U.S. patent application number 12/611495 was filed with the patent office on 2010-02-25 for receiver for estimating signal magnitude, noise power, and signal-to-noise ratio of received signals.
This patent application is currently assigned to INTERDIGITAL TECHNOLOGY CORPORATION. Invention is credited to Bin Li, Philip J. Pietraski, Gregory S. Sternberg.
Application Number | 20100046673 12/611495 |
Document ID | / |
Family ID | 34228840 |
Filed Date | 2010-02-25 |
United States Patent
Application |
20100046673 |
Kind Code |
A1 |
Li; Bin ; et al. |
February 25, 2010 |
RECEIVER FOR ESTIMATING SIGNAL MAGNITUDE, NOISE POWER, AND
SIGNAL-TO-NOISE RATIO OF RECEIVED SIGNALS
Abstract
A method and apparatus for estimating attributes of a received
signal that includes a plurality of transmitted signals are
provided. The amplitude of the received signal is estimated by
performing a method of demodulation based on known signal
information. The amplitude of an M-ary quadrature amplitude
modulated signal is estimated based upon known or ascertainable
phase information regarding a plurality of transmitted symbols. The
amplitude of a q-ary amplitude shift keyeing signal is estimated
based upon known or ascertainable magnitude information regarding a
plurality of transmitted symbols. Statistical information is also
used for amplitude estimation.
Inventors: |
Li; Bin; (Shenzhen, CN)
; Sternberg; Gregory S.; (Mt. Laurel, NJ) ;
Pietraski; Philip J.; (Huntington Station, NY) |
Correspondence
Address: |
VOLPE AND KOENIG, P.C.;DEPT. ICC
UNITED PLAZA, SUITE 1600, 30 SOUTH 17TH STREET
PHILADELPHIA
PA
19103
US
|
Assignee: |
INTERDIGITAL TECHNOLOGY
CORPORATION
Wilmington
DE
|
Family ID: |
34228840 |
Appl. No.: |
12/611495 |
Filed: |
November 3, 2009 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
12166702 |
Jul 2, 2008 |
7620123 |
|
|
12611495 |
|
|
|
|
10750203 |
Dec 31, 2003 |
7502426 |
|
|
12166702 |
|
|
|
|
60501302 |
Sep 9, 2003 |
|
|
|
Current U.S.
Class: |
375/320 |
Current CPC
Class: |
H04L 27/38 20130101;
H04L 1/20 20130101 |
Class at
Publication: |
375/320 |
International
Class: |
H04L 27/34 20060101
H04L027/34 |
Claims
1. A method for use in wireless communication, the method
comprising: estimating an amplitude of a received signal that
includes a plurality of transmitted symbols by: performing
ascertainable phase demodulation, on a condition that the received
signal is an M-ary quadrature amplitude demodulation (M-QAM) signal
and phase information of the plurality of transmitted symbols is
known; performing ascertainable magnitude demodulation, on a
condition that the received signal is a q-ary amplitude shift
keyeing (q-ASK) signal and magnitude information of the plurality
of transmitted symbols is known; and performing absolute value
demodulation, on a condition that magnitude information and phase
information regarding the plurality of transmitted symbols is
unknown.
2. The method of claim 1, wherein the performing ascertainable
phase demodulation includes: recovering a plurality of received
symbols corresponding to the plurality of transmitted symbols;
generating a plurality of products based on the plurality of
received symbols; summing the plurality of products; determining
the real part of the sum of products; generating a magnitude value
by summing the absolute values of the plurality of transmitted
symbols; and generating the estimated amplitude of the received
signal by dividing the real part of the sum of products by the
magnitude value.
3. The method of claim 2, wherein the generating the plurality of
products includes multiplying each of the plurality of received
symbols by a phase of a corresponding transmitted symbol.
4. The method of claim 1, wherein the performing ascertainable
magnitude demodulation includes: recovering a plurality of received
samples corresponding to the plurality of transmitted symbols,
generating a plurality of products by multiplying each sample in
the plurality of samples by a corresponding sign, summing the
plurality of products to generate a first sum, summing the absolute
values of the plurality of transmitted symbols to generate a second
sum, and generating the estimated amplitude of the received signal
by dividing the first sum by the second sum.
