Multi-channel transmission with flexible gains

A device includes a digital frontend. The digital frontend is configured to digitally modulate symbols for digital signals of a plurality of channels according to a transmission protocol. Each channel is associated with at least one respective carrier frequency within a transmission bandwidth. The digital frontend is further configured to combine the digital signals to obtain a digital output signal. The device further includes an analog frontend having a digital-to-analog converter configured to convert the digital output signal into an analog output signal. The analog frontend also includes a programmable gain amplifier configured to apply an analog gain to the analog output signal. The device further includes a control logic configured to determine the analog gain based on calibration data indicative of the frequency response of the analog frontend across a transmission bandwidth.

This application is a National Phase entry application of International Patent Application No. PCT/US2016/069151 filed on Dec. 29, 2016, entitled “MULTI-CHANNEL TRANSMISSION WITH FLEXIBLE GAINS” in the name of Shaul Shulman et al. and is hereby incorporated by reference in its entirety.

FIELD

Various embodiments of the invention generally relate to providing an analog output signal including symbols of a plurality of channels. Various embodiments of the invention specifically relate to determining an analog gain applied to the analog output signal.

BACKGROUND

In various communication systems, multi-channel transmission is employed. Here, multiple channels are multiplexed onto a transmission spectrum, wherein different channels occupy different bandwidths (BWs) within the transmission spectrum. Each channel may include data of a certain application and/or subscriber.

Sometimes, it can be required to set a signal level—e.g., defining the power or power spectral density (PSD)—individually for each one of the plurality of channels. Different channels of the plurality of channels may employ at different signal level.

An example of a multi-channel transmission protocol is Data-Over-Cable Service Interface Specifications (DOCSIS) 3.1, Cable Television Laboratories, Inc. 2013-2016. For example, the physical layer of the DOCSIS 3.1 transmission protocol requires a specific output power for upstream transmission, see DOCSIS 3.1, Physical Layer Specification, CM-SP-PHYv3.1-109-160602, e.g., Chapter Chapters 7.4.12.2 and 7.4.12.3.

To achieve this, typically, a certain gain is set at the transmitter. For example, according to reference implementations, the analog gain may be set individually for each channel of a plurality of channels. Thereby, the gain of each channel may be set accurately and with great flexibility.

However, such techniques face certain restrictions and drawbacks. For example, according to reference implementations, an analog programmable gain amplifier may be required for each channel. Provisioning a plurality of programmable gain amplifiers can be costly. Furthermore, this may restrict the flexibility with which channels can be created or discarded.

SUMMARY

Therefore, a need exists for advanced techniques of multi-channel transmission. In particular, a need exists for techniques of multi-channel transmission which enable to flexibly set the gains for the various channels. Furthermore, a need exists for techniques of multi-channel transmission which overcome or mitigate at least some of the above-identified restrictions and drawbacks.

This need is met by the features of the independent claims. The dependent claims define embodiments.

According to examples, a device includes a digital frontend. The digital frontend is configured to digitally modulate symbols for digital signals of a plurality of channels according to a transmission protocol. Each channel is associated with at least one respective carrier frequency within a transmission bandwidth. The digital frontend is further configured to combine the digital signals to obtain a digital output signal. The device further includes an analog frontend having a digital-to-analog converter configured to convert the digital output signal into an analog output signal. The analog frontend also includes a programmable gain amplifier configured to apply an analog gain to the analog output signal. The device further includes a control logic configured to determine the analog gain based on calibration data indicative of the frequency response of the analog frontend across a transmission bandwidth.

According to an example, a method includes digitally modulating symbols for digital signals of a plurality of channels according to a transmission protocol. Each channel is associated with at least one respective carrier frequency within a transmission bandwidth. The method further includes combining the digital signals to obtain a digital output signal. The method further includes converting the digital output signal into an analog output signal. The method further includes a programmable gain amplifier applying an analog gain to the analog output signal. The method further includes determining the analog gain based on calibration data which is indicative of the frequency response of the analog frontend across the transmission bandwidth.

