U.S. patent application number 14/192729 was filed with the patent office on 2015-08-27 for system and method for joint compensation of power amplifier's distortion.
This patent application is currently assigned to KING ABDULAZIZ CITY FOR SCIENCE AND TECHNOLOGY. The applicant listed for this patent is KING ABDULAZIZ CITY FOR SCIENCE AND TECHNOLOGY, KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS. Invention is credited to TAREQ YOUSEF AL-NAFFOURI, ANUM ALI, OUALID HAMMI, DAMILOLA SADIQ OWODUNNI.
Application Number | 20150244553 14/192729 |
Document ID | / |
Family ID | 53883320 |
Filed Date | 2015-08-27 |
United States Patent
Application |
20150244553 |
Kind Code |
A1 |
ALI; ANUM ; et al. |
August 27, 2015 |
SYSTEM AND METHOD FOR JOINT COMPENSATION OF POWER AMPLIFIER'S
DISTORTION
Abstract
The system and method for joint compensation of power
amplifier's distortion provides a linearization scheme for
transmitter power amplifiers driven by orthogonal frequency
division multiplexing signals. A pre-compensated over-driven
amplifier is employed at the transmitter. The over-driven
amplifier's distortions are considered as a sparse phenomenon and
compressive sensing (CS) algorithms are employed at the receiver to
estimate and compensate for these distortions. A bandwidth
efficient data aided scheme which does not require reserving
subcarriers specifically for CS measurements is utilized.
Inventors: |
ALI; ANUM; (ISLAMABAD,
PK) ; OWODUNNI; DAMILOLA SADIQ; (IKOSA GRA, NG)
; HAMMI; OUALID; (DHAHRAN, SA) ; AL-NAFFOURI;
TAREQ YOUSEF; (DHAHRAN, SA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
KING ABDULAZIZ CITY FOR SCIENCE AND TECHNOLOGY
KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS |
Riyadh
Dhahran |
|
SA
SA |
|
|
Assignee: |
KING ABDULAZIZ CITY FOR SCIENCE AND
TECHNOLOGY
Riyadh
SA
KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS
Dhahran
SA
|
Family ID: |
53883320 |
Appl. No.: |
14/192729 |
Filed: |
February 27, 2014 |
Current U.S.
Class: |
375/230 ;
375/285 |
Current CPC
Class: |
H04L 2025/03414
20130101; H04L 25/03114 20130101; H03F 1/3241 20130101; H04L 27/366
20130101; H03F 3/245 20130101; H04L 27/2646 20130101 |
International
Class: |
H04L 27/26 20060101
H04L027/26; H04L 25/03 20060101 H04L025/03; H04L 1/00 20060101
H04L001/00 |
Claims
1. In an orthogonal frequency division multiplexing (OFDM)
telecommunication system having an OFDM transmitter sending OFDM
signals amplified by a power amplifier to an OFDM receiver, a
method for joint compensation (at the transmitter and the receiver)
of the power amplifier's distortion, comprising the steps of: (a)
compensating distortion of the OFDM signals caused by the power
amplifier at the transmitter; (b) overdriving the linearized power
amplifier to increase transmission power efficiency of the OFDM
signals; (c) estimating and further compensating the distortion of
the OFDM signals using compressive sensing at the receiver, said
compressive sensing being performed without reserving subcarriers
specifically for said compressive sensing, thereby enhancing
spectral efficiency of the OFDM signals; and (d) using a priori
knowledge about the sparsity of the overdrive distortion to recover
the distortion introduced at the transmitter thereby facilitating
the estimation and compensation step (c), wherein the receiver
performs the following steps: iteratively estimating a modulated
data vector until a maximum number, j=J.sub.max, of modulated data
vectors has been estimated; iteratively comparing a j.sup.th
estimated modulated data vector U.sup.j with a constellation of
size P (P representing a number of data-free/pilot carriers) to
produce a vector set of reliable carriers S.sub.R'; iteratively
performing compressive sensing based on inputs of the vector set of
reliable carriers S.sub.R' and the estimated modulated data vector
U.sup.j, output of the iterative compressive sensing providing
{circumflex over (x)}.sub.d.sup.j; subtracting said {circumflex
over (x)}.sub.d.sup.j from an {circumflex over (x)}.sup.j output of
a front end compressive sensing and equalization step, said
subtracting said {circumflex over (x)}.sub.d.sup.j from said
{circumflex over (x)}.sup.j forming a compensation signal
{circumflex over (x)}.sup.j+1; performing a discrete Fourier
transform (DFT) on the compensation signal {circumflex over
(x)}.sup.j+1 to provide an updated estimated modulated data vector
U.sup.j+1 as input to said iterative constellation comparison and
iterative compressive sensing steps; and demodulating and removing
the data-free/pilot carriers of said enhanced, linearized OFDM
signals when the maximum number, j=J.sub.max, of modulated data
vectors has been estimated.