5. The method of claim 1, wherein the performing absolute value
demodulation includes: recovering a plurality of received samples
corresponding to the plurality of transmitted symbols, determining
the absolute values of the plurality of received samples, summing
the absolute values to generate a first sum, determining a mean of
the absolute values of the amplitudes of the plurality of
transmitted symbols, multiplying the mean of the absolute values by
the number of symbols in the plurality of transmitted symbols to
generate a product, and generating the estimated amplitude of the
received signal by dividing the first sum by the product.
6. A wireless transmit/receive unit (WTRU) comprising: a receiver
configured to receive a signal that includes a plurality of
transmitted symbols; and a processor configured to estimate an
amplitude of the received signal by: performing ascertainable phase
demodulation, on a condition that the received signal is an M-ary
quadrature amplitude demodulation (M-QAM) signal and phase
information of the plurality of transmitted symbols is known;
performing ascertainable magnitude demodulation, on a condition
that the received signal is a q-ary amplitude shift keyeing (q-ASK)
signal and magnitude information of the plurality of transmitted
symbols is known; and performing absolute value demodulation, on a
condition that magnitude information and phase information
regarding the plurality of transmitted symbols is unknown.
7. The WTRU of claim 6, wherein the processor is configured to
perform ascertainable phase demodulation by: recovering a plurality
of received symbols corresponding to the plurality of transmitted
symbols; generating a plurality of products based on the plurality
of received symbols; summing the plurality of products; determining
the real part of the sum of products; generating a magnitude value
by summing the absolute values of the plurality of transmitted
symbols; and generating the estimated amplitude of the received
signal by dividing the real part of the sum of products by the
magnitude value.
8. The WTRU of claim 7, wherein the processor is configured to
generate the plurality of products by multiplying each of the
plurality of received symbols by a phase of a corresponding
transmitted symbol.
9. The WTRU of claim 6, wherein the processor is configured to
perform ascertainable magnitude demodulation by: recovering a
plurality of received samples corresponding to the plurality of
transmitted symbols, generating a plurality of products by
multiplying each sample in the plurality of samples by a
corresponding sign, summing the plurality of products to generate a
first sum, summing the absolute values of the plurality of
transmitted symbols to generate a second sum, and generating the
estimated amplitude of the received signal by dividing the first
sum by the second sum.
10. The WTRU of claim 6, wherein the processor is configured to
perform absolute value demodulation by: recovering a plurality of
received samples corresponding to the plurality of transmitted
symbols, determining the absolute values of the plurality of
received samples, summing the absolute values to generate a first
sum, determining a mean of the absolute values of the amplitudes of
the plurality of transmitted symbols, multiplying the mean of the
absolute values by the number of symbols in the plurality of
transmitted symbols to generate a product, and generating the
estimated amplitude of the received signal by dividing the first
sum by the product.
11. A base station comprising: a receiver configured to receive a
signal that includes a plurality of transmitted symbols; and a
processor configured to estimate an amplitude of the received
signal by: performing ascertainable phase demodulation, on a
condition that the received signal is an M-ary quadrature amplitude
demodulation (M-QAM) signal and phase information of the plurality
of transmitted symbols is known; performing ascertainable magnitude
demodulation, on a condition that the received signal is a q-ary
amplitude shift keyeing (q-ASK) signal and magnitude information of
the plurality of transmitted symbols is known; and performing
absolute value demodulation, on a condition that magnitude
information and phase information regarding the plurality of
transmitted symbols is unknown.
12. The base station of claim 11, wherein the processor is
configured to perform ascertainable phase demodulation by:
recovering a plurality of received symbols corresponding to the
plurality of transmitted symbols; generating a plurality of
products based on the plurality of received symbols; summing the
plurality of products; determining the real part of the sum of
products; generating a magnitude value by summing the absolute
values of the plurality of transmitted symbols; and generating the
estimated amplitude of the received signal by dividing the real
part of the sum of products by the magnitude value.
13. The base station of claim 12, wherein the processor is
configured to generate the plurality of products by multiplying
each of the plurality of received symbols by a phase of a
corresponding transmitted symbol.
14. The base station of claim 11, wherein the processor is
configured to perform ascertainable magnitude demodulation by:
recovering a plurality of received samples corresponding to the
plurality of transmitted symbols, generating a plurality of
products by multiplying each sample in the plurality of samples by
a corresponding sign, summing the plurality of products to generate
a first sum, summing the absolute values of the plurality of
transmitted symbols to generate a second sum, and generating the
estimated amplitude of the received signal by dividing the first
sum by the second sum.
