Digital Predistortion for Cognitive Radio

Abstract

Embodiments of cognitive radio technology can recover and utilize under-utilized portions of statically-allocated radio-frequency spectrum. A plurality of sensing methods can be employed. Transmission power control can be responsive to adjacent channel measurements. Digital pre-distortion techniques can enhance performance. Embodiments of a high DNR transceiver architecture can be employed.

Description

BACKGROUND

1. Field of the Invention

The inventions herein described relate to systems and methods for cognitive radio.

2. Description of the Related Art

Spectrum Utilization Problems

A recent study by the FCC Spectrum Task Force [United States' Federal Communications Commission (FCC), “Report of the spectrum efficiency working group,” November 2002, http://www.fcc.gov/sptf/files/IPWGFinalReport.pdf] found that while the available spectrum becomes increasingly scarce, the assigned spectrum is significantly underutilized. This imbalance between spectrum scarcity and spectrum underutilization is especially inappropriate in this Information Age, when a significant amount of spectrum is needed to provide ubiquitous wireless broadband connectivity, which is increasingly becoming an indispensable part of everyday life.

Static spectrum allocation over time can also result in spectrum fragmentation. With lack of an overall plan, spectrum allocations in the US and other countries over the past several decades can appear to be random. Despite some efforts to serve best interests at the time, this leads to significant spectrum fragmentation over time. The problem is exacerbated at a global level due to a lack of coordinated regional spectrum assignments. In order to operate under such spectrum conditions, a device can benefit from operational flexibility in frequency and/or band shape; such properties can help to maximally exploit local spectrum availability.

To address the above problems, an improved radio technology is needed that is capable of dynamically sensing and locating unused spectrum segments, and, communicating using these spectrum segments while essentially not causing harmful interference to designated users of the spectrum. Such a radio is generally referred to as a cognitive radio, although strictly speaking, it may perform only spectrum cognition functions and therefore can be a subtype of a broad-sense cognitive radio [J. M. III, “Cognitive radio for flexible mobile multimedia communications,” Mobile Networks and Applications, vol. 6, September 2001.] that learns and reacts to its operating environment. Key aspects of a cognitive radio can include:

Sensing: a capability to identify used and/or unused segments of spectrum.

Flexibility: a capability to change operating frequency and/or band shape; this can be employed to fit into unused spectrum segments.

Non-interference: a capability to avoid causing harmful interference to designated users of the spectrum.

Such a cognitive radio technology can improve spectrum efficiency by dynamically exploiting underutilized spectrum, and, can operate at any geographic region without prior knowledge about local spectrum assignments. It has been an active research area recently.

FCC Spectrum Reform Initiatives

FCC has been at the forefront of promoting new spectrum sharing technologies. In April 2002, the FCC issued an amendment to Part 15 rules that allows ultra-wideband (UWB) underlay in the existing spectrum [FCC, “FCC first report and order: Revision of part 15 of the commission's rules regarding ultra-wideband transmission systems,” ET Docket No. 98-153, April 2002]. In June 2002, the FCC established a Spectrum Policy Task Force (SPTF) whose study on the current spectrum usage concluded that “many portions of the radio spectrum are not in use for significant periods of time, and that spectrum use of these ‘white spaces’ (both temporal and geographic) can be increased significantly”. SPTF recommended policy changes to facilitate “opportunistic or dynamic use of existing bands.” In December 2003, FCC issued the notice of proposed rule making on “Facilitating Opportunities for Flexible, Efficient and Reliable Spectrum Use Employing Cognitive Radio Technologies” [FCC, “Facilitating opportunities for flexible, efficient, and reliable spectrum use employing cognitive radio technologies,” ET Docket No. 03-108, December 2003] stating that “by initiating this proceeding, we recognize the importance of new cognitive radio technologies, which are likely to become more prevalent over the next few years and which hold tremendous promise in helping to facilitate more effective and efficient access to spectrum.”