2. (canceled)
3. An orthogonal frequency division multiplexing (OFDM)
telecommunication system including an OFDM receiver, comprising: a
first discrete Fourier transform (DFT) block that accepts time
domain OFDM free and data carrier signals as input, the first DFT
block performing a discrete Fourier transform on the time domain
OFDM free and data carrier signals; a first channel equalizer,
accepting the OFDM free and data carrier signals as input; a second
channel equalizer having an input operably connected to an output
of the first DFT block; a compressive sensing process block having
an input operably connected to an output of the second channel
equalizer, and an S.sub.p input, said S.sub.p input representing a
binary selection matrix of size N.times.P where N is a total number
of OFDM carrier signals presented at the receiver, and P is a
number of pilot/data-free OFDM carrier signals presented at the
receiver, distortion x.sub.d in said OFDM carrier signals being
estimated by a projection of the second equalization block's output
onto the selection matrix S.sub.p; a combiner having inputs
operably connected to outputs of the compressive sensing process
block, and the first channel equalizer, the combiner subtractively
combining the compressive sensing process block output and the
first channel equalizer output to provide an estimate {circumflex
over (x)} of the OFDM signals distortion free; a second DFT block
having an input operably connected to an output of the combiner;
and a demodulator having an input operably connected to an output
of the second DFT block, the demodulator discarding the free
carrier signals and demodulating the data carrier signals.
4. The OFDM telecommunication system according to claim 3, wherein
the compressive sensing block comprises a solver using convex
relaxation applied to an underdetermined system of equations
presented by the projection of the second equalization block's
output onto the selection matrix S.sub.p to provide the estimate of
the distortion x.sub.d.
5. The OFDM telecommunication system according to claim 3, further
comprising a performance enhancement block operably connected to
the second DFT block in a feedback path, wherein the performance
enhancement block iteratively updates a j.sup.th estimated
modulated data vector {circumflex over (X)}.sup.j output from the
second DFT block until a stopping criterion is reached.
6. The OFDM telecommunication system according to claim 5, wherein
the performance enhancement block further comprises: a second
compressive sensing block disposed in said feedback path; a second
combiner; and a P-size constellation comparator feeding a first
input of the second compressive sensing block, output of said
second DFT block feeding a second input of the second compressive
sensing block, output of the second compressive sensing block
providing an enhanced distortion estimate, current distortion free
estimate and enhanced distortion estimate being fed to the second
combiner, the second combiner subtractively combining the estimates
to provide an enhanced distortion free signal fed back to the input
of the second DFT block, wherein {circumflex over (X)}.sup.j is
compared with P size constellation points, R' reliable carriers
being obtained therefrom.
7. The OFDM telecommunication system according to claim 6, wherein
the second compressive sensing block includes a solver which
evaluates a system of equations characterized by the relations,
minimize x d 1 , subject to U R - .PSI. R x d 2 .ltoreq. ` ,
##EQU00011## where .PSI..sub.Rx.sub.d is a measurement matrix, and
U.sub.R is the estimated data at the reliable carriers based on the
R' reliable carriers.
8. The OFDM telecommunication system according to claim 6, wherein
the stopping criteria is a maximum number of iterations J.sub.max
performed by the performance enhancement block.
9. The OFDM telecommunication system according to claim 6, wherein
the P-size constellation comparator comprises: means for
calculating reliability of all N-P (if any) carriers; and means for
sorting their reliabilities in descending order.
10. The OFDM telecommunication system according to claim 9, further
comprising: an OFDM transmitter including an amplifier in an
overdriven configuration that produces distortion in the OFDM free
and data carrier signals transmitted to the OFDM receiver.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to telecommunication systems,
and particularly to a system and method for joint compensation of
power amplifier's distortion in an orthogonal frequency division
multiplexing (OFDM) telecommunication system.