15. The base station of claim 11, wherein the processor is
configured to perform absolute value demodulation by: recovering a
plurality of received samples corresponding to the plurality of
transmitted symbols, determining the absolute values of the
plurality of received samples, summing the absolute values to
generate a first sum, determining a mean of the absolute values of
the amplitudes of the plurality of transmitted symbols, multiplying
the mean of the absolute values by the number of symbols in the
plurality of transmitted symbols to generate a product, and
generating the estimated amplitude of the received signal by
dividing the first sum by the product.
Description
CROSS REFERENCE TO RELATED APPLICATION(S)
[0001] This application is a continuation of U.S. patent
application Ser. No. 12/166,702, filed Jul. 2, 2008, which is a
continuation of U.S. patent application Ser. No. 10/750,203, filed
Dec. 31, 2003, which issued as U.S. Pat. No. 7,502,426 on Mar. 10,
2009, which claims priority from provisional U.S. Application No.
60/501,302, filed Sep. 9, 2003, which are incorporated by reference
as if fully set forth.
FIELD OF INVENTION
[0002] The present invention relates generally to communication
systems and techniques which employ quadrature amplitude modulation
(QAM). More specifically, the present invention relates to
techniques for accurately demodulating an M-ary QAM signal at a
receiver.
BACKGROUND
[0003] At present, M-ary QAM (M-QAM) is used to provide high-speed
data transfer in conjunction with a number of mobile data
communication applications. However, a primary drawback of M-QAM is
its computational complexity. One prior art approach for addressing
this shortcoming involves the use of square M-QAM constellations,
such as 16QAM, 64QAM, and 256QAM. Square constellations may be
conceptualized as including two independent q-ary amplitude shift
keying (q-ASK) modulation signals as real and imaginary parts
(in-phase and quadrature-phase components of a modulated carrier),
where q= {square root over (M)}.
[0004] For example, a 16-QAM signal includes two independent real
and imaginary 4-ASK signals. A q-ASK signal takes on values
selected from the set
{ .+-. 1 2 , .+-. 3 2 , , .+-. q - 1 2 } . ##EQU00001##
Representing a square-constellation M-QAM signal in q-ASK format is
usually preferred because the complexity of processing a q-ASK
signal is significantly less than that of processing a general
M-QAM signal.
[0005] A received M-QAM signal (r.sub.k) may be represented by the
following expression:
r.sub.k=A*d.sub.k+n.sub.k; Equation (1)
where A is the signal amplitude; d.sub.k represents a set of data
symbols encoded onto a transmitted M-QAM or q-ASK signal; and
n.sub.k represents noise. While for M-QAM signals, d.sub.k and
n.sub.k are complex quanities, for Q-ASK signals they are both
purely real.
[0006] In order to demodulate M-QAM and q-ASK signals, it is
necessary to determine the values of one or more signal parameters
at the receiver, such as amplitude, noise power, and
signal-to-noise ratio (SNR). Even in the case of a Q-ASK signal
representation, which provides enhanced computational simplicity
relative to M-QAM representation, existing techniques for
estimating these signal parameters are inefficient and
computationally complex.
[0007] An improved technique for estimating signal parameters at
the receiver is needed to provide efficient demodulation of M-QAM
and Q-ASK signals.
SUMMARY
[0008] The present invention provides an improved system and method
for estimating one or more parameters of a received M-QAM or q-ASK
signal, such as amplitude and SNR. A first embodiment of the
invention estimates the amplitude of an M-QAM signal based upon
known or ascertainable phase information regarding a plurality of
transmitted symbols. A respective set of received symbols,
corresponding to the plurality of transmitted symbols, is
recovered. Each of the plurality of received symbols is multiplied
by a complex unit vector with a phase that is opposite in sign to
the complex transmitted data symbol to generate a set of products.
The set of products is summed, and the real part of the sum of
products is then determined. The absolute values of the known
transmitted symbols are summed to generate a total magnitude value.
The real part of the sum of products is divided by the sum of
transmitted magnitude values to generate an estimate of the
amplitude of the M-QAM signal.