While both UWB and cognitive radio are considered as spectrum sharing technologies, their approaches to spectrum sharing are substantially different. UWB is an underlay (below noise floor) spectrum sharing technology, while cognitive radio is an overlay (above noise floor) and interlay (between primary user signals) spectrum sharing technology as shown in FIG. 1. Through sensing combined with operational flexibility, a cognitive radio can identify and make use of spectral “white spaces” between primary user signals. Because a cognitive user signal resides in such “white spaces”, high signal transmission power can be permitted as long as signal power leakage into primary user bands does not embody harmful interference.

Broadcast TV Bands

Exemplary broadcast TV bands are shown in Graph 200 of FIG. 2. Each TV channel is 6 MHz wide. Between 0 and 800 MHz, there are a total of 67 TV channels (Channels 2 to 69 excluding Channel 37 which is reserved for radio astronomy). The NPRM [FCC, May 2004, op. cit.] excludes certain channels for unlicensed use: Channels 2-4, which are used by TV peripheral devices, and Channels 52-69, which are considered for future auction. Among the channels remaining, Channels 5-6, 7-13, 21-36, and 38-51 are available for unlicensed use in all areas. Unlicensed use in Channels 14-20 is allowed only in areas where they are not used by public safety agencies [FCC, May 2004, op. cit.].

It can be appreciated that Channels 52-69 are currently used by TV broadcasters and it is not clear if/when they will be vacated. There is significant interference in the lower channels 5-6 and 7-13. Based on these considerations, the spectrum segment 470-806 MHz covering TV channels 14-69 can be of particular interest.

Spectrum Opportunity in the TV Bands

Spectrum opportunity can be a direct result of incumbent system inefficiency. In TV bands, a signal from a TV tower can cover an area with a radius of tens of kilometers. TV receivers can be sensitive to interference such that TV cell planning may be very conservative to ensure there is essentially no co-channel interference. This can leave a substantial amount of “white spaces” between co-channel TV cells as illustrated in the Map 300 of FIG. 3. Those “white spaces” can constitute an opportunistic region for cognitive users on a particular TV channel. Each TV channel may have a differently shaped opportunistic region. The total spectrum opportunity at any location can comprise the total number of opportunistic regions covering the location. A measurement in one locality shows an average spectrum opportunity in TV channels 14-69 of about 28 channels; that can be expressed as an equivalent bandwidth of approximately 170 MHz.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 Graph of spectrum sharing technologies: UWB and cognitive radio.

FIG. 2 Graph of exemplary television channel bands.

FIG. 3 Map of television co-channel coverage areas and opportunistic region.

FIG. 4 Diagram of a cognitive radio system.

FIG. 5 Graph of a DTV transmission mask.

FIG. 6 Graph of simulated non-linearities.

FIG. 7 Diagram of an adjacent channel interference situation.

FIG. 8 Diagram of an adjacent channel measurement based adaptive transmission power control system.

DETAILED DESCRIPTION

FIG. 4 depicts an embodiment of a cognitive radio system in block diagram. A transceiver 401 can be coupled with and/or in communication with one or more antennae 402. Baseband signal processing can be provided by elements of a baseband processor 403. Elements of a baseband processor 403 can comprise a sensing processor 404, a transmit power control element 405, and a pre-distortion element 406. In some embodiments a pre-distortion element 406 can be coupled with and/or in communication with a transceiver 401. In some embodiments a transmit power control element can be coupled with and/or in communication with a transceiver 401. In some embodiments a collective sensing element 407 can be coupled with and/or in communication with a baseband processor 403 and/or elements comprising a baseband processor.

In some embodiments transceiver 401 can comprise transceiver and/or transmitter and/or receiver mechanisms disclosed herein. In some embodiments sensing element 404 can comprise one or more sensing mechanisms as described herein. By way of example and not limitation these sensing mechanisms can include energy sensing, NTSC signal sensing, and/or ATSC signal sensing. In some embodiments a collective sensing element 407 can provide collective sensing mechanisms as described herein.