[0003] 2. Description of the Related Art
[0004] Emerging communication systems intensively use orthogonal
frequency division multiplexing (OFDM) technique due to its
numerous advantages such as high spectral efficiency, robustness to
frequency selective fading, etc, which make it very attractive for
the majority of communication systems. However, OFDM signals often
result in time-domain wave-forms that have peak to average power
ratio (PAPR) of up to 10 dB. These amplitude modulated signals are
sensitive to the nonlinear distortions caused by the radio
frequency (RF) power amplifier (PA) of the RF front-end. Indeed,
the PA needs to linearly amplify the amplitude-modulated signals to
avoid high error vector magnitude (EVM) and symbol error rate (SER)
which will translate into loss of the information. Simultaneously,
the power efficiency of the PA needs to be maximized since the
amplifier consumes most of the power in the RF front-end. However,
power amplifiers have low power efficiency when they are operated
in their linear region, and their efficiency increases as they are
driven into the nonlinear region close to saturation. Practically,
power amplifiers are operated in their nonlinear region for power
efficiency considerations. Then, the linearity is restored by means
of system level architectures and mainly linearization techniques
such as digital predistortion and feedforward implemented at the
transmitter side.
[0005] Linearization techniques have been widely used to compensate
for the PA's nonlinear distortions at the transmitter side. This is
mainly motivated by the regulatory spectrum emission mask
requirements in the licensed spectrum bands used for cellular
communications and TV broadcasting. In fact, all these applications
require that the spectrum at the output of the amplifier meets
stringent linearity mask in order to avoid interference with
adjacent channels. Among the various linearization techniques,
digital predistortion is commonly used. It consists of applying a
complementary nonlinearity (predistorter) before the non-linear PA
such that the cascade of the predistorter and the amplifier behaves
as a linear amplification system. Yet there remains the motivation
to find a method for a more power efficient operation of digitally
predistorted power amplifiers that maintains spectral efficiency by
using a low number of pilot carriers.
[0006] Thus, a system and method for joint compensation of power
amplifier's distortion solving the aforementioned problems is
desired.
SUMMARY OF THE INVENTION
[0007] The system and method for joint compensation of power
amplifier's distortion provides a linearization scheme for
transmitter power amplifiers driven by orthogonal frequency
division multiplexing signals. A pre-compensated over-driven
amplifier is employed at the transmitter. The over-driven
amplifier's distortions are considered as a sparse phenomenon and
compressive sensing (CS) algorithms are employed at the receiver to
estimate and compensate for these distortions. A bandwidth
efficient data aided scheme which does not require reserving
subcarriers specifically for CS measurements is utilized.
[0008] These and other features of the present invention will
become readily apparent upon further review of the following
specification and drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1A is a plot of typical AM-AM characteristics of a
power amplifier (PA) according to the present invention.
[0010] FIG. 1B is a plot of typical AM-PM characteristics of a PA
according to the present invention.
[0011] FIG. 2A is a plot showing measured vs. approximated AM-AM
characteristics of a PA linearized using digital predistortion
according to the present invention.
[0012] FIG. 2B is a plot showing measured vs. approximated AM-PM
characteristics of a PA linearized using digital predistortion
according to the present invention.
[0013] FIG. 3 is a block diagram of a communication system
according to the present invention.
[0014] FIG. 4 is a plot of a sparse distortion signal caused by the
overdriven PA linearized using digital predistortion according to
the present invention.
[0015] FIG. 5 is a simplified block diagram of a transmission
system according to the present invention.
[0016] FIG. 6 is a simplified block diagram of a receiving system
according to the present invention.
[0017] FIG. 7 is a block diagram of the CS-based distortion
cancellation system implemented at the receiver according to the
present invention.
[0018] FIG. 8 is a pictorial diagram showing the signal relations
according to the present invention.
[0019] FIG. 9 is a plot showing EVM comparisons of the enhanced
communication system to legacy communication systems.
[0020] FIG. 10 is a plot showing SER comparisons of the enhanced
communication system to legacy communication systems.
[0021] Similar reference characters denote corresponding features
consistently throughout the attached drawings.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0022] At the outset, it should be understood by one of ordinary
skill in the art that embodiments of the present method can
comprise software or firmware code executing on a computer, a
microcontroller, a microprocessor, or a DSP processor; state
machines implemented in application specific or programmable logic;
or numerous other forms without departing from the spirit and scope
of the method described herein. The present method can be provided
as a computer program, which includes a non-transitory
machine-readable medium having stored thereon instructions that can
be used to program a computer (or other electronic devices) to
perform processes according to the method. The machine-readable
medium can include, but is not limited to, floppy diskettes,
optical disks, CD-ROMs, and magneto-optical disks, ROMs, RAMs,
EPROMs, EEPROMs, magnetic or optical cards, flash memory, or other
type of non-transitory, media or machine-readable medium suitable
for storing electronic instructions.