[0009] A second embodiment of the invention estimates the amplitude
of a q-ASK signal at a receiver based upon known or ascertainable
magnitude information regarding a plurality of transmitted symbols.
A respective set of N received samples corresponding to the
transmitted symbols is recovered. For each of the N samples, the
sample is multiplied by the corresponding sign of the transmitted
symbol to generate a set of products. This set of products is then
summed to generate a first sum. The absolute values of the
transmitted symbols are then summed to generate a second sum. The
first sum is divided by the second sum to generate an estimated
amplitude for the q-ASK signal.
[0010] A third embodiment of the invention estimates the amplitude
of an M-QAM or q-ASK signal with no assumed knowledge of the
specific transmitted data symbols. Only statistical knowledge of
the amplitude of the transmitted data symbols is assumed. A
respective set of received samples corresponding to the transmitted
symbols is recovered. The absolute values of the received samples
are determined and summed to generate a first sum. The mean of the
absolute values of the amplitudes of transmitted symbols is
determined and then multiplied by the total number of received
symbols to generate a product. The first sum is divided by the
product to generate an estimated amplitude for the M-QAM or q-ASK
signal.
[0011] Other embodiments of the present invention utilize
second-order and fourth-order moments of received samples, a
maximum likelihood searching process, or a Kurtosis estimation
process to estimate amplitude, noise power, and signal-to-noise
ratio of a received signal.
BRIEF DESCRIPTION OF THE DRAWING(S)
[0012] FIG. 1 is a flow diagram of a procedure for estimating the
amplitude of an M-QAM signal based upon known or ascertainable
phase information concerning a plurality of transmitted symbols,
according to a first embodiment of the invention.
[0013] FIG. 2 is a flow diagram of a process for estimating the
amplitude of a q-ASK signal at a receiver based upon known or
ascertainable magnitude information regarding a plurality of
transmitted symbols, pursuant to a second embodiment of the
invention.
[0014] FIG. 3 is a flow diagram of a procedure for using absolute
values of received samples to estimate the amplitude of an M-QAM or
q-ASK signal, pursuant to a third embodiment of the invention.
[0015] FIG. 4 is a flow diagram of a procedure for using
second-order and fourth-order moments of received samples to
estimate amplitude, noise power, and signal-to-noise ratio of an
M-QAM signal that includes a set of transmitted symbols, pursuant
to a fourth embodiment of the invention.
[0016] FIG. 5 is a flow diagram of a procedure for using
second-order and fourth-order moments of received samples to
estimate amplitude, noise power, and signal-to-noise ratio of a
q-ASK signal that includes a set of transmitted symbols, pursuant
to a fifth embodiment of the invention.
[0017] FIGS. 6A, 6B and 6C are a flow diagram of a procedure for
using a maximum likelihood searching process to estimate the
amplitude, noise power, and signal-to-noise ratio of a q-ASK or
M-QAM signal that includes a set of transmitted symbols, pursuant
to a sixth embodiment of the invention.
[0018] FIGS. 7A and 7B are a flow diagram of a Kurtosis estimation
process for estimating the signal-to-interference ratio of an M-QAM
or q-ASK signal using second-order and fourth-order moments of
received samples, pursuant to a seventh embodiment of the
invention.
DETAILED DESCRIPTION
[0019] Improved systems and methods are disclosed for estimating
one or more parameters of a received M-QAM or q-ASK signal, such as
amplitude and signal-to-noise ratio. A first embodiment of the
invention is a method 100 which estimates the amplitude of an M-QAM
signal based upon known or ascertainable phase information
concerning a plurality of transmitted symbols (d.sub.k). If the
receiver has knowledge of the transmitted M-QAM symbols d.sub.k,
for example in systems employing pilot signals, this information
may be used to estimate the amplitude, A, as:
A ^ = Re ( k = 1 N r k exp [ - j .theta. ( d k ) ] ) k = 1 N d k ;
Equation ( 2 ) ##EQU00002##
where .theta.(d.sub.k) is the phase of complex symbol d.sub.k and N
is the number of received symbols being processed. Re( ) represents
the Real operator, noting that one may substitute many other
operators without substantively changing the invention.