It is to be understood that the features mentioned above and features yet to be explained below can be used not only in the respective combinations indicated, but also in other combinations or in isolation, without departing from the scope of the present invention. Features of the above-mentioned aspects and embodiments may be combined with each other in other embodiments.

DETAILED DESCRIPTION OF EMBODIMENTS

Exemplary embodiments of the invention will be described with reference to the drawings. While some embodiments will be described in the context of specific fields of application, e.g. in the context of certain spectral ranges and communication techniques, the embodiments are not limited to this field of application. The features of the various embodiments may be combined with each other unless specifically stated otherwise.

Various techniques regarding multi-channel transmission over a transmission medium are described herein. For example, a number of 2-50 channels may be multiplexed on the transmission medium using frequency division duplex (FDD). Hence, one or more carrier frequencies of different channels may be offset from each other in frequency domain. Optionally, it is also possible to employ time division duplex (TDD). Each channel may be self-contained, i.e., decoding of a specific channel may be possible without relying on any information of a further channel. Different channels may be associated with different subscribers and/or applications.

The techniques described herein may be applied to various transmission media. Examples include wireless over-the-air communication and communication via wired transmission media such as coaxial cables and copper cables. For illustrative purposes, hereinafter, reference will be primarily made to a cable communication system such as one described by DOCSIS 3.1. However, similar techniques may be readily applied to different communication systems employing, e.g., different transmission media and/or different transmission protocols. Further examples include the Third Generation Partnership Project (3GPP) multi-carrier or carrier aggregation technology.

The techniques described herein may be employed for Internet-of-Things applications and Connected Home applications. For example, the techniques may be employed for a fast and reliable Internet connection to subscriber households.

The techniques described herein enable to flexibly and individually set gains for each channel of a plurality of channels. In other words, by the techniques described herein it is possible to flexibly and individually set the signal level of each channel of a plurality of channels. According to the techniques described herein, this may be achieved with high accuracy and hardware of reduced complexity.

For example, a cable modem communication system may include digital signal modulators configured to modulate digital signals of a plurality of channels, a digital-to-analog converter (DAC), and a programmable gain amplifier (PGA). The DOCSIS 3.1 transmission protocol requires the cable modem to transmit upstream power with high precision at a commanded signal level/output power. To achieve that, a digital gain needs to be set for the digital signals and an analog gain needs to be set for the PGA. Hereinafter, techniques are described which enable to accurately determine these gains so that the signal-to-noise ratio (SNR) of the transmitter is optimal under DOCSIS 3.1 specification restrictions.

In particular, according to some examples, it is possible that the digital signals of the plurality of channels are combined in the digital domain before digital-to-analog conversion takes place. Then, a common PGA can be used to apply an analog gain to the thus obtained combined analog output signal. Such a hardware architecture does not require multiple analog amplifiers for each digital signal of the plurality of channels. Thereby, the number of analog circuitry can be reduced. This simplifies the system architecture.

At the same time, the combined analog amplification does not compromise the flexibility of individually setting the gains for the various channels. In particular, according to various examples, it is possible to individually determine a digital gain for each digital signal of the digital signals of the plurality of channels. By using different digital gains for different channels of the plurality of channels, it is possible to provide different PSDs for different channels of the plurality of channels.

According to examples, the analog gain of the common PGA is determined based on calibration data. The calibration data is indicative of the frequency response of the analog frontend across the transmission BW. For example, the frequency response may specify an amplification characteristics and/or filtering characteristics of the analog frontend. The frequency response may specify deviations from a nominal gain as a function of frequency. For example, the PGA may amplify the analog output signal at a first frequency at a first gain which is different than second gain at which the PGA amplifies the analog output signal at a second frequency—even though the same nominal gain has been specified. Similarly, an analog filter may contribute significantly to the frequency response. By considering calibration data, it becomes possible to accurately set the signal level of the analog output signal for the various channels—even though one or more carrier frequencies of the various channels are spread across the transmission BW. For example, because the amplification characteristic of the PGA is not flat over frequency, the applied analog gain may correspond to the weakest frequency in the transmission BW or generally a low-amplification regime and the remaining frequencies in the transmission BW can be equalized by appropriately attenuating the digital signals, i.e., by appropriately setting the digital gains.