In some embodiments transmit power control 405 can support adaptive transmit power control mechanisms described herein. In some embodiments pre-distortion element 406 can provide digital pre-distortion mechanisms as described herein.

In some embodiments baseband processor 403 can support additional processing mechanisms as described herein. By way of example and not limitation these mechanisms can include filtering and/or reconstruction.

Adaptive Transmission Power Control:

In some embodiments, a cognitive user device (cognitive user) can transmit on a channel after determining that channel to be vacant through sensing. The TV-band NPRM [FCC, May 2004, op. cit.] allows a maximum transmission power of 30 dBm (1 W). However, because of transmitter windowing and nonlinearity, a portion of cognitive user transmission power can leak into the adjacent channels and can create adjacent channel interference. Adjacent channel interference can be maintained below a specified level in order to guarantee performance in adjacent channels. Maximum transmission power from a cognitive user can be limited by such an adjacent channel interference requirement. Adaptive transmission power control can be performed by a cognitive user in order to optimize and/or maximize transmission potential for a specified channel while causing essentially no harm to operational use of adjacent channels.

Adjacent Channel Interference Requirement:

The FCC may adopt the DTV transmit mask as shown in the graph 500 of FIG. 5 for a TV-band cognitive radio. This can define exemplary constraints for a cognitive radio transmitter, notably regarding interference with adjacent channels.

Graph 600 of FIG. 6 illustrates simulations of signal power spectra for embodiments of a transmitter with specified nonlinearities. These spectra illustrate exemplary leakage behavior in some transmitter embodiments.

Given a specified inband signal transmission power P_TX, an amount of adjacent channel leakage (ACL) can be expressed in decibel (dB) units as:

P _ACL =P _TX −R _ACL  (1)

where R_ACL 701 is a ratio between inband signal power and out-of-band leakage power due to a combined effect of windowing and nonlinearity, as discussed herein with regards to non-linearity analysis and simulation. In practice, leakage can typically be dominated by transmitter nonlinearity as shown in FIG. 6 such that (in dB units):

R_ACL=2D  (2)

where D is the IP3 (third-order intercept point) clearance of Equation (19) discussed herein. In some embodiments, a digital pre-distortion technique can further reduce the above leakage. In some embodiments a digital predistortion technique can further reduce the above leakage by approximately 20 dB.

The graph 700 of FIG. 7 illustrates an adjacent channel interference situation wherein a signal transmission on a cognitive user channel 702 can cause interference to one or more adjacent TV channels 703704. A maximum tolerable interference on a TV channel can be specified by a desired-to-undesired ratio (DU ratio), R_DU 705. In some embodiments, R_DU 705 can have a typical value of approximately 30 dB. A maximum allowable interference power P_ACL 706 at any TV receiver can be expressed as a received TV signal power P_TV minus a DU ratio in dB units, i.e.

A _ACL =P _TV −R _DU  (3)

In order to set an interference-free condition that can be guaranteed on both adjacent TV channels,

P_TV=min{P_TVL,P_TVR}  (4)

where P_TVL 708 and P_TVR 710 are received signal powers on left and right adjacent TV channels, respectively.

Combining equations (1) and (3), a cognitive user transmission power requirement P_TX 712 can be obtained (in dB):

P _TX =P _TV −R _DU +R _ACL  (5)

Equation (5) expresses a cognitive user transmission power requirement for a TV receiver disposed at essentially the same location as a cognitive transmitter. However, in some embodiments, each cognitive transmitter can have a specified clearance region within which interference can be ignored. In the TV-band NPRM [FCC, May 2004. op. cit.], a radius of such a clearance region is specified as 10 meters. A worst-case interference can occur at an edge of a clearance region. Signal power loss K (r₀) from a transmitter to an edge of the clearance region can be derived from the Friis free-space equation [T. S. Rappaport, op. cit.]. Thus a cognitive user transmission power requirement P (r₀) can be expressed:

P(r₀)=P_TV−R_DU+R_ACLP_TX=P_TV−R_DU+R_ACL+K(r₀)  (6)

In an exemplary embodiment, P_TV=−60 dBm, R_DU=30 dB, R_ACL=60 dB, and K(r₀)=48 dB, so a maximum allowed cognitive user transmission power can be:

P _TX=−60−30+60+48=18 dBm  (7)

or approximately 60 mW.