[0020] More specifically, referring to FIG. 1, a respective set of
received symbols (r.sub.k), corresponding to the plurality of
transmitted symbols, is recovered (step 101). Each of the plurality
of received symbols (r.sub.k) is multiplied by exp
[-j.theta.(d.sub.k)] to generate a set of products (step 103),
where .theta.(d.sub.k) represents the phase of a corresponding
transmitted symbol (d.sub.k). The set of products is summed (step
105), and the real part of the sum of products is then determined
(step 107). The absolute values of the transmitted symbols
|(d.sub.k)| are summed to generate a magnitude value (step 109).
The real part of the sum of products is divided by the magnitude
value to generate an estimated amplitude for the M-QAM signal (step
111).
[0021] A second embodiment of the invention is a method 200 which
estimates the amplitude of a q-ASK signal at a receiver based upon
known or ascertainable magnitude information regarding a plurality
of transmitted symbols (d.sub.k). If d.sub.k is q-ASK signal, then
amplitude estimation may proceed in accordance with the following
equation:
A ^ = k = 1 N y k sign ( d k ) k = 1 N d k . Equation ( 3 )
##EQU00003##
With reference to FIG. 2, a respective set of N received samples
(y.sub.k) corresponding to the transmitted symbols (d.sub.k) is
recovered (step 201). For each of the N samples, the sample
(y.sub.k) is multiplied by a corresponding sign (d.sub.k) to
generate a set of products (y.sub.k)*sign(d.sub.k) (step 203). This
set of products is then summed to generate a first sum (step 205).
The absolute values of the transmitted symbols |(d.sub.k)| are then
summed to generate a second sum (step 207). The first sum is
divided by the second sum to generate an estimated amplitude for
the q-ASK signal (step 209).
[0022] A third embodiment of the invention is a method 300 which
uses absolute values to estimate the amplitude of an M-QAM or q-ASK
signal which includes a set of N transmitted symbols (d.sub.k),
where N is a positive integer greater than one. In many cases, the
receiver lacks information about the transmitted symbols d.sub.k,
such as the phases and magnitudes of the symbols. Accordingly, the
amplitudes of the received samples may be utilized to generate an
amplitude estimate for both M-QAM and q-ASK signals from the
relationship:
A ^ = k = 1 N y k N E d k ; Equation ( 4 ) ##EQU00004##
where E|d.sub.k| is the mean of the amplitude of signal d.sub.k and
may be computed theoretically or empirically. For example, for
4-ASK modulation with
d k .di-elect cons. { .+-. 1 2 , .+-. 3 2 } ##EQU00005##
with equal probability, E|d.sub.k|=1, the amplitude estimate
is:
A ^ = 1 N k = 1 N y k . Equation ( 5 ) ##EQU00006##
[0023] With reference to FIG. 3, a respective set of received
samples (y.sub.k) corresponding to the transmitted symbols
(d.sub.k) is recovered (step 301). The absolute values of the
received samples |(y.sub.k)| are determined (step 303) and summed
(step 305) to generate a first sum. The mean of the absolute values
of the amplitudes of transmitted symbols, E|(d.sub.k)|, is
determined (step 307) and then multiplied by N to generate a
product, N*E|(d.sub.k)| (step 309). The first sum is divided by the
product to generate an estimated amplitude for the M-QAM or q-ASK
signal (step 311).
[0024] Through the use of second-order and fourth-order moments of
received samples, a method 400 of a fourth embodiment of the
invention estimates the amplitude, noise power, and signal-to-noise
ratio of an M-QAM signal that includes a set of transmitted symbols
(d.sub.k). The noise at the receiver takes the form,
n.sub.k=n.sub.k.sup.R+jn.sub.k.sup.I, where n.sub.k.sup.R and
n.sub.k.sup.I can be approximated as two independent Gaussian
variables with zero means and same variance .sigma..sub.r.sup.2,
E|n.sub.k|.sup.2=2.sigma..sub.r.sup.2 which is often exact, or at
least a good approximation. The amplitude is estimated as:
A ^ = 2 ( E r k 2 ) 2 - E r k 4 2 ( E d k 2 ) 2 - E d k 4 .
Equation ( 6 ) ##EQU00007##
The noise power is estimated as:
{circumflex over
(.sigma.)}.sub.n.sup.2=E|r.sub.k|.sup.2-A.sup.2E|d.sub.k|.sup.2.