[0023] The system and method for joint compensation of power
amplifier's distortion provides a linearization scheme for
transmitter power amplifiers (PAs) driven by orthogonal frequency
division multiplexing signals. A pre-compensated over-driven
amplifier is employed at the transmitter. The over-driven
amplifier's distortions are considered as a sparse phenomenon and
compressive sensing (CS) algorithms are employed at the receiver to
estimate and compensate for these distortions. A bandwidth
efficient data aided scheme which does not require reserving
subcarriers specifically for CS measurements is utilized.
[0024] In the present power amplifier distortions' joint
compensation method, the PA is first linearized using, for example,
a digital pre-distorter, and then over-driven for power efficiency.
The distortion caused by the over-driven linearized PA is modeled
as a sparse phenomenon recovered at the receiver.
[0025] Recently, there has been an increased interest in the
recovery of sparse signals using compressive sensing (CS). The
significance of CS lies in the fact that it can reconstruct a
sparse signal by utilizing a few linear projections over a basis
that is incoherent with the basis in which the signal is sparse.
Thus, CS can be applied to recover and then compensate for these
distortions using a few frequency-domain data-free or pilot
carriers. The use of a data-aided technique along with CS can
further improve bandwidth efficiency by alleviating the need for
frequency-domain free carriers. In such a case, the over-driven
amplifier's distortions can be mitigated without using any
frequency-domain free carriers. This will circumvent the bandwidth
limitation of conventional CS techniques that require free carriers
in order to estimate the over-drive distortions.
[0026] The AM-AM and AM-PM characteristics of a typical PA are
nonlinear. As an example consider the characteristics shown in FIG.
1A and FIG. 1B. As can be seen from the AM-AM curve 100a of FIG.
1A, the amplitude response is nonlinear, especially for high
amplitude input signals, resulting in severe nonlinear distortion
on the peaks. Furthermore, as shown in the AM-PM curve 100b of FIG.
1B the phase response is also nonlinear.
[0027] A linear amplification system may be obtained by using the
cascade of a nonlinear PA and a DPD circuit matched to the
characteristics of the PA. The measured AM-AM characteristics 200a
of the linearized amplifier are shown in FIG. 2A. It is apparent,
that the DPD-PA cascade has a constant gain response to a point
where the amplifier saturates, and starts compressing. In the
saturation region, the gain of the DPD-PA combination decreases
linearly with increasing input power. However, AM-PM measured
characteristics 200b shown in FIG. 2B reveals that the phase
response of the linearized PA is constant throughout the range of
interest. To simulate the DPD-PA, a look-up table (LUT) behavioral
model, derived from the measured AM-AM and AM-PM characteristics of
the linearized PA, using an exponential moving average algorithm is
adopted in this work. The characteristics of the linearized
amplifier based on the LUT model are also shown in FIGS. 2A and 2B.
For any linear amplification system if the characteristics of DPD
match closely with that of the PA, a system having the
characteristics such as shown in FIGS. 2A and 2B results.
[0028] The block diagram of communication system 300 with an
overdriven jointly-compensated PA 324 is shown in FIG. 3. The
exemplary communication system 300 has a transmitter 320 with a
signal generation block 321 feeding the DPD 322 which feeds a
digital to analog converter and a frequency up-converter 323 which
drives power amplifier 324. The amplified signal that is
transmitted by the antenna 325 propagates through a multipath
fading channel 340 before being processed at a receiver 360 where
an antenna 361 receives the signal and feeds it to an RF front end
362 where frequency down conversion and analog to digital
conversion occur and feeds a channel equalization block 363. Output
of the channel equalization block feeds a distortion
post-compensation block 364 which then feeds a demodulation block
365. As shown in plot 400 of FIG. 4, the distortions from the
overdriven linearized PA are sparse.
