introduced by a non-linear transponder of the satellite. Particular implementations of a transmitter-based correction <NUM> that applies data predistortion are further described below. As an alternative to transmitter data predistortion, transmitter signal predistortion may be applied by placing transmitter-based correction <NUM> after transmit pulse-shaping filters <NUM>.

As illustrated in the example of <FIG>, transmitter-based correction <NUM> applies data predistortion after OFDM modulator <NUM> (e.g., to complex-valued data symbols modulated with narrowband OFDM subcarriers x output by an IFFT), which is in the time domain. Alternatively, in other implementations, transmitter-based correction <NUM> may apply data predistortion before OFDM modulator <NUM> (i.e., to complex-valued data symbols X), which is in the frequency domain. In implementations, it may be preferable to apply transmitter-based correction <NUM> in the time domain to avoid the need for conversions between the time domain and frequency domain in transmitter correction <NUM>.

Transmit pulse-shaping or interpolating filter <NUM> converts the complex-valued data symbols, modulated with the OFDM subcarriers, to a transmit waveform signal. As shown in the example of <FIG>, filter <NUM> is applied on the aggregate of OFDM subcarriers to convert an error-corrected signal xm(S) to a waveform signal sm(t). In implementations, the pulse-shaping filter may be implemented as a root-raised cosine (RRC) filter, a partial response filter, or other suitable pulse shaping filter. Following filtering of the transmit signal at filter <NUM>, mixer <NUM> of transmitter <NUM> mixes the waveform signal sm(t) of each of the filter outputs with a carrier signal z(t) from a local oscillator (not shown) to modulate it onto an appropriate carrier for transmission. In implementations, the carrier signal function for a particular carrier m may be represented as <MAT>, where fm is the center frequency and θm is the carrier phase of m-th channel.

The application of a filter <NUM> on an aggregate of OFDM subcarriers for each signal x<NUM>(S) may provide the benefits of oversampling, suppression of interference leaking into adjacent signals in the transmitted signal composite, and limiting the level of out-of-band (OOB) emissions (which is typically high for conventional terrestrial OFDM networks) to provide compatibility with a satellite uplink transmission.

An adder <NUM> adds output signals sm(t) from a plurality of transmitting carrier sources to provide a composite signal sc(t). The output signal from the transmitter (e.g., composite signal) is transmitted to satellite transponder <NUM>. The compositing of multiple independent signals sm(t) in the example of <FIG> for subsequent transmission to a satellite transponder (e.g., for sharing by a single on-board high-power amplifier <NUM> of the satellite) provides the benefit of maximizing payload mass efficiency of the satellite. In alternative implementations, transmitter <NUM> may be implemented as a single carrier transmitter that generates signals carrying OFDM subcarriers.

In a particular implementation, the inputs and outputs of each component of ODFM-like transmitter <NUM> may be mathematically described as follows. The input to the OFDM-like transmitter may be complex-valued symbol sequences, at the symbol rate <MAT>, {Xm,n;n = <NUM>,<NUM>,···,Ns -<NUM>;m = <NUM>,<NUM>,···,Mc}, from M-ary amplitude and phase shift keying (APSK) constellation, using a well-chosen bit-to-symbol mapping, of independent FEC-encoded, bit-interleaved bit stream for each signal. The parameter Ns is the length of the data block which spans a codeblock of symbols.

Let Xm be the vector of complex-valued data symbols of size Nf ×<NUM>, associated with the m th signal, that lie in the frequency domain, or <MAT>.

The vector Xm may be segmented into NOFDM blocks to modulate N orthogonal subcarriers, which for ease of discussion is chosen to be the same for all signals (but need not be), where <MAT> Padding of a small number of extra symbols, (Nf - Ns), may be needed to make NOFDM in (<NUM>) a whole integer. The padding symbols can be distributed into different blocks or introduced as one segment. The vectors relating to OFDM blocks are stacked to form Xm in (<NUM>), which can be equivalently represented as <MAT> where <MAT> is of size N×<NUM>, l = <NUM>,<NUM>, ···, NOFDM -<NUM>, and m = <NUM>,<NUM>, ···, Mc. Each vector X̃m,l in (<NUM>) is further processed by an N -point IFFT to generate the l th OFDM symbol for the m th signal as <MAT> where X̃m,l,n is the n th component of vector X̃m,l in (<NUM>) and k = <NUM>,<NUM>···, N -<NUM>. The samples <MAT> in (<NUM>) are stacked to form the input xm in the time domain as <MAT> where <MAT> is of size N×<NUM>.

Alternatively, the OFDM block x̃m,l in (<NUM>) can be generated by a matrix-vector multiplication as <MAT> where F is an N × N discrete Fourier transform (DFT) matrix and l = <NUM>,<NUM>, ···, NOFDM -<NUM>. An optional time-domain successive compensator, with S stages (e.g., transmitter-based correction <NUM>) and further described below, may process the resulting complex-valued symbol sequences, generating a modified set of symbols, also at rate <MAT>. The individual waveforms sm(t) may be digitally modulated using the transmit pulse shaping filter pm,T(t) and given by <MAT> They may then be used to form the baseband composite signal sc(t) as <MAT> Where θm represents the normalized difference in signal carrier phase and fm is the m th-signal center frequency. For better utilization of bandwidth, the case of uniform spacing in frequency, say Δf , is considered but the techniques presented herein are applicable to any other frequency plan.

<FIG> is a power spectral density (PSD) plot illustrating the PSD in decibels as a function of the frequency / symbol rate of an individual pulse-shaped signal sm(t) of a conventional terrestrial OFDM, conventional terrestrial OFDM with a cyclic prefix (CP), and OFDM-like signaling using a RRC and 16APSK modulation in accordance with implementations described herein. As illustrated, the spectrum of conventional terrestrial OFDM exhibits a slowly decaying sin(x)/x behavior in the frequency domain. This is due to the rectangular pulse shaping utilized in conventional terrestrial OFDM. When a CP is present in conventional terrestrial OFDM, the spectrum exhibits large ripples (about <NUM> dB) in the in-band region. Spectral ripples require reducing the transmit power so as not to violate strict emission limits, set by regulatory bodies based on the peak level of the spectrum. By contrast, the spectrum associated with an OFDM-like signal in accordance with implementations described herein does not suffer from in-band ripples and has excellent containment of its frequency content within the frequency band of interest (i.e., a sharp frequency cutoff). The latter provides minimum levels of interference leaking into adjacent signals even if orthogonality amongst them is compromised due to different OFDM numerology or synchronization offsets. This also may ensure that the OOB emission level is consistent with that of a traditional satellite signal using single-carrier modulation (SCM).