Reducing adjacent channel leakage ratio—through windowing and/or digital pre-distortion techniques—can be key to increasing cognitive user transmission power allowed. A 10 dB reduction in R_ACL can result in a tenfold increase in allowed transmission power.

Adaptive Transmission Power Control:

Cognitive user transmission power for a specified channel can be maximized while causing less than a harmful level of interference in adjacent channels; cognitive user transmission power can be responsive to received signal powers on adjacent TV channels in accord with Equations (4) and (6).

In some embodiments that employ collective sensing techniques, each cognitive user can periodically broadcast its sensing results in a specified manner; such results can comprise per channel SNR estimates. By collecting sensing results, in some embodiments a cognitive user can obtain a consensus estimate of signal power on one or more specified channels. Estimated signal powers on adjacent channels can then be used to derive a suitable transmission power using Equations (4) and (6). It can be appreciated that if one of the adjacent channels is deemed vacant, that vacant channel can be advantageously removed from consideration in equation (4). An adjacent channel leakage ratio R_ACL in equation (6) can be obtained based on pre-tabulated transmitter nonlinearity characteristics and/or through active monitoring of a transmitted signal in an embodiment employing a digital predistortion technique.

Diagram 800 of FIG. 8 depicts a system embodiment of adjacent channel measurement based adaptive transmission power control. A cognitive radio receiver RX 806 can receive a broadcast signal from antenna 802 via coupler 804. The receiver RX 806 can provide processing to a received signal (e.g., a broadcast signal) so as to provide specified bands and/or channels to a power measurement and control unit PMC 801. PMC 801 can comprise power measurement elements 810812814 corresponding respectively to adjacent left channel signal power P_TVL, adjacent right channel signal power P_TVR, and adjacent channel leakage ratio R_ACL. Each of the elements 810812814 can operate on a signal received from RX 806 to provide a corresponding power measurement; P_TVL, P_TVR, and R_ACL respectively. PMC 801 can further comprise elements that provide specified parameters: desired-to-undesired ratio R_DU and clearance region attenuation K(r₀). A control element 820 can receive parameters P_TVL, P_TVR, R_ACL, R_DU, and K(r₀) from respectively corresponding elements 810812814816818 and responsively provide a control signal to cognitive radio transmitter TX 808. Control element 820 can process parameters P_TVL, P_TVR, R_ACL, R_DU, and K(r₀) according to Equation (6) and provide a control signal to TX 808 that specifies a power transmission level P_TX as specified by Equation (6), given the values of the parameters supplied by elements 810812814816818. Cognitive transmitter TX 808 can be adapted to provide transmission power P_TX for a channel at a level specified by a control signal received from control element 820. It can be appreciated that control element 820 can also provide evaluation of Equation (4), so as to provide a P_TV term to Equation (6) from the contributing parameters P_TVL and P_TVR. Thus, TX 808 can provide cognitive radio transmission of a channel through antenna 802 via coupler 804 at an advantageous power level P_TX specified by control element 820 and corresponding to Equation (6). It can be appreciated that in some embodiments this system comprises an adaptive system; a provided power transmission level P_TX can change, that is, adapt, over time and in response to variations of specified and/or measured parameters.