[0029] With reference to OFDM transmitter with linearized PA 500,
the serial stream of data d to be transmitted is divided into N
parallel streams that are modulated using either phase-shift keying
(PSK) or quadrature amplitude modulation (QAM) to obtain a set of N
data symbols, X=[X(0) X(1) . . . X(N-1)]. This process occurs in
the modulation and free-carrier insertion block 510. The
time-domain signal that serves as an input to the linearized PA
(DPD-PA) is obtained by performing an inverse discrete Fourier
transform (IDFT) operation on X in the IDFT block 520. This
operation is characterized by the relations,
x=F.sup.HX (1)
where F denotes the unitary discrete Fourier transform (DFT) matrix
with (a, b) element,
F a , b = 1 N - j 2 .pi. ab / N , a , b .di-elect cons. { 1 , 2 , ,
N - 1 } . ( 2 ) ##EQU00001##
[0030] Furthermore in OFDM systems, a cyclic prefix is appended to
x to avoid inter-symbol interference. This signal then passes
through the DPD-PA combination before transmission. The DPD module
530 is inserted before PA 540 to synthesize a linear amplification
system. In FIG. 5, the DAC and frequency up conversion module 323
of FIG. 3 is not reported for simplicity. The time domain signal
that passes through a linear amplification system that is not
over-driven will go undistorted. However, the amplifier over-drive
will result in a distorted transmitted signal. This distortion can
be modeled as addition of a distortion signal x.sub.d to the
transmission signal. Hence the output of the PA can be written
as,
x.sub.p=x+x.sub.d (3)
[0031] Here, the small signal gain of the PA is taken to be unity
for simplicity, as it doesn't affect the generality of the system
model. Since the main focus of this work is to study the effects of
the PA's distortions, the transmitter's RF front end is considered
to be ideal except for the nonlinear distortions generated by the
amplifier. Thus the transmitter's RF front end is modeled using the
baseband equivalent behavioral model of the PA. To take into
consideration the presence of the DPD module in the baseband
processing unit, while using a realistic model based on the
measured data of the linearized PA, the DPD-PA combination 530 and
540 is simulated using the LUT synthesized from the measured data
presented in the plots of FIGS. 2A-2B. The time-domain received
signal is modeled as
y=Hx.sub.p+z. (4)
where y.epsilon..quadrature..sup.N is the time-domain received OFDM
symbol (after removing the cyclic prefix) and z is the circular
complex additive white Gaussian noise (AWGN),
z.quadrature.(N(0,.sigma..sub.x.sup.2I), where .sigma..sub.z.sup.2
is the variance of noise samples. In OFDM systems, the linear
convolution between the transmitted data, x.sub.p, and the channel
impulse response (CIR), h=[h(0) h(1) . . . h(N-1)] is converted
into a cyclic convolution due to the presence of the cyclic prefix.
The cyclic prefix length is assumed to be greater than L to avoid
inter-symbol interference. Thus, H denotes the circulant channel
matrix in (4) that can be decomposed as, H=F.sup.H.LAMBDA.F, where
H=diag(H), and H= {square root over (N)}Fh is the DFT of the CIR.
In reference to the receiver system 600 shown in FIG. 6, using the
fact that the aforementioned circulant channel matrix can be
decomposed, a DFT block 610 takes the DFT of both sides of (4),
yielding,
Y=.LAMBDA.X.sub.p+Z, (5)
where Y and Z are the DFT's of y and z respectively. As the present
system and method is focused on nonlinear distortion estimation,
the CIR is assumed to be perfectly known at the receiver. Thus, the
frequency-domain received signal (after equalization performed by
post DFT equalization block 620) is given by
Y.sub.eq=Fx.sub.p+.LAMBDA..sup.-1Z, (6)
where Y.sub.eq=.LAMBDA..sup.-1Y. Substituting the value of x.sub.p
from (3) in (6) yields,
Y.sub.eq=Fx+Fx.sub.d+Z.sub.col, (7)
where Z.sub.col represents the AWGN noise colored by the inverse
channel matrix. The time-domain equivalent of the received signal
can thus be written as,
y.sub.eq=x+x.sub.d+z.sub.col, (8)
where y.sub.eq is the IDFT of Y.sub.eq and z.sub.col is the IDFT of