Equation (7)
Using the above two Equations (6) and (7), the SNR is estimated
as:
SNR=A.sup.2E|d.sub.k|.sup.2/{circumflex over
(.sigma.)}.sub.n.sup.2. Equation (8)
[0025] Referring now to FIG. 4, the method 400 begins when a
respective set of received samples (r.sub.k) corresponding to the
transmitted symbols (d.sub.k) is recovered (step 401). The mean of
the absolute values of the amplitudes of the transmitted symbols,
E|(d.sub.k)|, as well as the mean of the absolute values of the
amplitudes of the received samples, E|(r.sub.k)|, are determined
(step 403). The estimated amplitude A is determined using Equation
6 (step 405). Estimated noise power .sigma..sup.2.sub.n is
determined from estimated amplitude A using equation 7 (step 407).
Optionally, estimated SNR is then determined using Equation 8 (step
409)).
[0026] Through the use of second-order and fourth-order moments of
received samples, a method 500 of a fifth embodiment of the
invention estimates amplitude, noise power, and SNR of a q-ASK
signal that includes a set of transmitted symbols (d.sub.k). When a
real q-ASK signal is transmitted, the second and fourth order
moments may be used to estimate the signal amplitude and power
as:
A ^ = 3 ( E ( r k 2 ) ) 2 - E ( r k 4 ) 3 ( E ( d k 2 ) ) 2 - E ( d
k 4 ) 4 ; and Equation ( 9 ) A ^ 2 = 3 ( E ( r k 2 ) ) 2 - E ( r k
4 ) 3 ( E ( d k 2 ) ) 2 - E ( d k 4 ) . Equation ( 10 )
##EQU00008##
The noise power is estimated as:
{circumflex over
(.sigma.)}.sub.n.sup.2=E(r.sub.k.sup.2)-A.sup.2E(d.sub.k.sup.2).
Equation (11)
Using Equations (10) and (11), the SNR is estimated as:
SNR=A.sup.2E(d.sub.k.sup.2)/{circumflex over
(.sigma.)}.sub.n.sup.2. Equation (12)
[0027] Expectations involving d.sub.k may be computed empirically
or theoretically. For example, for 4-ASK modulation
E(d.sub.k.sup.2)=1.25 and E(d.sub.k.sup.4)=2.5625. The signal
amplitude and power may be estimated by substitution with the
determined values e.g.,
A ^ = 3 ( E ( r k 2 ) ) 2 - E ( r k 4 ) 2.125 4 ##EQU00009## and
##EQU00009.2## A ^ 2 = 3 ( E ( r k 2 ) ) 2 - E ( r k 4 ) 2.125 ,
##EQU00009.3##
respectively. The SNR is estimated by using Equation (12). Various
methods for generating estimates of the expectations involving
r.sub.k may be used.
[0028] With reference to FIG. 5, the method 500 begins when a
respective set of received samples (r.sub.k) corresponding to the
transmitted symbols (d.sub.k) is recovered (step 501). The mean of
the amplitudes of the transmitted symbols, E(d.sub.k), as well as
the mean of the amplitudes of the received samples, E(r.sub.k), are
determined (step 503). Estimated amplitude A is determined using
Equation 9 (step 505). Optionally, estimated power is determined
using Equation 10 (step 507). Estimated noise power
.sigma..sup.2.sub.n is determined from estimated amplitude A using
Equation 11 (step 509). Optionally, estimated SNR may then
determined using Equation 12 (step 511).
[0029] Using a maximum likelihood searching process, a method 600
of a sixth embodiment of the invention estimates at least one of
the amplitude, noise power, and signal-to-noise ratio of a q-ASK or
M-QAM signal that includes a set of transmitted symbols (d.sub.k).
Assuming the received samples are sufficiently independent, the
joint probability density function of r.sub.1, r.sub.2, . . . ,
r.sub.N may be assumed to be the product of the marginal
distributions of r.sub.k, that is:
f ( A , .sigma. n ; r 1 , r 2 , , r N ) = k = 1 N f ( A , .sigma. n
; r k ) ; Equation ( 13 ) ##EQU00010##
where f(A, .sigma..sub.n; r.sub.k) is an estimate of the density of
r.sub.k. The goal of the maximum-likelihood amplitude estimator is
to find the amplitude, A, that maximizes the joint probability
density function as shown by Equation (13), i.e.:
A ^ = arg max A f ( A , .sigma. n ; r 1 , r 2 , , r N ) . Equation
( 14 ) ##EQU00011##
[0030] The following search algorithm finds the maximum likelihood
estimate for amplitude, and optionally for noise power and SNR:
First, the received vector r.sub.k is normalized such that its
average power is unity, (i.e.