Transmitter Nonlinearity Analysis and Simulation:

Transmitter nonlinearity can be a cause of adjacent channel leakage. A transmitter nonlinearity can be modeled as:

y(t)=α₀+α₁x(t)+α₂x²(t)+α₃x³(t)+ . . .  (8)

For a passband signal with appropriate filtering, a nonlinearity model can be approximated as:

y(t)≈α₁x(t)+α₃x³(t)  (9)

and an equivalent baseband representation of a signal that has experienced such nonlinearity can be expressed as

$\begin{array}{cc}y\left(t\right)={\alpha }_1s\left(t\right)+\frac{3{\alpha }_3}{4}{s\left(t\right)}^2s\left(t\right)\mathrm{Let}& \left(10\right)\\ y_1\left(t\right)=s\left(t\right)& \left(11\right)\\ y_3\left(t\right)={s\left(t\right)}^2s\left(t\right)& \left(12\right)\end{array}$

Using a baseband signal expression for s(t), it follows that:

$\begin{array}{cc}\begin{array}{c}{Y}_1\left(f\right)={\int }_{-\infty }^{\infty }y_1\left(t\right){}^{-\mathrm{j2\pi }ft}t\\ =\sum _{k\in \Omega }X\left(k\right){\int }_{-\infty }^{\infty }h\left(t\right){}^{\mathrm{j2\pi }\frac{k}{T}t}{}^{-\mathrm{j2\pi }ft}t\\ =\sum _{k\in \Omega }X\left(k\right)H\left(f-\frac{k}{T}\right)\end{array}\mathrm{and}& \left(13\right)\\ \begin{array}{c}{Y}_3\left(f\right)={\int }_{-\infty }^{\infty }y_3\left(t\right){}^{-\mathrm{j2\pi }ft}t\\ ={\int }_{-\infty }^{\infty }s\left(t\right)s\left(t\right)s^{*}\left(t\right){}^{-\mathrm{j2\pi }ft}t\\ =\sum _{k,l,m\in \Omega }X\left(k\right)X\left(l\right)X^{*}\left(m\right){\int }_{-\infty }^{\infty }g\left(t\right){}^{\mathrm{j2\pi }\frac{k+l-m}{T}t}{}^{-\mathrm{j2\pi }ft}t\\ =\sum _{k,l,m\in \Omega }X\left(k\right)X\left(l\right)X^{*}\left(m\right)G\left(f-\frac{k+l-m}{T}\right)\end{array}& \left(14\right)\end{array}$

where in the second equality

g(t)=h³(t)  (15)

whose Fourier transform can be expressed as

G(f)=H(f)H(f)H(f)  (16)

Note that the window h(t) is a real function.

A signal spectrum can be expressed

$\begin{array}{cc}\begin{array}{c}Y\left(f\right)={\alpha }_1Y_1\left(f\right)+\frac{3{\alpha }_3}{4}Y_3\left(f\right)\\ ={\alpha }_1\sum _{k\in \Omega }X\left(k\right)H\left(f-\frac{k}{T}\right)+\frac{3{\alpha }_3}{4}\sum _{k,l,m\in \Omega }X\left(k\right)X\left(l\right)X^{*}\left(m\right)G\\ \left(f-\frac{k+l-m}{T}\right)\end{array}& \left(17\right)\end{array}$

and the power spectrum can be expressed

$\begin{array}{cc}\begin{array}{c}I\left(f\right)=E\left[{Y\left(f\right)}^2\right]\\ =E\left[\left\{{\alpha }_1Y_1\left(f\right)+\frac{3{\alpha }_3}{4}Y_3\left(f\right)\right\}\left\{{\alpha }_1Y_1^{*}\left(f\right)+\frac{3{\alpha }_3}{4}Y_3^{*}\left(f\right)\right\}\right]\\ ={\alpha }_1^2E\left[{Y_1\left(f\right)}^2\right]+2{\alpha }_1\frac{3{\alpha }_3}{4}\mathrm{Re}\left\{E\left[Y_3\left(f\right)Y_1^{*}\left(f\right)\right]\right\}+\\ {\left(\frac{3{\alpha }_3}{4}\right)}^2E\left[{Y_3\left(f\right)}^2\right]\end{array}& \left(18\right)\end{array}$

A relationship between device nonlinearity coefficients α₁ and α₃ can be expressed in terms of a two-tone IP3. Specifically, input power to the two-tone test can be P_In at a distance D (in dB units) from an IP3 point P_IP3, i.e.