In implementations such as the one illustrated by <FIG>, the CP that repeats the last part of an OFDM symbol may be avoided. While using a CP may be advantageous in dispersive channels, it induces spectral efficiency loss due to redundancy, and causes energy loss as the CP symbols require additional energy to transmit, but are then discarded at the receiver. This energy loss is computed in decibel (dB) as <NUM> · log((N + NCP )/N), where NCP is the number of CP symbols. Also, as illustrated by <FIG>, using CP creates prominent ripples in the in-band region of a conventional OFDM spectrum, requiring power reduction to ensure regulatory compliance. However, in some implementations, the techniques described herein may be applicable to the case of including CP when needed to remove inter-symbol interference encountered in frequency-selective multipath channels.

Referring again to <FIG>, the satellite transponder <NUM> that receives the composite signal sc(t) from an OFDM-like transmitter <NUM> includes an input multiplexing (IMUX) filter <NUM>, a nonlinear amplifier <NUM>, and an output multiplexing (OMUX) filter <NUM>. The IMUX <NUM> may select a desired group of Mc signals, thereby limiting the impact of adjacent uplink signals. Amplifier <NUM> may be a high-power amplifier (HPA) such as traveling-wave tube amplifier (TWTA), that amplifies its input signal at a back-off level that requires optimization. Following amplification, OMUX filter <NUM> is applied to limit nonlinear interference to adjacent transponders, and composite signal sNL(t) is output.

In implementations, the frequency responses associated with the IMUX and OMUX filters described herein may be taken from Fig. H7. <NUM> of <NPL>. The frequency responses may be used with scaling formula <MAT> <MAT> for cases when the number of signals Mc exceeds unity, where R is the amplitude response, and G is the group delay response.

In implementations, the amplitude and phase distortions introduced by amplifier <NUM>, in terms of amplitude modulation (AM)/AM and AM/phase modulation (PM) conversions, respectively, may be taken from Fig. H7. <NUM> of <NPL>.

During downlink transmission from transponder <NUM> to OFDM-like receiver <NUM>, the signal may be contaminated by downlink noise n(t) on the satellite channel such that the input to the receiver may be described by r(t) = sNL(t) + n(t). The downlink noise added by the satellite channel may be assumed as additive white Gaussian noise (AWGN) with single-sided PSD level of N0 (Watt/Hz), which corrupts the signal at the OMUX output. In implementations, the uplink noise may be assumed negligible relative to the downlink noise, a situation achieved through proper satellite link parameters including the size of the transmit antenna.

<FIG> is a block diagram illustrating one example implementation of an OFDM-like receiver <NUM> that may be implemented to receive and process a downlink satellite signal r(t) on a carrier m (e.g., signal coming from satellite transponder plus noise), modulated with multiple OFDM subcarriers, to output an estimate of the carrier m's bits. In the example of <FIG>, single-user detection is applied, such that no information is exchanged with receivers of other users, as is typical in satellite forwarding applications. However, in other implementations, the design of receiver <NUM> may be adapted for multiple-user detection. For example, the receiver may instead receive a composite of multiple signals, in which case receiver-based distortion correction <NUM> may account for the non-linearities introduced by having multiple signals share the same satellite transponder.

Receiver <NUM> may include a mixer <NUM>, a receive pulse-shaping filter <NUM>, an equalizer <NUM>, an OFDM demodulator <NUM>, an optional receiver-based correction <NUM>, a log-likelihood ratio (LLR) computation module <NUM>, a de-interleaver <NUM>, an FEC decoder <NUM>, an interleaver <NUM>, and a summer <NUM>. As would be understood by one having ordinary skill in the art, in some embodiments other configurations of receiver <NUM> may be implemented, and one or more components of receiver <NUM> can be implemented in either digital form (e.g., as software running on a DSP or other processing device, with the addition of a DAC) or as analog components. Further, although receiver <NUM> is described with respect to exemplary mathematical implementations and constructions, it is not limited to these precise implementations and constructions.

Mixer <NUM> mixes the input waveform signal r(t) received from transponder <NUM> with a carrier down conversion signal from a local oscillator (not shown) to downconvert the received signal to baseband. Following the mathematical implementation from above, the carrier downconversion signal may take the form <MAT>, where fm is the center frequency and θm is the carrier phase of the m -th channel.

At block <NUM>, a receive pulse-shaping filter corresponding to (i.e., matched to) the transmit pulse-shaping filter <NUM> is applied to the downsampled carrier signal to generate an output signal x(t). For example, receive pulse-shaping filter <NUM> may take the form of an RRC receive filter matched to a transmit RRC filter. For example, following the mathematical implementation discussed above, the signal at the output of filter <NUM> may be expressed as <MAT> Where pm,R(t) is the receive pulse shaping filter for a given carrier m, matched to the filter on the transmit side.

Equalizer <NUM> is configured to compensate for the linear phase distortion (i.e., group delay) introduced by the IMUX and OMUX filters of transponder <NUM>. In various embodiments, output signal x(t) of filter <NUM> is downsampled by a downsampler (not shown) at multiples of the symbol rate (e.g., two samples per symbol), which allows for fractionally spaced (FS) group-delay (GD) equalization at equalizer <NUM>. For example, following the mathematical implementation discussed above, at the output of equalizer <NUM> may be samples {ym,k;k = <NUM>,<NUM>,···,Nf -<NUM>;m = <NUM>,<NUM>,···,Mc}, at the symbol rate.

The samples output by equalizer <NUM> may be segmented into NOFDM blocks of symbols, each containing N samples, and converted into a frequency domain by OFDM demodulator <NUM>, which may perform the inverse operations of a transmit OFDM modulator <NUM>. For example, OFDM demodulator <NUM> may be an FFT that converts the samples into the frequency domain, as <MAT> for l = <NUM>,<NUM>, ···, NOFDM -<NUM>, n = <NUM>,<NUM>,···, N -<NUM>, and assembled back into vector of size Nf ×<NUM>, per individual m th signal, as <MAT> where <MAT>.

In an alternative implementation, the frequency-domain block of symbols Ỹm,l in (<NUM>) may generated by a matrix-vector multiplication as <MAT>.

As illustrated in <FIG>, receiver <NUM> includes an LLR computation module <NUM> to compute the likelihood that particular symbols were transmitted by a transmitter <NUM>. This likelihood may be iteratively improved and provided to an FEC decoder <NUM> to improve an estimate of the source bits that were received from a transmitter. During each iteration (if any), LLR computation module <NUM> also considers the a priori information on the code bits provided by FEC decoder <NUM> during a prior iteration.

In implementations, LLR computation module <NUM> may directly couple to the output of OFDM demodulator <NUM>. Alternatively, it may couple to the output of optional receiver-based correction module <NUM>. In implementations where a receiver-based correction module <NUM> is utilized, it may provide improved performance to receiver <NUM> by cancelling out signal distortion at the receiver, thereby improving the quality of the input to LLR computation module <NUM>. In particular, as further described below, correction <NUM> may provide frequency-domain distortion cancellation, iteratively exchanging soft information with FEC decoders <NUM>, to provide successively improved estimation of the transmitted symbols.