1 N k = 1 N r k 2 = 1. ##EQU00012##
) A.sub.min and A.sub.max are selected according to the minimum and
maximum SNR over which to search as follows:
A min = S N R min 1 + S N R min ; and Equation ( 15 ) A max = S N R
max 1 + S N R max . Equation ( 16 ) ##EQU00013##
[0031] The amplitude search step size .DELTA. is selected such that
it achieves the desired amplitude resolution. Next,
A.sub.k=A.sub.min+k.DELTA. is determined, where 0.ltoreq.k.ltoreq.K
and
K = A max - A min .DELTA. . ##EQU00014##
For each amplitude A.sub.k, a corresponding noise power is
determined as:
.sigma..sub.n.sup.2=1-E|d.sub.k|.sup.2A.sub.k.sup.2. Equation
(17)
[0032] The joint probability density function f(A.sub.k,
.sigma..sub.n; r.sub.1, r.sub.2, . . . , r.sub.N) is calculated for
each A.sub.k. The value A.sub.k that corresponds to the maximum
joint PDF, (i.e.,
A ^ = arg max A k ; k .di-elect cons. { 1 , 2 , , K } f ( A k ,
.sigma. n ; r 1 , r 2 , , r N ) ) , ##EQU00015##
is searched for, and then A is the estimated amplitude.
[0033] Additionally, (and optionally,) a value for the estimated
noise power can be determined from the estimated amplitude A as the
total power less the product of the amplitude estimate squared and
the expected data symbol power, (i.e.,
.sigma..sup.2.sub.n=E(r.sub.k).sup.2-A.sup.2E(d.sub.k).sup.2).
Optionally, a value for the estimated SNR can be determined by
taking the ratio of the estimated signal power and the estimated
noise power, (i.e., from the relationship
SNR=[A.sup.2*E(d.sub.k).sup.2]/.sigma..sup.2.sub.n.)
[0034] With reference to FIGS. 6A, 6B and 6C, the method 600
briefly described in the foregoing paragraphs is described in
greater detail. A respective set of received samples (r.sub.k)
corresponding to the transmitted symbols (d.sub.k) is recovered
(step 601). N received samples (r.sub.k) are normalized, (N being a
positive integer greater than one), such that
1 N k = 1 N r k 2 = 1 ##EQU00016##
(step 603). Trial values for A.sub.min and A.sub.max are selected
according to the minimum and maximum SNRs over which to search
using Equation 15 and 16 (step 605).
[0035] An amplitude search step size .DELTA. is selected to achieve
a desired or predetermined amplitude resolution (step 607). Next, a
value for A.sub.k=A.sub.min+k.DELTA. is determined, where
0.ltoreq.k.ltoreq.K and
K = A max - A min .DELTA. ##EQU00017##
(step 609). For each amplitude A.sub.k, a corresponding noise power
is then estimated using Equation 17 (step 611).
[0036] A joint probability density function f(A.sub.k,
.sigma..sub.n; r.sub.1, r.sub.2, . . . , r.sub.N) is then
determined for each A.sub.k (step 613).
[0037] For both M-QAM and q-ASK signals, a main objective of the
maximum-likelihood searching process is to find a value for the
estimated amplitude, A, that maximizes the joint probability
density function using Equation 14 (step 615). At step 617, a
search is conducted to find a value for A.sub.k that corresponds to
the maximum joint probability density function. This value for
A.sub.k is substituted into the Equation
A ^ = arg max A k ; k .di-elect cons. { 1 , 2 , , K } f ( A k ,
.sigma. n ; r 1 , r 2 , , r N ) ##EQU00018##
to obtain a value for A, representing an estimated amplitude value
(step 619).