FIG. 1schematically illustrates aspects with respect to a communication system90. For example, the communication system90may employ a coaxial cable85for communication between different modems91-94. Here, the modem91may be at a central distribution point (DP). The modems92-94may be located at subscriber premises and, therefore, are sometimes referred to customer premises equipment (CPE). Hence, the DP modem91can transmit downstream (DS) data to the plurality of CPE modems92-94associated with different subscribers/users. Furthermore, the DP modem91can receive upstream (US) data from the plurality of CPE modems92-94.

Typically, the DP modem91is referred to as Cable Modem Termination System (CMTS) or head end modem. In some examples, it is possible that the DP modem91is configured different than the CPE modems92-94. For example, the DP modem91may implement different rules for determining a transmit power if compared to the CPE modems92-94. For example, the DP modem91may implement a plurality of individual nodes, each with it's own power calculation taking place.

As illustrated inFIG. 1, it is possible that the line length of the coaxial cables85is different for different modems92-94. This may be one of the reasons why transmitters of the modems91-94can be configured to flexibly set the transmission power. For example, by adjusting the transmission power based on the line length, a certain signal-to-noise ratio (SNR) may be ensured at the receiving side.

FIG. 2schematically illustrates aspects with respect to the modems91-94. The modems91-94include a transmitter96. The transmitter96may be configured to output an analog radio frequency (RF) signal (analog output signal) to the coaxial cable85. For example, the analog output signal may occupy a transmission BW having a lower band edge of 5 MHz and an upper band edge situated in the range of 5 MHz-205 MHz; this may apply, e.g., for US transmission. For DS transmission, the analog output signal may occupy a transmission BW having a lower edge situated in the range of 20 MHz-260 MHz and an upper edge situated in the range of 1200 MHz-1800 MHz. The transmitter96may include a digital frontend (DFE) configured to modulate symbols for one or more digital signals. The transmitter96may also include an analog frontend (AFE) configured to amplify and filter the analog output signal which is determined based on the one or more digital signals (inFIG. 2, both, the DFE and the AFE are not shown).

The transmitter96is controlled by a control logic95. The control logic95may be implemented as hardware and/or software. For example, the control logic95may be implemented by a microcontroller, a field programmable gate array (FPGA), a processor, etc. In some examples, the control logic95may load control instructions stored in a non-volatile memory95A and execute the control instructions; this may cause execution of techniques regarding determining of an analog gain of a PGA of the transmitter96and/or of digital gains of the transmitter96according to various techniques described herein.

FIG. 3schematically illustrates aspects with respect to the transmitter96.FIG. 3illustrates the DFE961and the AFE962. For example, the DFE961may be implemented by a system-on-chip (SOC). According to the SOC architecture, a plurality of logical blocks are integrated on the same die as digital circuitry. For example, it would be possible that the control logic95is integrated into the SOC architecture of the DFE961.

Generally, the transmitter96illustrated inFIG. 3may operate according to the DOCSIS 3.1 transmission protocol. The transmitter96illustrated inFIG. 3may implement functionality of the physical layer. The physical layer corresponds to Layer 1 of the Open Systems Interconnection (OSI) model. Hence, the transmitter96may interface the transmission medium, e.g., the coaxial cable85. It can provide for modulation of symbols.

InFIG. 3, the DFE961includes a branched architecture. In the example ofFIG. 3, the DFE961defines a number of five signal flow branches, wherein each branch is associated with a respective channel121-125.

For each channel121-125, data161-165is received. For example, the data161-165could be encoded in Layer 2 protocol data units (PDUs). The data161-165associated with the different channels121-125may encode information of different applications. For example, different applications may be associated with different TV shows, Internet data, etc. For example, the data161-165may be received as packetized data or as a data stream. Alternatively or additionally, the DS data161-165associated with the different channels121-125may be associated with different subscribers, i.e., may be intended for different CPE modems92-94.

Then, the DFE961is configured to digitally modulate symbols for digital signals171-175. For this, digital modulators101-105are implemented, e.g., in software code and/or in hardware. The digital signals171-175may correspond to a stream of data. The digital signals171-175may include padding or zero-filled periods.