Referring again to the example mathematical implementation, discussed above, variables {Ym,n;n = <NUM>,<NUM>,···,Ns -<NUM>;m = <NUM>,<NUM>,···,Mc}, the n th components of Ym in (<NUM>), may be used to generate LLRs for individual FEC decoders after removal of extra (Nf - Ns) padded symbols. Alternatively, the receiver includes an option of implementing a frequency-domain successive compensator (e.g., receiver-based correction <NUM>), further discussed below, using soft-information provided by the FEC decoder, over S iterations. In that case, a vector of frequency-domain samples at the output of the compensator during iteration s +<NUM>, denoted by <MAT> ,may be used to generate LLRs for the FEC decoder. In generating the required LLR, the clustering and warping experienced by Ym,n due to the nonlinear distortion may be taken into account by receiver-based correction <NUM>. This clustering can be different for symbols on different constellation rings and is non-circular, with some rotation, in which case a bivariate Gaussian model may be used for the evaluation of the LLRs. This may be used in conjunction with the principle of bit-interleaved coded modulation with iterative decoding, which involves exchange of soft information with the FEC decoder. More specifically, in the context of <FIG>, the LLR computation module <NUM> may take as input as input Ym,n and <MAT> , the a priori information on the code bits provided by the FEC decoder <NUM> during the s th iteration. LLR computation module <NUM> may calculate the bit extrinsic information for the log<NUM> M bits that map to a particular symbol Xm,n and can be expressed in terms of an LLR as <MAT> for the case of code bit bm,i corresponding to symbol Xm,n. In (<NUM>), gi(Xm,n) is defined as a function returning the i th bit used to label Xm,n such that i = <NUM>,<NUM>, ···, log<NUM> M and fbi(Ym,n | X̃) represents an improvement in evaluating the likelihood probability based on the bivariate Gaussian model, which is further described below. For the specific case of iteration s = <NUM>, no soft-information is available from the FEC decoder, so <MAT> is used. The vector of extrinsic information <MAT> may be provided as an input to the FEC decoder, after deinterleaving, and the decoder may generate an estimate of the source bits after a maximum number of iterations is reached.

As discussed above, a transmitter-based correction <NUM> or receiver-based correction <NUM> may be introduced to correct for linear and nonlinear distortion that results in a satellite communications system that uses OFDM-like signaling. This distortion correction may account for the linear and nonlinear distortion introduced by the HPA, the linear and nonlinear distortion caused by the interaction of the signals in the composite, the linear and nonlinear distortion caused by the interaction between OFDM subcarriers, and/or the linear and nonlinear distortion caused by inter-carrier interference. To this end, particular methods are described below for correcting for the nonlinear distortion resulting from sharing multiple OFDM-like signals through a single nonlinearity (e.g., amplifier <NUM>). As further described below, a computationally efficient polyphase construction of the distortion may be implemented to provide for novel compensation methods that may be applied at an OFDM-like transmitter and/or OFDM-like receiver, entailing correction to successively minimize nonlinear distortion.

In accordance with implementations described herein, a nonlinear distortion construction in an OFDM-like satellite communication system may provide vectors containing estimates of the distorted symbols for a desired signal, in the frequency and time domains, resulting from sharing signals by a single nonlinearity such as a HPA of a satellite transponder.

As further described below, the determined distortion construction may provide vectors <MAT> and <MAT> containing estimates of the distorted symbols for the desired mdth signal, in the frequency and time domains, respectively, resulting from sharing Mc signals by a single nonlinearity, for a given double-sided memory span L. The input vectors Ξ and ξ are related through the application of N -point IFFT on a per-block basis. More specifically, Ξ may be composed by the stacking of inputs from Mc signals, denoted as <MAT> where each individual vector is of size Nf ×<NUM> as <MAT>. Individual vector <MAT> may be segmented into NOFDM blocks, each with N symbols to modulate N orthogonal subcarriers in the frequency domain, where NOFDM is defined in (<NUM>). The vector <MAT> can be formed by stacking vectors relating to blocks as <MAT> where <MAT> is of size N ×<NUM>, l = <NUM>,<NUM>, ···, NOFDM -<NUM>, and m = <NUM>,<NUM>, ···,Mc. Each vector <IMG>m,l in (<NUM>) is further processed by an N -point IFFT to generate l th OFDM symbol as <MAT> where Ξ̃m,l,n in (<NUM>) is the n th component of vector <IMG>m,l of (<NUM>) and k = <NUM>,<NUM>···, N -<NUM>. The components ξm,l,k in (<NUM>) are stacked to form the input in the time domain as <MAT> where <MAT> is of size N ×<NUM>. The vector ξ is then formed by stacking <MAT> of (<NUM>) across Mc signals as <MAT>.

In implementations, a computationally efficient polyphase filter structure is utilized to implement the interpolating filter operation that provides oversampling of Nss samples per symbol, and models the cascade of the transmit pulse and the IMUX filter. Toward this, let <MAT>, where m = <NUM>,<NUM>, ···, Mc and k = <NUM>,<NUM>, ···, Nss · L -<NUM>, be the set of filter coefficients representing the cascade of transmit filter pm,T and the IMUX model. Let <MAT> denote the arms of a polyphase filter bank, for l = <NUM>,<NUM>, ···, Nss -<NUM>, associated with the m th signal, each arm operating at one sample per symbol, expressed as <MAT> where k = <NUM>,<NUM>,. , L -<NUM>. The filter bank in (<NUM>) is used to process the time-domain data <MAT>, contained in <MAT> of (<NUM>), producing outputs <MAT> as <MAT> where k = <NUM>,<NUM>,···, Nf -<NUM>. The desired interpolating filter output bm,k can then be supplied by the filter bank outputs in (<NUM>) through sequential interleaving, with frequency-translation to the respective center frequency of the m th signal, in the following manner <MAT> where l' = k(modNss) and <MAT>, for k = <NUM>, <NUM>,···, Nf · Nss -<NUM>. The value Nss in (<NUM>)-(<NUM>) is preferably large enough to avoid the aliasing effect of distortion when Mc signals share the same transponder.

The composite of bm,k in (<NUM>) may then be formed across signals and scaled to the correct input back-off (IBO) level of the HPA by multiplying by a real-valued parameter γIBO, to generate ζk <MAT> The AM/AM and AM/PM distortions may be computed based on the corresponding HPA's conversion model and applied to the samples ζk producing the distorted sample ζ̃md,k, including the frequency-translation to the desired md th signal whose distortion is being estimated. This is mathematically expressed as <MAT> where | ζk | and ∠ζk are the amplitude and phase of the input ζk, respectively, and βHPA(x) and ψHPA(x) are the amplitude and phase distortions, respectively, of the HPA model.