Z.sub.col. In the present OFDM telecommunication method, the
overdrive linearized PA's distortions, x.sub.d, are estimated using
CS based techniques by exploiting the free carriers inserted in the
OFDM symbol. Let w of cardinality |w|=N be the set of all carriers
available in the OFDM symbol and w.sub.p.OR right.w of cardinality
|w.sub.p=P with P<N denoting the set of free or pilot carriers
that will be used to estimate x.sub.d. As we use CS-based
techniques to estimate x.sub.d, it is desirable for the P free
carriers to be randomly placed and known to the receiver. Let D be
the number of active tones used for data transmission with D=N-P
and define S.sub.D as a binary selection matrix (of size N.times.D)
with only one non-zero element equal to 1 per row and column that
selects the data carriers and all zero rows with indices belonging
to w.sub.p. Then, the time-domain OFDM signal can be re-defined
as
x=F.sup.HS.sub.DX.sub.D, (9)
where X.sub.D is the D.times.1 frequency-domain modulated data
vector. The frequency-domain received signal (8) is thus modified
as
Y.sub.eq,D=S.sub.DX.sub.D+Fx.sub.d+z.sub.col (10)
Let us denote by S.sub.p the selection matrix (of size N.times.P)
that spans the orthogonal complement of the columns of S.sub.D
(i.e. S.sub.p is a binary matrix of size N.times.P with only one
non-zero element equal to 1 per row and column and all zero rows
with indices belonging to (w-w.sub.p)). The distortion x.sub.d is
estimated by projecting Y on S.sub.P.sup.T as follows
Y.sub.eq,P=S.sub.P.sup.TY.sub.eq=S.sub.P.sup.TFx.sub.d+Z.sub.col,p
(11)
where Z.sub.col,p=S.sub.p.sup.TZ.sub.col is a Gaussian vector of
length P. For notational convenience, we re-write the above
equation as
Y.sub.p=.PSI..sub.px.sub.d+Z.sub.p (12)
where .PSI..sub.p.quadrature.S.sub.P.sup.TF a measurement matrix of
size P.times.N. Note that (12) forms an underdetermined system of
linear equations as x.sub.d.epsilon..quadrature..sup.N and
Y.sub.p.epsilon..quadrature..sup.P with P<N and hence cannot be
solved by using the conventional linear techniques. This is in fact
a typical CS problem when it is known a priori that the signal of
interest x.sub.d is sparse. This problem can be solved by using the
convex relaxation approach that solves an l.sub.1-norm minimization
problem using linear programming. Following the notation used, the
problem can be casted as
minimize x d 1 , subject to Y P - .PSI. P x d 2 .ltoreq. ` , ( 13 )
##EQU00002##
where
= .sigma. z 2 ( P + 2 P ) . ##EQU00003##
It is important to mention here that the above convex relaxation
approach used to estimate x.sub.d from (12) is exemplary only, but
any other CS-based technique (for example, Bayesian methods and
matching pursuits) can be utilized. After obtaining an estimate of
the distortion {circumflex over (x)}.sub.d using CS block 640, an
estimate of the distortion-free signal can be obtained by
subtracting output of pre-DFT equalization block 630 from the
distortion {circumflex over (x)}.sub.d at combiner 650 as
follows,
{circumflex over (x)}=y.sub.eq-{circumflex over (x)}.sub.d (14)
[0032] The signal, {circumflex over (x)} is then transformed by a
DFT operation at DFT block 660 to the frequency-domain data signal,
{circumflex over (X)}. Finally, this is demodulated at demodulation
block 670 to obtain an estimate of the transmitted data,
{circumflex over (d)}. If one has some a priori information related
to the sparse signal x.sub.d, an alternative approach to (13)
called weighted CS (WCS) can be pursued by penalizing the less
probable locations of x.sub.d as follows
minimize w T x d 1 , subject to Y P - .PSI. P x d 2 .ltoreq. ` , (
15 ) ##EQU00004##
where w is a vector consisting of weights for each location in
x.sub.d. The major distortions caused by the linearized PA occur at
the locations where the input amplitude is large. Accordingly, we
can define w to be the inverse of the magnitude of the received
signal y.sub.eq, i.e.,
w ( n ) = { 1 y eq ( n ) , y ( n ) .noteq. 0 , .infin. , y ( n ) =
0. ( 16 ) ##EQU00005##
where n={1, 2, . . . , N}. This way, the small entries in w
correspond to the most probable locations where the overdriven