The modulation is implemented in accordance with the transmission protocol. For example, according to the DOCSIS 3.1 transmission protocol, it is possible to employ different modulation schemes for modulating the symbols of different digital signals171-175. In the example ofFIG. 3, the modulators101,102are configured to modulate the respective digital signals171,172according to the Orthogonal Frequency Division Multiplexing (OFDM) modulation scheme. Here, a plurality of subcarriers is employed per channel121-125. For OFDM, different modulation formats may be employed; examples include binary phase shift keying, Quadrature phase shift keying, Quadrature Amplitude Modulation (QAM) using different constellations, e.g., in the range of 8-4096-QAM. For OFDM, different bit loading per subcarrier can be employed. Further, in the example ofFIG. 3, the modulators103-105are configured to modulate the respective digital signals173-175according to Single Carrier QAM (SC-QAM). Here, per channel123-125a single carrier frequency is employed.

Once the modulated digital signals171-175are obtained, a digital gain can be set by the digital amplifiers111-115. Sometimes, the digital gain is also referred to as digital attenuation; sometimes, digital gain and digital attenuation may be used as different representations of the same quantity. Here, the DFE961can be configured to apply a respective digital gain to each digital signal171-175. Different digital gains can be applied to different digital signals171-175. Thereby, it becomes possible to individually set the signal level of the analog output signal183for different channels121-125.

Next, the digital signals171-175—after application of the digital gain—are combined to obtain a digital output signal181. The digital output signal181is then fed to a DAC132which is configured to convert the digital output signal181into an analog output signal182. It is possible that the DAC132applies a certain gain. Also, the DAC132may add certain noise such as quantization noise and DAC aliases. An anti-aliasing filter133may be provided.

The filtered analog output signal182is then fed to the PGA134of the AFE962. The PGA134is configured to amplify the analog output signal182using a variable analog gain. Sometimes, the analog gain setting of the PGA134may be adjustable at a certain discrete adjustment increment.

In the example ofFIG. 3, a further filter135is provided before the analog output signal182—which has been amplified and filtered—is eventually output to the coaxial cable85. The filter135may be configured to filter out-of-band spurious emissions and ensure that the upstream transmissions do not generate interferences in the downstream spectrum. The filter135may contribute significantly to the frequency response of the analog frontend.

The hardware architecture of the transmitter96as illustrated inFIG. 3relies on a single PGA134which provides combined analog amplification in the analog domain. If compared to reference implementations where each channel121-125has a dedicated PGA, such a hardware architecture provides reduced complexity.

FIG. 4illustrates aspects with respect to the transmission BW401. The transmission BW401is fractioned using an FDD approach. Different channels121-125occupy different BWs.

FIG. 5is a flowchart of a method according to various examples. For example, the method according toFIG. 5could be executed by the control logic95of a respective modem91-94.

First, in block5001, an analog gain of the PGA134is determined. Next, in block5002, digital gains are determined for the digital amplifiers111-115of each channel121-125.

Then, it is possible to implement the determined analog gain and digital gains by appropriately controlling the DFE961and the AFE962.

Depending on the implementation, the method according toFIG. 5may be re-executed over the course of ongoing communication in the communication system90from time to time. Different trigger criteria for executing the method according toFIG. 5are conceivable. In one example, it would be possible that the transmission protocol defines a protected time duration during which data is not communicated on the various channels121-125. For example, a protected time duration may be used for training once the architecture of the communication system90changes, e.g., if a new modem comes online or if a modem goes off-line. Then, it would be possible that the control logic95is configured to determine the analog gain in block5001and optionally the digital gains in block5002in response to the protected time duration.

Hereinafter, various techniques of determining the analog gain in block5001and the digital gains in block5002will be described. For example, it would be possible to take into account calibration data when determining the analog gain in block5001.

FIG. 6illustrates aspects with respect to calibration data600. The calibration data is indicative of the frequency response600of the analog frontend962. The frequency response600may be influenced by the PGA134, the filter133, and/or the filter135. The frequency response600specify a dependency of the signal output power on the frequency. As can be seen from the example ofFIG. 6, a non-flat frequency response600can be encountered. For example, a low-amplification regime601is encountered where the amplification of the PGA134is particularly small. Hence, despite setting a certain nominal analog gain, certain frequencies will be amplified less than other frequencies.