Next may be replicated the impact of the cascade of OMUX, receive filter, and group-delay equalizer, appropriately decimated at the output to one sample per symbol. Toward this, the polyphase filter structure for computationally efficient implementation of decimation may be used. Let <MAT>, where k = <NUM>,<NUM>, ···, Nss · L - <NUM>, denote the set of filter coefficients that represents the cascade of receive filter pmd ,R, the OMUX model, and the group-delay equalizer. We further introduce <MAT>, for l = <NUM>,<NUM>, ···, Nss -<NUM>, as the arms of a polyphase filter bank, each arm operating at one sample per symbol, defined as <MAT> where k = <NUM>,<NUM>,. , L -<NUM>. The input to the filter bank of (<NUM>) is <MAT>, generated by delaying and decimating ζ̃md ,k of (<NUM>) as <MAT> where k = <NUM>, <NUM>,···, Nf -<NUM>. The desired decimating filter output vmd,k can then be computed using the polyphase filter structure in (<NUM>)-(<NUM>) by summing up across the outputs of the filter bank, or <MAT>.

The output of the decimating filter in (<NUM>) may then be segmented into NOFDM blocks, each with N time-domain distorted symbols, and can be formed by stacking vectors relating to blocks as <MAT> where <MAT> is of size N×<NUM> and l = <NUM>,<NUM>, ···, NOFDM -<NUM>. Each vector ṽmd ,l in (<NUM>) can be further processed by an N-point FFT to produce the distorted symbols in the frequency domain as <MAT> where ṽmd,l,k in (<NUM>) is the k th component of vector ṽmd,l in (<NUM>) and n = <NUM>,<NUM>,···, N -<NUM>. The set of distorted symbols Υ̃md,l,n of (<NUM>) are collected per block as <MAT> and the contributions from all the OFDM blocks, <MAT> in (<NUM>), can be stacked to form Υmd as <MAT>.

In this implementation, the vector of time-domain distorted symbols <MAT>, of size Nf ×<NUM>, is equal to the vector of the decimating filter output vmd of (<NUM>) or <MAT> whereas the vector of frequency-domain distorted symbols <MAT>, of size Nf ×<NUM>, is equal to the vector of the N -point FFT blocks Υmd of (<NUM>) or <MAT>.

<FIG> is an operational flow diagram illustrating an example method <NUM> of creating a frequency-domain distortion construction (e.g., <MAT>) that may be used by transmitter-based correction <NUM> and/or receiver-based correction <NUM> to correct for distortion in accordance with implementations. It should be noted that although method <NUM> is annotated with exemplary variables and functions that may be utilized in particular mathematical implementations, described above with reference to Equations (<NUM>)-(<NUM>), method <NUM> is not limited to these particular mathematical implementations.

At operation <NUM>, an input, consisting of frequency-domain symbols received from the output of an IFFT for each signal Mc may be processed. For example, the input may be processed in accordance with equations (<NUM>)-(<NUM>). At operation <NUM>, the output of operation <NUM> may processed through an interpolating filter with an oversampling of Nss samples per symbol. For example, operation <NUM> may be implemented in accordance with equations (<NUM>)-(<NUM>). At operation <NUM>, the output of operation <NUM> may be frequency translated such that each of the Mc signals is translated to its respective center frequency. For example, operation <NUM> may be implemented in accordance with equation (<NUM>).

At operation <NUM>, a composite sum of the signals may be formed and scaled to maintained a desired IBO of a HPA. For example, operation <NUM> may be implemented in accordance with equation (<NUM>). At operation <NUM>, the composite sum may be processed through a model of the HPA. For example, operation <NUM> may be implemented in accordance with equation (<NUM>). At operation <NUM>, the output of operation <NUM> may be translated to the desired md th signal. At operation <NUM>, the output of operation <NUM> may be processed through a decimating filter to produce one sample per symbol at a correct timing instant. For example, operation <NUM> may be implemented in accordance with equations (<NUM>)-(<NUM>). At operation <NUM>, the output of the decimating filter may be segmented into a plurality of OFDM blocks and processed using a FFT. For example, operation <NUM> may be implemented in accordance with equations (<NUM>)-(<NUM>).

<FIG> is an operational flow diagram illustrating an example method <NUM> of creating a time-domain distortion construction (e.g., <MAT>) that may be used by transmitter-based correction <NUM> and/or receiver-based correction <NUM> to correct for distortion in accordance with implementations. As illustrated, method <NUM> may be implemented similarly to method <NUM> except that the input in this case is an input of time-domain symbols, for each signal Mc prior to being processed by an IFFT. Additionally, method <NUM> does not require performing operation <NUM>.

In implementations, a transmitter-based correction <NUM> may take the form of data predistortion that entails the successive updating of a vector of input symbols to drive the distortion vector toward zero. This data predistortion may be implemented at the symbol rate and may be placed before the transmit filters <NUM>.

By way of mathematical example, Let <MAT> be the vector of complex-valued time-domain data symbols, namely, following the OFDM modulator <NUM> in <FIG>, associated with the m th-signal at the s th-stage as <MAT> where s = <NUM>,<NUM>,···,S -<NUM> and m = <NUM>,<NUM>, ···, Mc. Also define the augmented input vector from the Mc signals participating in the correction as <MAT> The input from the previous stage <MAT> may be updated by a recursion that is intended for finding zero-crossing of an unknown function when only its noisy measurements are available as <MAT> where {µ(s)} is a step-size sequence satisfying certain conditions, including being positive and decreasing, to ensure progress toward a solution. The choice of step-size sequence {µ(s)} can be made to achieve a good compromise between convergence speed and amount of residual error. For initialization, the input to the zeroth-stage may use the undistorted vector of time-domain data symbols, or <MAT>.

In (<NUM>), <MAT> is the time-domain error vector that incorporates the distortion within the md th signal itself and the other Mc -<NUM> signals sharing the nonlinearity. More specifically, it can be mathematically described as the difference between the undistorted vector of symbols xmd and its distorted version, constructed through <MAT>, as discussed above, or <MAT> where λmd is a complex-valued gain correction aimed at removing the warping effect caused by the nonlinear distortion, obtained by <MAT>.

In an alternative implementation, the data predistortion can be implemented in the frequency domain (e.g., preceding the OFDM modulator <NUM> in <FIG>). For this case, the recursion to update the data symbols may be <MAT> where Ξ(s) is composed by stacking the predistorted frequency-domain symbols during the s th-stage from the Mc signals, or <MAT> and <MAT> For initialization, the zeroth-stage may use the undistorted vector of frequency-domain data symbols, or <MAT>. In (<NUM>), the error to be driven toward zero is computed using the frequency-domain construction <MAT> as <MAT> where λmd is a complex-valued gain correction computed as <MAT>.

<FIG> is an operational flow diagram illustrating an example method <NUM> of using a transmitter-based correction <NUM> to apply transmitter data predistortion to an OFDM-like transmission channel in accordance with implementations. It should be noted that although method <NUM> is annotated with exemplary variables and functions that may be utilized in particular mathematical implementations, described above with reference to Equations (<NUM>)-(<NUM>), method <NUM> is not limited to these particular mathematical implementations.