DPD-PA combination might have distorted the signal and thus, this
forces (15) to concentrate on them. One disadvantage of the
previous algorithm is that a few carriers need to be reserved and
be used for estimating the distortion. This causes a reduction in
the available bandwidth. Alternatively, a data-aided CS algorithm
can be used. This algorithm utilizes reliable data to aid in CS
estimation. The advantages of the present iterative data-aided CS
(DACS) algorithm include the fact that it enhances the performance
of the CS/WCS algorithms while helping to increase the bandwidth
efficiency of the system (by reducing the number of free or pilot
carriers required) with a nominal increase in the receiver
complexity. This algorithm is based on the assumption that even
after the nonlinear distortions caused by the overdriven DPD-PA, a
part of the data samples still remains within its corresponding
decision regions. Let w.sub.R .OR right.w of cardinality
|w.sub.R|=R denote the set of these carriers in which the
perturbations are not severe i.e. the carriers are reliable. In
other words, the noisy and perturbed data samples would remain in
the decision regions of their respective constellation points, so
that the following would hold with high probability;
{circumflex over (X)}.sub.R=X.sub.R, (17)
where {circumflex over (X)}.sub.R is the estimated data at the
reliable carriers. Let S.sub.R be a binary selection matrix (of
size N.times.R) with only one non-zero element equal to 1 per
column that selects the reliable carriers. Multiplying both sides
of (21) by S.sub.R.sup.T yields,
S.sub.R.sup.TY.sub.eq=S.sub.R.sup.TX+S.sub.R.sup.TFx.sub.d+S.sub.R.sup.T-
Z.sub.col, (18)
which, following the convention used in equations (11) and (12),
can be written as
Y.sub.R=X.sub.R+.PSI..sub.Rx.sub.d+Z.sub.R (19)
where Y.sub.R=S.sub.R.sup.TY.sub.eq, X.sub.R=S.sub.R.sup.TX, and
Z.sub.R=S.sub.R.sup.TZ. The perturbations,
.PSI..sub.Rx.sub.d+Z.sub.R, at the reliable carriers do not push
the data outside the reliable regions i.e.,
.left brkt-bot.Y.sub.R.right brkt-bot.=X.sub.R (20)
where the .left brkt-bot..cndot..right brkt-bot. operator denotes
rounding to the nearest neighbor. Thus, we can write (19) as
Y.sub.R-X.sub.R=.PSI..sub.Rx.sub.d+Z.sub.R (21)
or
U.sub.R=.PSI..sub.Rx.sub.d+Z.sub.R (22)
where U.sub.R=Y.sub.R-X.sub.R. It is important to note that it is
not needed to determine all reliable carriers, w.sub.R, rather, it
is sufficient to determine a subset of these carriers, w.sub.R.OR
right.w.sub.R and use them. Here onwards, R' is used to distinguish
the variables corresponding to the subset w.sub.R', from the
variables corresponding to the set w.sub.R). The system of
equations (22) can be solved using a CS-based approach similar to
(13) as follows;
minimize x d 1 , subject to U R - .PSI. R x d 2 .ltoreq. , ( 23 )
##EQU00006##
The above procedure can be repeated J.sub.max times to further
enhance the performance as shown in Table 1.
TABLE-US-00001 TABLE 1 Performance enhancement procedure block 702
STEP Procedure 1 Let {circumflex over (X)}.sup.j be the the
j.sup.th estimated modulated data vector (obtained by taking the
DFT 740 of {circumflex over (x)}). 2 Compare {circumflex over
(X)}.sup.j with the P size constellation points and obtain the R'
reliable carriers. 3 Find S.sub.R', U.sub.R' and .PSI..sub.R' based
on R'. 4 Evaluate (23) to obtain {circumflex over (x)}.sub.d.sup.j
using 750 5 Obtain {circumflex over (x)}.sup.j+1 = {circumflex over
(x)}.sup.j - {circumflex over (x)}.sub.d.sup.j by 735 6 Repeat
steps 2-5 till j = J.sub.max in 745
[0033] FIG. 7 illustrates the receiver algorithms design 700 based
on DACS algorithm. The blocks 710, 715, 720, 725, 730, 740 and 760
correspond to the blocks 610, 620, 630, 640, 650, 660, and 670,
respectively. Note that the above procedure can also be applied to
the case when no free carriers are used for CS estimation in the
first iteration. In this case, the algorithm will highly rely on
the set of reliable carriers available. To find the reliable set of
carriers from the observed data, we pursue a geometrical approach.