P_IP3=Dα₁²P_In  (19)

it follows that

$\begin{array}{cc}\frac{3{\alpha }_3}{4}=-\frac{{\alpha }_1^3}{P_{\mathrm{IP}3}}=-\frac{{\alpha }_1}{{\mathrm{DP}}_{\mathrm{In}}}& \left(20\right)\end{array}$

where compressive third-order nonlinearity can be assumed with α₃<0. A multi-carrier (such as OFDM) signal of substantially the same input power can be applied to a nonlinear device; the output power spectrum can be expressed

$\begin{array}{cc}I\left(f\right)={\alpha }_1^2E\left[{Y_1\left(f\right)}^2\right]-2{\alpha }_1^2\frac{1}{{\mathrm{DP}}_{\mathrm{In}}}\mathrm{Re}\left\{E\left[Y_3\left(f\right)Y_1^{*}\left(f\right)\right]\right\}+{\alpha }_1^2\frac{1}{D^2P_{\mathrm{In}}^2}E\left[{Y_3\left(f\right)}^2\right]& \left(21\right)\end{array}$

where the input power of the multi-carrier signal can be expressed

$\begin{array}{cc}\begin{array}{c}{P}_{\mathrm{In}}=E\left[\frac{1}{T_W}{\int }_{-\infty }^{\infty }{y_1\left(t\right)}^2t\right]\\ =E\left[\frac{1}{T_W}{\int }_{-\infty }^{\infty }{Y_1\left(f\right)}^2f\right]\\ =\frac{1}{T_W}{\int }_{-\infty }^{\infty }E\left[{Y_1\left(f\right)}^2\right]f\end{array}& \left(22\right)\end{array}$

The graph 600 of FIG. 6 shows simulated multi-carrier signal power spectrums at different IP3s (or different Ds). Nonlinearity can cause spectrum “shoulders” in adjacent bands. A difference (in decibel units, (dB)) between inband signal power and the shoulder can be roughly 2D, or the system dynamic range P_DR.

The graph 600 illustrates simulated signal power spectra under varying device nonlinearities in a multi-carrier system with subcarrier spacing 100 kHz, β=0.16, number of guard band subcarriers 8 (and number of valid data subcarriers 52). Individual curves 602604606608 are shown for IP3-related distance D values of (respectively) 15 dB, 25 dB, 35 dB, and ∞.

In some embodiments with a fixed output power, a higher device IP3 can be required in order to reduce adjacent channel leakage. In some embodiments, an IP3 requirement can be reduced by applying a digital predistortion technique and/or process.

Digital Predistortion:

Diagram 900 depicts an embodiment of a system adapted to provide digital predistortion. An RF signal can be coupled with an antenna 902 for transmission. A signal representative of such a transmitted signal can be obtained via a coupling device 904; such a representative signal can be of significantly lower power than the transmitted signal. A representative signal can be down-converted, sampled, and fed back to a baseband distortion estimator where it can be compared with a corresponding source baseband signal in order to estimate distortion. In the depicted embodiment 900, down-conversion can be provided by an RF down-converter 906, sampling and conversion to a digital representation can be provided by an analog to digital converter ADC 908, and a baseband distortion estimator BDE 910 can provide comparison and/or estimation. Resulting distortion information can be provided to a baseband pre-distortion generator such as BPG 908. BPG 908 can pre-compensate a baseband signal for distortion that the signal can be expected to experience as it passes through elements of a transmitter RF chain. That is, a signal can be pre-compensated for estimated distortion. It can be appreciated that an estimated distortion can comprise contributions from any and/or all nonlinear elements in a transmitter chain. In some typical embodiments a major contribution to distortion can be attributed to a power amplifier such as PA 914 depicted in Diagram 900. In some embodiments, a distortion compensation loop such as the system of Diagram 900 can run continuously during a signal transmission process in order to track and/or adapt to any variations of transmitter nonlinearity. By way of non-limiting example, in some embodiments a distortion compensation loop—that is, a digital predistortion system—can track and/or adapt to a transmitter nonlinearity corresponding to variations in temperature.