At operation <NUM>, a vector of time-domain symbols output by an OFDM modulator (e.g., OFDM modulator <NUM>) is received as an input at a first data predistorter stage. For example, the input vector of time-domain symbols may be an output xm of an IFFT modulator. At operation <NUM>, the first data predistortion stage outputs the received vector undistorted. For example, the vector xmd may be output.

At operations <NUM>-<NUM>, subsequent data predistortion stages may be iterated as follows. At operation <NUM>, the predistorted data from the previous s-th stage (not predistorted if previous stage is s=<NUM>) belonging to each of the OFDM-modulated signals is processed through a time-domain distortion construction to obtain an estimate of distorted symbols. For example, the predistorted data from the previous s-th stage <MAT> belonging to each of the Mc signals may be processed through the time-domain distortion construction <MAT>, discussed above, to obtain an estimate of distorted symbols that accounts for the distortion of the md th signal itself and the other Mc -<NUM> signals sharing the nonlinearity.

At operation <NUM>, the estimate of the distorted symbols may be divided by a complex-valued gain to form a gain-adjusted estimate of the distorted symbols. For example, the output of operation <NUM> may be divided by complex-valued gain λmd, discussed above with reference to Equation (<NUM>), to remove any warping effect caused by nonlinear distortion. At operation <NUM>, an estimated error may be computed by taking the difference between the input symbols (ideal data) and the gain-adjusted estimate calculated at operation <NUM>. For example, operation <NUM> may be implemented in accordance with equation (<NUM>). At operation <NUM>, the predistorted symbols for the current stage are computed by adjusting the predistorted symbols from the previous stage by an amount proportional to the error computed at operation <NUM>. For example, operation <NUM> may be implemented in accordance with equation (<NUM>).

At decision <NUM>, it is determined if there is another predistortion correction stage iteration. If there is, operations <NUM>-<NUM> may be repeated. Otherwise, at operation <NUM>, the predistortion corrected vector of time-domain symbols (e.g., <MAT>) is output.

In implementations, a receiver-based correction <NUM> may take the form of frequency-domain distortion cancellation, iteratively exchanging soft information with FEC decoders <NUM>, to provide a successively improved estimation of the transmitted symbols.

By way of mathematical example, the estimate of the nonlinear distortion that achieves minimum mean-square error (MMSE) can be represented as <MAT> where Ξ(<NUM>) is the vector containing the undistorted data symbols {Xm,n} from Mc signals as defined in (<NUM>), and L(s) denotes the LLRs on the code bits associated with all users as provided by their respective FEC decoders, after interleaving, in the previous iteration. Also, <MAT> is a vector of centroids of the frequency-domain received samples Ymd, associated with one of M possible values of the transmitted constellation symbols. The first expectation operation in (<NUM>) may be evaluated using the multicarrier Volterra formulation of <NPL>, as it would be intrinsically linear in terms of its input vector.

The case of single-user detection at the receiver (consistent with satellite broadband system transmission in the forward direction) is now considered. In this case, no information exchange occurs between user terminals sharing a transponder, only distortion from the OFDM subcarriers within the md th signal itself is incorporated. Further, a simplifying assumption may be made processing soft symbols through the distortion constructor <MAT>, i.e., moving the expectations to its input. Instead of (<NUM>), this simplified distortion estimation may be mathematically described by <MAT> Where the second argument of the distortion constructor function <MAT> is set to unity to realize single-user detection at the receiver. In (<NUM>), the components of the expectation <MAT> may be computed using the expression <MAT> where the conditional symbol probability P{Xmd,n = Xl|L(s)} is obtained by converting the bit-wise LLRs into symbol probabilities, at the s th-stage, using the bit-to-symbol labelling chosen for the constellation. The LLR computation module described above with reference to the receiver may take as input <MAT> and <MAT> to generate extrinsic likelihoods for the code bits using (<NUM>). The soft distortion cancellation technique implements subtraction of the distortion estimate <MAT>, in an iterative framework, such that at iteration s + <NUM>, <MAT>.

In implementations, the evaluation of the likelihoods in (<NUM>) may be improved by taking into account the clustering and warping induced by the nonlinear distortion. More specifically, a bivariate Gaussian model may be used. To this end, the conditional probability expression for a particular constellation point X(k), k = <NUM>,<NUM>, ···, M , expressed in the log-domain, may be <MAT> where the centroids P(k,s+<NUM>), standard deviations <MAT>, and correlation coefficient ρ(k,s+<NUM>), associated with the k th constellation point, are computed during training mode. The extrinsic information for the code bits <MAT> can be found using <MAT> of (<NUM>) in (<NUM>), and is provided as input to the FEC decoder. For initialization, the expectations <MAT> during the zeroth-stage are replaced by symbol hard decisions obtained relative to P(s=<NUM>) in the decision metric instead of the nominal signal constellation.

<FIG> is an operational flow diagram illustrating an example method <NUM> of using a receiver-based correction <NUM> in combination with LLR computation blocks to apply receiver-based soft distortion correction at the receiver to an OFDM-like channel in accordance with implementations. It should be noted that although method <NUM> is discussed in the context of exemplary variables and functions that may be utilized in particular mathematical implementations, described above with reference to Equations (<NUM>)-(<NUM>), method <NUM> is not limited to these particular mathematical implementations.

At operation <NUM>, the vector of frequency-domain symbols obtained from the receiver FFT block, Y m, where m = <NUM>,<NUM>,. Mc, is received as an input. At operation operations <NUM>-<NUM>, for the initial receiver correction iteration (e.g., s = <NUM>), make hard-decisions on Ym relative to centroids <IMG> (operation <NUM>) and process hard-decisions through the distortion construction <MAT> (operation <NUM>). For subsequent receiver correction iterations (e.g., s > <NUM>), operations <NUM>-<NUM> may be implemented. At operation <NUM>, compute symbol expectations using LLRs provided by the FEC decoders of Mc carriers. At operation <NUM>, process symbol expectations through the distortion constructor <MAT>. At operation <NUM>, perform subtractive soft-distortion cancellation by subtracting from Ymd, the output of <MAT> and conditional expectations of <IMG>, to give Ymd(s+<NUM>). At operation <NUM>, process inputs, comprising of Ymd(s+<NUM>), a priori information from FEC decoder, centroids, standard deviations and correlation coefficients through the LLR computation block. At operation <NUM>, deinterleave bit-wise LLRs obtained from the LLR computation block. At operation <NUM>, process deinterleaved bit-wise LLRs through FEC decoder to generate LLRs information required for next iteration.

At decision <NUM>, it is determined if there is additional distortion correction stage. If there is, at operation the generated LLRs may be interleaved and operations <NUM>-<NUM> may be repeated. Otherwise, at operation <NUM>, hard-decisions may be formed on the LLRs, which may be treated as an estimate of the transmitted source bits.