For example, the calibration data600could be obtained during a calibration phase. The calibration phase may be performed in a backend test during manufacturing at the factory. It is generally possible that each individual transmitter96is calibrated; in other examples, it would be possible that a batch calibration is performed. In particular, in such an example, it is possible that the calibration data600also specifies tolerances610of the frequency response600which may originate from manufacturing spread.

Based on such calibration data600, it is possible to determine the analog gain. In an example, the calibration data may specify the frequency response of the PGA at a plurality of calibrated frequencies within the transmission BW (full circles inFIG. 6). It is then possible to interpolate the frequency response between multiple calibrated frequencies to obtain the frequency response at the carrier frequencies (non-filled circles inFIG. 6) of the plurality of channels.

For example, the calibration data600may include a calibration table which contains several frequency points. A reference frequency point may specify the absolute power of the analog output signal measured at that point, designated as Pcal_table_ref. The remaining frequency points may contain the delta between power measured at that frequency and Pcal_table_ref. Alternatively or additionally, the table may contain the absolute power at each calibrated point or at least at some calibrated points. In addition, the calibration table may be associated with the analog gain used during calibration, PGA_Setcal, the digital gains for the various digital signals used during calibration, D_Attcal, and the modulation scheme used during calibration Modcal. In some examples, such values may be indicated by the calibration table. It would also be possible that they are known to the system designer as a general framework within which the calibration table is defined.

A compensation of the frequency response based on a constellation gain difference between the modulation scheme used during calibration and at least one modulation scheme used to digitally modulate the symbols according to the transmission protocol can then be performed. After adjusting for the constellation gain difference between the constellation used in calibration and the 64QAM that is assumed in power commands in DOCSIS SC-QAM, the compensated calibration point Pcal_refis then given by:

After compensating the calibration data for the parameters of the calibrating signal, the calibration points are given by:

Each calibrated point Pcal_point_nmay be represented as the delta from a reference point or as absolute measured power at that point.
Pcal-pointk==Pcal-ref+ΔPcal-pointk

An arbitrary calibration point may be selected as a reference, e.g. the first data point in the table, and the rest of the calibration points may then be referenced to as delta from the selected reference point.

Out of all the calibration points over frequency, a single value is then assigned for each channel121-125, Pcal_channel_n, by means of first linearly interpolating the calibration points (compensated for the parameters of the calibrating signal) and then averaging the points that belong to the channel's frequency band.

The analog gain may be determined by mapping the low-amplification regime601of the frequency response to a predefined target output power. For example, the analog gain may be determined relative to the frequency point where minimum power was measured during calibration to guarantee sufficient gain for any frequency: Pcal_mindenotes the lowest power that was measured in the relevant frequency band during calibration.
Pcal-min[dBmV]=Pcal_ref+min[ΔPcal_point1. . . ΔPcal_pointcal_table_size]=min[Pcal_point1. . . Pcal_pointcal_table_size]  (2)

In one example, it is possible to determine the analog gain based on a reference signal level of the digital output signal. For example, the reference signal level may correspond to an upper boundary of a dynamic range window of the transmission protocol. For example, in the context of DOCSIS 3.1 the reference signal level may be specified as the maximum equivalent channel power P1.6hi, see DOCSIS 3.1, Physical Layer Specification, CM-SP-PHYv3.1-109-160602, chapter 7.4.12.2 Transmit Power Requirements.

In DOCSIS3.1, the commanded power per 1.6 MHz for digital signal/channel n is designated as P1.6r_nor P1.6c_n, the maximum power per 1.6 MHz is designated as P1.6hiand the back-off of all channels from P1.6hiis designated as P1.6load_min_set. When the power of a digital signal is within the dynamic rage window, fidelity requirements are to be met. A typical size of the dynamic range window is 12 dB. P1.6load_nof each digital signal during operation may be higher than P1.6load_min_set, but the digital signal power levels may be increased so that P1.6load_n=P1.6load_min_setand the fidelity requirements would still need to be met. The commanded power P1.6c_nshould be within the dynamic range window.