In some embodiments, a baseband distortion estimator BDE 910 can determine and/or provide a distortion factor, herein described, to a baseband predistortion generator BPG 912. In some embodiments, a baseband predistortion generator can operate on a baseband signal s(t) to provide a predistorted signal s_PD(t), as specified herein, to an RF transmission chain. An RF transmission chain can comprise a digital to analog converter DAC 914, an RF upconverter 916, and a power amplifier PA 918, as depicted in Diagram 900. A baseband predistortion generator BPG 912 can be adapted to provide a predistorted signal s_PD(t) responsive to a baseband signal s(t) and a distortion factor, as specified by Equation (30).

In some embodiments, information provided to a baseband predistortion generator BPG 912 from a baseband distortion estimator BDE 910 can comprise any known and/or convenient representation of nonlinearity terms. By way of non-limiting example, such nonlinearity terms can comprise coefficients of a nonlinearity model such as those of Equation (8).

In a multi-carrier system, after appropriate signal processing, e.g. window truncation and FFT, a frequency-domain signal seen by a baseband distortion estimator can be expressed

$\begin{array}{cc}\sum _{n\in \Omega }X\left(n\right)+\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}\sum _{k,l,m\in \Omega }X\left(k\right)X\left(l\right)X^{*}\left(m\right)& \left(23\right)\end{array}$

A signal on a channel nεΩ can be expressed

$\begin{array}{cc}Y\left(n\right)=X\left(n\right)+\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}\sum _{k+l-m=n}X\left(k\right)X\left(l\right)X^{*}\left(m\right)& \left(24\right)\end{array}$

and a signal on any channel n∉Ω can be expressed

$\begin{array}{cc}Y\left(n\right)=\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}\sum _{k+l-m=n}X\left(k\right)X\left(l\right)X^{*}\left(m\right)& \left(25\right)\end{array}$

A distortion factor

$\begin{array}{cc}\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}& \left(26\right)\end{array}$

can be estimated using signals on channels of adjacent bands. Since signal values X(k)s can be known, it can be possible to compute

$\begin{array}{cc}\sum _{k+l-m=n}X\left(k\right)X\left(l\right)X^{*}\left(m\right)& \left(27\right)\end{array}$

and then to estimate a distortion factor as

$\begin{array}{cc}{\left[\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}\right]}_{\mathrm{est}}=\frac{Y\left(n\right)}{\sum _{k+l-m=n}X\left(k\right)X\left(l\right)X^{*}\left(m\right)}& \left(28\right)\end{array}$

However, the complexity of computing an intermodulation product sum Σ_k+l−m=nX(k)X(l)X*(m) can discourage such an approach. The case of a preamble for which an intermodulation product sum can be pre-computed can be an exception.

A low-complexity approach can be to use signal power in order to estimate a distortion factor:

$\begin{array}{cc}{\left[{\left(\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}\right)}^2\right]}_{\mathrm{est}}=\frac{E\left[{Y\left(n\right)}^2\right]}{E\left[{\sum _{k+l-m=n}X\left(k\right)X\left(l\right)X^{*}\left(m\right)}^2\right]}& \left(29\right)\end{array}$

since E[|Σ_k+l−m=mX(k)X(l)X*(m)|²] can be a constant that depends primarily on a position of a target channel n relative to a channel set Ω and thus can be pre-computed. In some embodiments, this approach can take a relatively long time to reach a desired accuracy due to an averaging operation that can contribute to estimating E[|Y(n)|²].