[0038] Optionally, a value for estimated noise power can be
determined from the estimated amplitude A as the estimated total
power less the product of the amplitude estimate squared and the
expected data symbol power, (i.e.,
.sigma..sup.2.sub.n=E(r.sub.k).sup.2-A.sup.2E(d.sub.k).sup.2 (step
621)). Additionally, (and optionally), a value for estimated SNR
can be determined as a ratio of the estimated signal power and the
estimated noise power, (i.e.,
SNR=[A.sup.2*E(d.sub.k).sup.2]/.sigma..sup.2.sub.n) (step 623).
[0039] Pursuant to a method 700 of a seventh embodiment of the
invention, a Kurtosis estimation process estimates the
signal-to-noise ratio of an M-QAM or q-ASK signal using
second-order and fourth-order moments of received samples
(r.sub.k). As a first step, the Kurtosis of the noise only
(K.sub.CG) and signal only (K.sub.sig) present is computed. In this
example, complex Gaussian noise is used for illustrative purposes.
However, other noise distributions may be assumed and do not
deviate substantively from this invention. Expectations involving
d.sub.k and n.sub.k may be computed empirically or theoretically,
e.g., the Kurtosis values are determined as follows:
K CG .ident. E { n k 4 } E { n k 2 } 2 = 2 ; and Equation ( 18 ) K
sig .ident. E { d k 4 } E { d k 2 } 2 ; Equation ( 19 )
##EQU00019##
where complex, circularly symmetric Gaussian noise is assumed. For
example, with QPSK data, K.sub.sig=K.sub.QPSK=1, for square 16QAM
data, K.sub.sig=K.sub.16QAM=1.32. The K.sub.sig parameter for any
signal constellation can be readily obtained.
[0040] The Kurtosis for rectangular and `cross` QAM constellations
can also be used with this method and determined as outlined above.
The Kurtosis may be written in terms of, and solved for the SNR as
follows:
S N R = ( 2 - Kurt ( r ) ) + ( 4 - 2 K M - QAM ) - ( 2 - K M - QAM
) Kurt ( r ) ( Kurt ( r ) - K M - QAM ) . Equation ( 20 )
##EQU00020##
Any of a variety of Kurtosis estimates or approximations may be
used.
[0041] Referring to FIGS. 7A and 7B, a flow diagram of the details
of the foregoing Kurtosis process is shown. As a preliminary
matter, the second-order moment is defined as
E{|r.sub.k|.sup.2}=E{|n.sub.k|.sup.2}+E{|d.sub.k|.sup.2}, and the
fourth-order moment is defined as
E{|r.sub.k|.sup.4}=E{|n.sub.k|.sup.4}+E{|d.sub.k|.sup.4}+4E{|n.sub.k|.sup-
.2}E{|d.sub.k|.sup.2}, where d.sub.k denotes the transmitted
symbols and n.sub.k denotes a noise component that is recovered
with the received samples r.sub.k (step 701). At step 703, the
fourth-order moment is divided by the second-order moment so as to
implement a Kurtosis operation as follows:
Kurt ( r ) .ident. E { r k 4 } E { r k 2 } 2 = E { d k 4 } + E { n
k 4 } + 4 E { d k 2 } E { n k 2 } E { d k 2 } 2 + E { n k 2 } 2 + 2
E { d k 2 } E { n k 2 } . Equation ( 21 ) ##EQU00021##
[0042] In order to estimate the SNR, it is necessary to determine
the Kurtosis attributable to noise alone (step 705). For example,
assuming the complex circularly symmetric Gaussian noise, the
Kurtosis of the noise alone is determined using Equation 18. The
Kurtosis attributable to the signal alone, (K.sub.sig), is
determined using Equation 19 (step 707). For example, with QPSK
data, K.sub.sig=K.sub.QPSK=1 may be used. For square 16QAM data,
K.sub.sig=K.sub.16QAM=1.32 may be used. For high order modulation,
square M-QAM, the signal Kurtosis K.sub.sig approaches that of the
square complex uniform distribution:
lim M .fwdarw. .infin. ( K M - QAM ) = 1.4 . ##EQU00022##
However, use of a square constellation is not required, since the
Kurtosis for rectangular and `cross` QAM constellations can also be
utilized in conjunction with this method and pre-computed in the
same way.
[0043] Once an appropriate value for K.sub.sig (e.g., K.sub.M-QAM
in the case of a M-QAM signal) is determined, the method 700 of
FIG. 7 advances to step 709 where the signal-to-noise ratio (SNR)
is estimated using Equation 20.
* * * * *