Then, the total power output across all frequencies when all digital signals corresponding to the various channels are at the top of the dynamic range window equals to:

The first step is to calculate the required PGA gain for the low amplification regime601, limited to maximal gain setting:
PGA_Setcalc=PGA_Setcal+Pdrw_top_total(RF_Out)−Pcal_min, and  (4)
PGA_Setstep1=min(PGA_Setmax,roundup(PGA_Setcalc)).  (5)

PGA_Setcalcaccording to Eq. (4) is the “ideal” setting that would bring the output power to the target output power, not constrained by the actual range and granularity of the gain of a PGA.

PGA_Setstep1according to Eq. (5) is the actual PGA gain setting, found by rounding up PGA_Setcalcto the nearest existing PGA gain setting and clipping it if the result is above the max available setting. For example, the PGA may provide the adjustable analog gains with a certain granularity or minimum step width so that discrete settings are available. In other words, the PGA may be configured to implement different analog gains at a certain adjustment increment. The roundup calculation allows to identify the difference between the determined analog gain and the adjustment increment of the PGA.

Sometimes, the PGA may have a certain tolerance of amplification or, generally, there may be a tolerance specified for the frequency response. For example, certain gain settings may be associated with an inaccuracy. For example, if a nominal analog gain is applied, the actual amplification may deviate. This is schematically indicated inFIG. 6by the error bars. It is possible to determine the analog gain further based on this tolerance. Since the PGA may have inaccuracy in the gain step, it can be desirable to verify that the actual PGA gain is not too low. This can be done to avoid an error in the output power or a potential violation of the target back-off if the error is compensated for by digital gain.

The correction that may be applied when using the PGA_Setstep1setting to get the desired gain is given by:
Corrstep1=PGA_Setcalc−[PGA_Setstep1+PGA_Gain_Step_Err(PGA_Setstep1)−PGA_Gain_Step_Err(PGA_Setcal)],  (6)
where PGA_Gain_Step_Err is a lookup table containing the cumulative error from a specific gain setting to all other gain settings. This table may be obtained from characterization of gain errors of large number of PGA components of the same model.

Corrstep1is indicative of how much gain is lacking. If Corrstep1is negative then there is no lack of gain. If the number is positive, i.e., correction should be applied, then the gain deficit can be compensated for by increasing the analog gain setting accordingly. For example, if there is 1.4 dB gain deficit and PGA adjustment increment is 1 dB, the analog gain of the PGA134may be increased by 2 dB and the digital gains may be reduced for all digital signals171-175by 0.6 dB. Thus, generally, it is possible to determine the digital gains of the digital signals based on the determined analog gain.

The updated setting can be calculated as:

PGA_Setcomp={PGA_Setstep⁢⁢1when⁢⁢Corrstep⁢⁢1<0PGA_Setstep⁢⁢1+roundtop⁡(Corrstep⁢⁢1)otherwise,(7)
where PGA_Setcompis the analog gain compensated for the potential lack of gain due to the finite adjustment increment.

To get the final analog gain, PGA_Setcompmust be limited to the maximum available setting if it is above PGA_Setmaxsetting, i.e., the maximum setting available by the PGA.
PGA_Set=min(PGA_Setmax,PGA_Setcomp)  (8)

PGA_Set is the analog gain programmed to the PGA.

Once the analog gain has been determined, the digital gains for the various digital signals171-175can be determined. In other examples, it would also be possible to first determine the digital gains and then determine the analog gain.

For example, the digital gains of the digital signals171-175may be determined by mapping a reference signal level of the digital output signal to a predefined input signal level of the DAC. For example, the reference signal level of the digital output signal may correspond to the upper boundary of a dynamic range window of the transmission protocol, i.e., where all digital signals171-175are at their respective upper boundary permissible under the transmission protocol. This enables calculating digital gains and the analog gain such that when all digital signals171-175are commanded to be at the upper boundary of the dynamic range window, the DAC will be optimally loaded, i.e., the signal level of the digital output signal is at the target back-off from full-scale of the DAC. Clipping is avoided. Optimally loading the DAC reduces clipping; while at the same time increasing the available dynamic range, because the signal is as high above noise floor as possible, but not too high to keep clipping at a low level.