Once a distortion factor can be obtained, a signal pre-distortion operation can be carried out as expressed here:

$\begin{array}{cc}{s}_{\mathrm{PD}}\left(t\right)=s\left(t\right)-\left(1+e\right)\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2s\left(t\right)& \left(30\right)\end{array}$

where s_PD(t) can be a pre-distorted signal sent to a RF transmitter chain and |e|<<1 can accounts for estimation error. After passing through the transmitter chain, the signal can be expressed:

$\begin{array}{cc}{\alpha }_1s_{\mathrm{PD}}\left(t\right)+\frac{3{\alpha }_3}{4}{s_{\mathrm{PD}}\left(t\right)}^2s_{\mathrm{PD}}\left(t\right)={\alpha }_1\left[s\left(t\right)-\left(1+e\right)\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2s\left(t\right)\right]+\frac{3{\alpha }_3}{4}{{s\left(t\right)}^2\left[1-\left(1+e\right)\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2\right]}^2·\left[s\left(t\right)-\left(1+e\right)\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2s\left(t\right)\right]\approx {\alpha }_1s\left(t\right)-\left(1+e\right)\frac{3{\alpha }_3}{4}{s\left(t\right)}^2s\left(t\right)+\frac{3{\alpha }_3}{4}{s\left(t\right)}^2s\left(t\right)-2\left(1+e\right)\frac{1}{{\alpha }_1}{\left(\frac{3{\alpha }_3}{4}\right)}^2{s\left(t\right)}^4s\left(t\right)-\left(1+e\right)\frac{1}{{\alpha }_1}{\left(\frac{3{\alpha }_3}{4}\right)}^2{s\left(t\right)}^4s\left(t\right)\approx {\alpha }_1s\left(t\right)-e\frac{3{\alpha }_3}{4}{s\left(t\right)}^2s\left(t\right)-3\frac{1}{{\alpha }_1}{\left(\frac{3{\alpha }_3}{4}\right)}^2{s\left(t\right)}^4s\left(t\right)={\alpha }_1s\left(t\right)\left\{1-\underset{\underset{\mathrm{Estimation}\mathrm{error}}{}}{e\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2}-\underset{\underset{\mathrm{Higher}\text{-}\mathrm{order}\mathrm{distortion}}{}}{{3\left[\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2\right]}^2}\right\}& \left(31\right)\end{array}$

Since without pre-distortion, the signal can be expressed

$\begin{array}{cc}{\alpha }_1s\left(t\right)\left[1+\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2\right]& \left(32\right)\end{array}$

Intermodulation can be assumed to be about 30 dB below signal power, e.g.

$\begin{array}{cc}{\left[\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2\right]}^2\approx -30\mathrm{dB}& \left(33\right)\end{array}$

if the estimation accuracy is about 20 dB, i.e.

10 log₁₀e²≈−20 dB  (34)

then an estimation error power can be expressed:

$\begin{array}{cc}{\left[e\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2\right]}^2\approx -20+\left(-30\right)=-50\mathrm{dB}& \left(35\right)\end{array}$

A high-order distortion power can be expressed:

$\begin{array}{cc}{\left\{{3\left[\frac{1}{{\alpha }_1}\frac{3{\alpha }_3}{4}{s\left(t\right)}^2\right]}^2\right\}}^2\approx 10+\left(-60\right)=-50\mathrm{dB}& \left(36\right)\end{array}$

Overall intermodulation power after pre-distortion can then be about −50 dB. Intermodulation power can be limited by estimation error and/or higher-order distortion. In order to reduce intermodulation power further, a 5th-order distortion compensation can be specified, in addition to specifying a 3rd-order distortion compensation process as described above.

In the foregoing specification, the embodiments have been described with reference to specific elements thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the embodiments. For example, the reader is to understand that the specific ordering and combination of process actions shown in the process flow diagrams described herein is merely illustrative, and that using different or additional process actions, or a different combination or ordering of process actions can be used to enact the embodiments. For example, specific reference to NTSC and/or ATSC and/or DTV embodiments are provided by way of non-limiting examples. Systems and methods herein described can be applicable to any other known and/or convenient channel-based communication embodiments; these can comprise single and/or multiple carriers per channel. The specification and drawings are, accordingly, to be regarded in an illustrative rather than restrictive sense.

Claims

1. A method comprising: receiving a signal;modifying said signal; anddetermining a pre-distortion based, at least in part, on said received signal and said modified signal.