The performance of implementations of the OFDM signaling techniques described herein were tested. To this end, a simulation setup was implemented that considered the example OFDM-like signaling satellite communication illustrated by <FIG> and the nonlinear distortion correction using successive compensation techniques discussed above.

As in a mass-efficient broadband system, the scenario of operating the satellite transponder in a multicarrier mode where Mc independent signals share a single nonlinear transponder was considered. Results described herein are reported for the specific cases of Mc = <NUM> and Mc = <NUM>. For each individual signal into the transponder, the tested OFDM-like signaling used N-point IFFT and N-point FFT, at the transmitter and receiver, respectively, where N = <NUM>. Filters with RRC shaping and rolloff of <NUM> were applied on each signal at the transmitter, pm,T(t), and for matched filtering at the receiver, pm,R(t). The per-signal symbol rate was 37Baud, with uniform carrier spacing of Δf = <NUM> when Mc = <NUM>. A considered constellation was 16APSK with bit-to-symbol labeling as defined in the satellite standard <NPL>. Another considered constellation was 64APSK with bit-to-symbol labeling as defined in the satellite standard <NPL>.

During testing, the operating level of the HPA of the satellite transponder was expressed in terms of OBO for a modulated carrier as measured at its output. The computationally efficient module of the nonlinear distortion construction <MAT> or <MAT>, discussed above, was used with a memory span set as L=<NUM>, with an oversampling factor internally set at Nss = <NUM>. Both, the successive multicarrier data predistortion technique and the successive signal predistortion technique implemented S = <NUM> stages of successive distortion cancellation. Ideal receiver synchronization was assumed for all simulations.

Six different compensation strategies for the OFDM-like signaling system were evaluated:.

Performance comparisons were also made with a traditional system employing single carrier modulation (SCM)-based signaling, along with the enhanced receiver architecture from <NPL>, while also taking advantage of the centroid-based calculations of the bivariate Gaussian function, described herein.

<FIG> provide a comparison of the uplink (<FIG>) and downlink (<FIG>) PSDs when using a signal predistortion technique versus a data predistortion technique for the case of a single OFDM-like 16APSK signal, at their optimal OBO levels. The signal predistortion scheme is widely used in applications where the HPA and the predistorter are co-located. Methods include the classical Volterra-based inverse method, and a more recent successive signal predistortion method. However, signal predistortion is implemented at the oversampled signal after the transmit filtering operation. Thus, it requires a high sampling rate that is proportional to the product of the individual bandwidth of the signal, number of Mc signals, their frequency separation Δf, and the degree of the nonlinearity to be compensated. In addition, signal predistortion causes spectral regrowth prior to the HPA, making it less suitable for broadband satellite applications with their strict uplink emission requirements. By contrast, the data predistortion technique in accordance with implementations described herein requires a sampling rate that equals the symbol rate only, does not cause uplink spectral regrowth, and provides better performance. It may contribute to the spectral regrowth on the downlink, but this is suppressed by the OMUX filtering present on-board a satellite.

For systems employing powerful FEC codes, a signal achievable information rate (AIR) may provide valuable insights into the expected outcome of coded packet error rate (PER) simulations and can be used to provide an instructive performance comparison between the implementations described herein. The achievable information rate in these examples is defined as the maximum rate at which information can be transmitted through a desired channel and is quantified in units of bits-per-symbol. This is illustrated in <FIG> which plot the AIR, in units of bits/symbol, as a function of <MAT>, in dB, for the cases of Mc = <NUM> and Mc = <NUM>, where <MAT> is the SNR used in operating the nonlinear transponder. The ordinate values in the AIR curves are selected to align with the spectral efficiencies, in bits/symbol, made available by the modulation-coding (MODCOD) pairs within the DVB-S2X standard. Data points in <FIG> are reported at their respective optimum back-off value and are obtained by generating AIR curves over a range of OBO chosen with sufficient granularity and selecting the operating point value that minimizes the SNR at the desired AIR.

The AIR curves illustrate the effectiveness of the successive multicarrier data pre-distortion technique described herein when using OFDM-based signaling over nonlinear satellite channels. By way of example, <FIG> shows notable gains of <NUM> dB to <NUM> dB over a wide range of spectral efficiencies when using 16APSK. It is useful to note that the biggest improvement is observed at higher spectral efficiencies, thus making the data predistortion technique described herein particularly attractive in applications with high data rates. This is also evident in <FIG>, which considers the case of 64APSK and Mc = <NUM>, and in which improvements of <NUM> dB to <NUM> dB are observed over the considered range of spectral efficiency. It is also noteworthy that the data predistortion technique described herein outperforms the successive signal predistortion technique by up to <NUM> dB. AIR results are extended to cover the case of the inner signal when Mc = <NUM> for 16APSK shown in <FIG>. These point to gains of <NUM> dB to <NUM> dB over an OFDM-based system with the enhanced receiver. The data predistortion technique described herein is seen to offer an improvement of <NUM> dB to <NUM> dB over the signal predistortion technique, with larger gains noted at the higher levels of spectral efficiency.

To pursue the gains indicated in the AIR figures, the case when capacity- approaching low-density parity-check (LDPC) codes are applied to generate PER performance curves was considered. In this case, all signals used the same code rate Rc and had the same codeblock length of <NUM>,<NUM> bits. The systems using predistortion also used a receiver that employed BICM-ID where the number of internal LDPC decoder iterations was set at <NUM>, while the number of outer iterations was set at <NUM>. The receiver parameters, centroids, variances and correlation coefficients, that are used for the improved LLR computation, discussed above with reference to <FIG>, were determined using an offline training mode involving transmitting known-symbol sequences through the system model under consideration. The OFDM-based system as well as the SCM-based system, employed an enhanced receiver architecture using an LDPC decoder with <NUM> internal iterations without BICM-ID.

<FIG> is a plot showing, for a single 16APSK signal with code rate <NUM>/<NUM> passing through a nonlinear satellite transponder, modulated using six different satellite signaling schemes, the packet error rate (PER) as a function of <MAT>, in decibels. Also reported in <FIG>, denoted by bold vertical lines, are the information-theoretic SNR thresholds obtained from the AIR results in <FIG> at <NUM> bits/symbol. All curves are at their respective optimum OBO values. The PER data indicates an improvement of <NUM> dB for an OFDM-based system in accordance with the disclosure when data predistortion is applied at the transmitter. Additionally, data predistortion is <NUM> dB better than successive signal predistortion. The receiver-based successive soft distortion cancellation in accordance with the disclosure provides close to <NUM> dB improvement with OFDM-based signaling and an additional <NUM> dB improvement over a more conventional receiver-based iterative distortion cancellation scheme.