FIG. 7illustrates aspects with respect to a dynamic range window701of the digital signals171-175and, hence, of the digital output signal181. InFIG. 7, the upper boundaries711and lower boundaries712of the dynamic range windows of the various digital signals171-173are illustrated (while, for sake of simplicity, inFIG. 7the dynamic range windows701are only illustrated for the digital signals171-173, similar dynamic range windows could be defined for all digital signals171-175; generally, there may be more or fewer channels, e.g., ten channels). These are defined according to DOCSIS 3.1, Physical Layer Specification, CM-SP-PHYv3.1-109-160602, chapter 7.4.12.2 Transmit Power Requirements.

For determining the digital gains, a reference digital gain per digital signal171-175can be determined. For example, this reference digital gain can be defined as the digital gain that would bring the RMS level of that digital signal171-175to be at the target back-off752of the DAC132against its maximum (full scale) input level751. Digital signal RMS that is backed off from the digital full scale value by X dB will normally result in analog signal RMS at the output that is backed off from the analog full-scale output power by the same X dB.

Reference_Channel⁢_Gainn==Valpeak⁡(DAC_In)DAC_Gain*10(TBOF⁡[dB]20)*Init_val⁢_RMSchanneln*Fixed_Gainchanneln,(9)
where Init_val_RMSchannel_nis the root mean square (RMS) value of the digital samples of channel n, before application of any variable gain, Fixed_Gainchannel_nis the constant gain of the channel that depends on the channel type, Valpeakis the input value to the DAC that sets maximum voltage at the output, DAC Gain is the digital gain that is applied to the sum of all channels.

The parameter TBOF specifies the target backoff752provided as headroom to avoid clipping at the DAC. This specifies a predefined input signal level of the DAC.

Here, the same reference digital gain can be obtained for all SC-QAM modulated digital signals.

Eq. 9 can also be re-written for a digital signal171-172employing OFDM modulation:

Here, different reference digital gains can be obtained for different digital signals171-172using OFDM modulation, depending on the frequencies.

Based on the reference digital gains according to Eqs. 10 and 11, the digital gain for the various digital signals171-175can be determined based on one or more of the following parameters: Overall modulated BW (FBW), see Eq. 12; Frequency response (Ffr_response), see Eq. 13; Commanded power P1.6c_n(Fpwr), see Eq. 14; Commanded power offset related to the configuration of a channel, e.g. to account for boosted pilots in OFDMA (Fconfig); Compensation of the gain deficit for the used PGA gain setting (FPGAcomp), see Eq. 16. I.e., the required analog gain as determined and the actual analog gain that can be set resulting from the adjustment increment of the PGA may differ. This relates to a difference between the determined analog gain and an adjustment increment of the PGA.

A cumulative correction value with respect to the reference digital gain is given by:
Attn=FBWn+Ffr_responsen+Fpwrn+Fconfign+FPGA-comp(17)

The digital gain for each digital signal173-175modulated by SC-QAM is given by:

The digital gain for each digital signal171-172modulated by OFDM is given by:

Summarizing, above techniques have been described which enable to determine the digital gains of a plurality of digital signals which are then combined to a digital output signal. The digital output signal is converted to an analog output signal which is again amplified by a PGA at an analog gain.

Determination of the digital gains and the analog gain receives as inputs the calibration data of the PGA, i.e., characterization results of the PGA, the number of digital signals, the BW of each digital signal, the commanded signal levels per digital signal, e.g., according to a transmission protocol, and the desired back-off from full scale of the DAC to avoid clipping. Then, the digital gains of the digital signals and the analog gain are determined such that the combined SNR which includes thermal noise and digital quantization noise is optimized.

For illustrative purposes, while above various techniques have been described with respect to US communication, similar techniques may be readily employed for DS communication.

Likewise, while above techniques have been described for DOCSIS 3.1 transmission, similar techniques may be readily applied for other multi-carrier transmission protocols.