In order to explain the adopted approach, we consider as a
motivating example the constellation 800 shown in FIG. 8. Here
{circumflex over (X)}.sub.1 and {circumflex over (X)}.sub.2 are two
equalized data samples which are equidistant from the closest
constellation point, X. However, in spite of being equidistant from
X, {circumflex over (X)}.sub.1, and {circumflex over (X)}.sub.2
have different reliability values. This is because the distances of
these two points from their respective next nearest neighbors are
different. Specifically, note that X.sub.a is next nearest neighbor
of {circumflex over (X)}.sub.1 and X.sub.x is next nearest neighbor
of {circumflex over (X)}.sub.2, respectively. Note also that, given
that {circumflex over (X)}.sub.1 and {circumflex over (X)}.sub.2
are equidistant from X, it is clear that {circumflex over
(X)}.sub.2 is more reliable than {circumflex over (X)}.sub.1 and in
relative terms we have,
X ^ 2 - X X ^ 2 - X c < X ^ 1 - X X ^ 1 - X ^ a , ( 24 )
##EQU00007##
This motivates the following reliability matrix (n),
= - log ( X ^ - X ^ X ^ - X ^ NN ) , ( 25 ) ##EQU00008##
where, as defined before, .left brkt-bot.{circumflex over
(X)}.right brkt-bot. denotes rounding to the nearest constellation
point, while .left brkt-bot.{circumflex over (X)}.right
brkt-bot..sub.NN denotes rounding to the next nearest constellation
point. Thus, it is possible to calculate the reliability of all N-P
carriers (or N carriers in the case when no free/pilot carriers are
used), sort the reliabilities in descending order
(n.sub.1).gtoreq.(n.sub.2).gtoreq. . . . .gtoreq.(n.sub.N-P) and
choose the R' carriers with the highest reliability
w.sub.R'={n.sub.1, n.sub.2, . . . , n.sub.R}.
[0034] In the simulations presented, the number of subcarriers is
fixed at N=256 and 64QAM modulation scheme is employed. The
following two performance measures are used for comparing the
present methods:
Error Vector Magnitude ( EVM ) = 1 N r = 1 N X ( r ) - X ^ ( r ) 2
1 N r = 1 N X ( r ) 2 . and ( 26 ) Symbol Error Rate ( SER ) =
symbol errors ( comparing d and d ^ ) total number of symbols in d
. ( 27 ) ##EQU00009##
Both performance measures are plotted as functions of the signal to
noise ratio (SNR) ranging from 15 dB to 35 dB. The SNR is given
by:
SNR = .sigma. Z 2 .sigma. X P 2 . ( 28 ) ##EQU00010##
where .sigma..sub.z.sup.2 and .sigma..sub.x.sub.p.sup.2 are the
variances of the noise and PA output signal, respectively.
[0035] The performance of joint-compensation approach is compared
with only post-compensating DACS in plot 900 of FIG. 9 and plot
1000 of FIG. 10. The number of reliable carriers and iterations for
implementing DACS algorithm is fixed at R'=40% of N-P and
J.sub.max. It can be easily seen that joint-compensation performs
better than DACS with post-compensation only. These figures also
demonstrate the performance of the bandwidth efficient algorithm
that uses no free carriers at all. It can be observed that the
joint-compensation approach using no free carriers achieves a
performance that is even better than post-compensating DACS with
P=10% free carriers. According to the results shown in FIG. 9 and
FIG. 10, CS makes it possible to overdrive the amplifier by up to 4
dB while compensating for the EVM. Accordingly, this results, for
the tested amplifier, in an operating power added efficiency (PAE)
of 40%. This represents 15% increase or 60% relative increase
compared to the case where only digital predistortion is performed
(i.e. PAE of 25%). This clearly demonstrates the effectiveness of
the present joint-compensation technique to boost the operating
power efficiency while maintaining low EVM and SER. This efficiency
increase is critical for micro-satellite applications and military
applications were the efficiency of the remote transmitter is a
major concern. Advantages of the present invention are detailed in
Table 2.
TABLE-US-00002 TABLE 2 Enhancement procedure advantages Advantage
Feature 1 uses joint-compensation between transmitter and receiver
to improve transmitter's efficiency 2 Amplifier over-drive ensures
power efficiency of the mobile terminal. 3 use of compressive
sensing at the receiver improves EVM and SER performances. 4 use of
DACS method ensures bandwidth efficient operation of the whole
communication system 5 compensation at the receiver does not
require prior knowledge of the transmitter and its nonlinearity 6
pre-compensation at the transmitter can be implemented by other
means than digital pre- distortion 7 pre-compensation can be
designed to fully or partly compensate for the nonlinearity of the
amplifier prior to overdrive 8 post-compensation may be implemented
by means other than CS
[0036] It is to be understood that the present invention is not
limited to the embodiments described above, but encompasses any and
all embodiments within the scope of the following claims.
* * * * *