In a nonlinear satellite channel, the results of the coded simulations may be reported by plotting the total degradation (TD) required to achieve a target PER as a function of a target PER as a function of the OBO. The parameter TD, in dB, is defined as <MAT> where <MAT> is the SNR required in a linear-AWGN channel to achieve a PER of <NUM>-<NUM>.

<FIG> shows the total degradation versus OBO performance of 16APSK using the rate <NUM>/<NUM> LDPC code, in a setup of single signal per transponder. Each point on a total degradation chart represents the outcome of a complete coded error rate curve displayed at a target PER of <NUM><NUM>. From (<NUM>), it can be seen than an improvement in SNR translates directly to an improvement in total degradation. The combined solution of using data predistortion at the transmitter and soft interference cancellation at the receiver in accordance with the disclosure provides additional gain of about <NUM> dB beyond predistortion alone. In the combined solution, the estimate of the predistorted symbols are used in the distortion construction at the receiver.

<FIG> shows the total degradation versus OBO performance of 64APSK using the rate <NUM>/<NUM> LDPC code, in a setup of single signal per transponder. The data predistortion technique in accordance with the disclosure reduces the degradation of the OFDM-based system by almost <NUM> dB. The proposed receiver-based soft distortion cancellation technique in accordance with the disclosure also offers a comparable reduction in total degradation. The signal predistortion technique performs moderately worse, incurring an additional <NUM> dB in total degradation. These improvements are consistent with the margins predicted by the AIR results in <FIG> for 64APSK. In addition to a reduction in the total degradation, transmitter and receiver-based techniques in accordance with the disclosure also provide a substantial reduction in the required OBO for an OFDM-based system. As an example, <FIG> shows close to <NUM> dB and <NUM> dB reduction in required OBO when using successive data predistortion and iterative soft cancellation, respectively. Further, combined successive compensation at the transmitter and at the receiver extracts an additional <NUM> dB improvement beyond predistortion alone.

<FIG> shows the performance of the inner signal for the case when three signals share a transponder, each using 16APSK and LDPC code with rate <NUM>/<NUM>. In this case, successive multicarrier data predistortion in accordance with the disclosure can accurately reconstruct the distortion experienced by the desired signal, leading to the successful mitigation of the resulting distortion. The results indicate a reduction of close to <NUM> dB in the minimum total degradation and a <NUM> dB improvement in the required OBO. The successive signal predistortion technique is worse by <NUM> dB. As illustrated, the gap between the OFDM-based system and the SCM system with enhanced receivers is significantly smaller than what is observed in the results of single signal per transponder case. Also, the predistorted systems are within <NUM> dB of each other.

<FIG> illustrates a computer system <NUM> upon which example embodiments according to the present disclosure can be implemented. Computer system <NUM> can include a bus <NUM> or other communication mechanism for communicating information, and a processor <NUM> coupled to bus <NUM> for processing information. Computer system <NUM> may also include main memory <NUM>, such as a random access memory (RAM) or other dynamic storage device, coupled to bus <NUM> for storing information and instructions to be executed by processor <NUM>. Main memory <NUM> can also be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor <NUM>. Computer system <NUM> may further include a read only memory (ROM) <NUM> or other static storage device coupled to bus <NUM> for storing static information and instructions for processor <NUM>. A storage device <NUM>, such as a magnetic disk or optical disk, may additionally be coupled to bus <NUM> for storing information and instructions.

Computer system <NUM> can be coupled via bus <NUM> to a display <NUM>, such as a cathode ray tube (CRT), liquid crystal display (LCD), active matrix display, light emitting diode (LED)/organic LED (OLED) display, digital light processing (DLP) display, or plasma display, for displaying information to a computer user. An input device <NUM>, such as a keyboard including alphanumeric and other keys, may be coupled to bus <NUM> for communicating information and command selections to processor <NUM>.

According to one embodiment of the disclosure, OFDM-like signaling and nonlinear distortion correction, in accordance with example embodiments, are provided by computer system <NUM> in response to processor <NUM> executing an arrangement of instructions contained in main memory <NUM>. Such instructions can be read into main memory <NUM> from another computer-readable medium, such as storage device <NUM>. Execution of the arrangement of instructions contained in main memory <NUM> causes processor <NUM> to perform one or more processes described herein. One or more processors in a multi-processing arrangement may also be employed to execute the instructions contained in main memory <NUM>. In alternative embodiments, hardwired circuitry is used in place of or in combination with software instructions to implement various embodiments. Thus, embodiments described in the present disclosure are not limited to any specific combination of hardware circuitry and software.

Computer system <NUM> may also include a communication interface <NUM> coupled to bus <NUM>. Communication interface <NUM> can provide a two-way data communication coupling to a network link <NUM> connected to a local network <NUM>. By way of example, communication interface <NUM> may be a digital subscriber line (DSL) card or modem, an integrated services digital network (ISDN) card, a cable modem, or a telephone modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface <NUM> may be a local area network (LAN) card (e.g. for Ethernet™ or an Asynchronous Transfer Model (ATM) network) to provide a data communication connection to a compatible LAN. Wireless links can also be implemented. In any such implementation, communication interface <NUM> sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information. Further, communication interface <NUM> may include peripheral interface devices, such as a Universal Serial Bus (USB) interface, a PCMCIA (Personal Computer Memory Card International Association) interface, etc..

By way of example, network link <NUM> can provide a connection through local network <NUM> to a host computer <NUM>, which has connectivity to a network <NUM> (e.g. a wide area network (WAN) or the global packet data communication network now commonly referred to as the "Internet") or to data equipment operated by service provider. Local network <NUM> and network <NUM> may both use electrical, electromagnetic, or optical signals to convey information and instructions. The signals through the various networks and the signals on network link <NUM> and through communication interface <NUM>, which communicate digital data with computer system <NUM>, are example forms of carrier waves bearing the information and instructions.

Computer system <NUM> may send messages and receive data, including program code, through the network(s), network link <NUM>, and communication interface <NUM>. In the Internet example, a server (not shown) might transmit requested code belonging to an application program for implementing an embodiment of the present disclosure through network <NUM>, local network <NUM> and communication interface <NUM>. Processor <NUM> executes the transmitted code while being received and/or store the code in storage device <NUM>, or other non-volatile storage for later execution. In this manner, computer system <NUM> obtains application code in the form of a carrier wave.

The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to processor <NUM> for execution. Such a medium may take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Volatile media may include dynamic memory, such as main memory <NUM>. Transmission media may include coaxial cables, copper wire and fiber optics, including the wires that comprise bus <NUM>. Transmission media can also take the form of acoustic, optical, or electromagnetic waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD ROM, CDRW, DVD, any other optical medium, punch cards, paper tape, optical mark sheets, any other physical medium with patterns of holes or other optically recognizable indicia, a RAM, a PROM, and EPROM, a FLASH EPROM, any other memory chip or cartridge, a carrier wave, or any other medium from which a computer can read.

Various forms of computer-readable media may be involved in providing instructions to a processor for execution. By way of example, the instructions for carrying out at least part of the present disclosure may initially be borne on a magnetic disk of a remote computer. In such a scenario, the remote computer loads the instructions into main memory and sends the instructions over a telephone line using a modem. A modem of a local computer system receives the data on the telephone line and uses an infrared transmitter to convert the data to an infrared signal and transmit the infrared signal to a portable computing device, such as a personal digital assistance (PDA) and a laptop. An infrared detector on the portable computing device receives the information and instructions borne by the infrared signal and places the data on a bus. The bus conveys the data to main memory, from which a processor retrieves and executes the instructions. The instructions received by main memory may optionally be stored on storage device either before or after execution by processor.

<FIG> illustrates a chip set <NUM> in which embodiments of the disclosure may be implemented. Chip set <NUM> can include, for instance, processor and memory components described with respect to <FIG> incorporated in one or more physical packages. By way of example, a physical package includes an arrangement of one or more materials, components, and/or wires on a structural assembly (e.g., a baseboard) to provide one or more characteristics such as physical strength, conservation of size, and/or limitation of electrical interaction.

In one embodiment, chip set <NUM> includes a communication mechanism such as a bus <NUM> for passing information among the components of the chip set <NUM>. A processor <NUM> has connectivity to bus <NUM> to execute instructions and process information stored in a memory <NUM>. Processor <NUM> includes one or more processing cores with each core configured to perform independently. Alternatively or in addition, processor <NUM> includes one or more microprocessors configured in tandem via bus <NUM> to enable independent execution of instructions, pipelining, and multithreading. Processor <NUM> may also be accompanied with one or more specialized components to perform certain processing functions and tasks such as one or more digital signal processors (DSP) <NUM>, and/or one or more application-specific integrated circuits (ASIC) <NUM>. DSP <NUM> can typically be configured to process real-world signals (e.g., sound) in real time independently of processor <NUM>. Similarly, ASIC <NUM> can be configured to performed specialized functions not easily performed by a general purposed processor.

Processor <NUM> and accompanying components have connectivity to the memory <NUM> via bus <NUM>. Memory <NUM> includes both dynamic memory (e.g., RAM) and static memory (e.g., ROM) for storing executable instructions that, when executed by processor <NUM>, DSP <NUM>, and/or ASIC <NUM>, perform the process of example embodiments as described herein. Memory <NUM> also stores the data associated with or generated by the execution of the process.

As used herein, the term module might describe a given unit of functionality that can be performed in accordance with one or more embodiments of the present application. As used herein, a module might be implemented utilizing any form of hardware, software, or a combination thereof. For example, one or more processors, controllers, ASICs, PLAs, PALs, CPLDs, FPGAs, logical components, software routines or other mechanisms might be implemented to make up a module. In implementation, the various modules described herein might be implemented as discrete modules or the functions and features described can be shared in part or in total among one or more modules. In other words, as would be apparent to one of ordinary skill in the art after reading this description, the various features and functionality described herein may be implemented
in any given application and can be implemented in one or more separate or shared modules in various combinations and permutations. Even though various features or elements of functionality may be individually described or claimed as separate modules, one of ordinary skill in the art will understand that these features and functionality can be shared among one or more common software and hardware elements, and such description shall not require or imply that separate hardware or software components are used to implement such features or functionality.

Where components or modules of the application are implemented in whole or in part using software, in one embodiment, these software elements can be implemented to operate with a computing or processing module capable of carrying out the functionality described with respect thereto. One such example computing module is shown in <FIG>. Various embodiments are described in terms of this example-computing module <NUM>. After reading this description, it will become apparent to a person skilled in the relevant art how to implement the application using other computing modules or architectures.

Although described above in terms of various exemplary embodiments and implementations, it should be understood that the various features, aspects and functionality described in one or more of the individual embodiments are not limited in their applicability to the particular embodiment with which they are described, but instead can be applied, alone or in various combinations, to one or more of the other embodiments of the present application, whether or not such embodiments are described and whether or not such features are presented as being a part of a described embodiment. Thus, the breadth and scope of the present application should not be limited by any of the above-described exemplary embodiments.

Terms and phrases used in the present application, and variations thereof, unless otherwise expressly stated, should be construed as open ended as opposed to limiting. As examples of the foregoing: the term "including" should be read as meaning "including, without limitation" or the like; the term "example" is used to provide exemplary instances of the item in discussion, not an exhaustive or limiting list thereof; the terms "a" or "an" should be read as meaning "at least one," "one or more" or the like; and adjectives such as "conventional," "traditional," "normal," "standard," "known" and terms of similar meaning should not be construed as limiting the item described to a given time period or to an item available as of a given time, but instead should be read to encompass conventional, traditional, normal, or standard technologies that may be available or known now or at any time in the future. Likewise, where this document refers to technologies that would be apparent or known to one of ordinary skill in the art, such technologies encompass those apparent or known to the skilled artisan now.

The use of the term "module" does not imply that the components or functionality described or claimed as part of the module are all configured in a common package. Indeed, any or all of the various components of a module, whether control logic or other components, can be combined in a single package or separately maintained and can further be distributed in multiple groupings or packages or across multiple locations.

Claim 1:
A method (<NUM>) of applying transmitter data predistortion to an orthogonal frequency-division multiplexing, OFDM,-like transmission channel of a satellite transmitter (<NUM>) that includes an OFDM modulator (<NUM>) to modulate a plurality of data symbols output from a bit-to-symbol modulator (<NUM>) onto a plurality of OFDM subcarriers to form a plurality of OFDM modulated data symbols, wherein the method is implemented in the time domain following the OFDM modulator (<NUM>) or in the frequency domain preceding the OFDM modulator (<NUM>), the method comprising:
receiving (<NUM>), at a first data predistorter stage of a multi-stage data predistorter (<NUM>), an input vector of symbols (xmd; Xmd) obtained from a modulator (<NUM>; <NUM>) of a satellite transmitter (<NUM>);
outputting (<NUM>) the undistorted input vector of symbols (xmd; Xmd) from the first data predistorter stage;
for each data predistorter stage of the multi-stage data predistorter after the first data predistorter stage:
processing (<NUM>) a symbol data vector output of the previous sth data predistorter stage through a distortion construction <MAT> to obtain an estimate of distorted symbols;
dividing (<NUM>) the estimate of distorted symbols by a complex-valued gain (λmd) to form a gain-adjusted estimate of the distorted symbols;
estimating (<NUM>) an error <MAT> by calculating a difference between the undistorted input vector of modulated symbols (xmd; Xmd) and the gain-adjusted estimate; and
computing (<NUM>) a vector of predistorted symbols for the data predistorter stage <MAT> <MAT> by adjusting the symbol data vector output from the previous data predistorter stage by an amount proportional to the error; and
outputting (<NUM>), from the last stage of the multi-stage data predistorter, a signal comprising a predistortion corrected output vector of symbols <MAT>.