Note: Descriptions are shown in the official language in which they were submitted.
CA 02347747 2001-04-19
EQUALIZATION METHOD ESPECIALLY FOR OFFSET
MODULATION MODES
Technical field
S The invention relates to a ;nethod for
equalizing a received signal in a digital receiver with
the aid of a DFE (Decision Feedback Equalizer)
structure, the received signal being based on a signal
constellation which is one-dimensional or can be
transformed to be one-dimensional.
CA 02347747 2001-04-19
PCT/CH99/00509
Owner ASCOm Systec AG et al.
- lA-
10
Prior art
The transmition channels typically occurring in
the case of GSM (Global System for Mobile
Communication), HIPERLAN (High PErformance Radio Local
Area Netzwork), DECT (Data Exchange for Cordless
Telephone) etc. are characterized by the interfering
effects of multipath propagation.
It is known that a Decision Feedback Equalizer
(DFE) can be used in order to equalize in the digital
communication system a signal which ha:~ been disturbed
by a linear frequency-selected process (such as the
multipath propagation in a radio channel., for example).
The performance of a DFE depends on the quality
with which the filter coefficients are calculated
and/or fixed in the feedforward part and in the
feedback part. In the case of an unknown channel, the
coefficients are typically fixed by adaptive training.
If the pulse response of the channel is known, by
contrast, the optimum coefficients of the DFE can then
be derived therefrom.
The structure of a DFE is very simple per se
and therefore very readily used. However, it is not
always possible to achieve the desired performance.
From [sic] the publication entitled Optimum
MMSE Equalization for staggered modulations by J.C. Tu
RS/mg-13842 AMENDED SHEET xeller & Partner
09.10.00
Patentanwalte AG
CA 02347747 2001-04-19
PCT/CH99/00509
Owner: Ascom Systec AG et al.
lb
describes a DFE for signals in the case of which the
modulation of the quadrature and in-phase components is
performed in a staggered fashion. The mean quadratic
error is minimized only in one dimension of the
modulated symbols during symbol estimation.
Scary of the invention
The object of the invention is to specify a
method of the type mentioned at the beginning which
permits the determination of optimum coefficients with
as little outlay on computation as possible on the
basis of the known and/or previously estimated channel
unit pulse response, an enhanced performance being
achieved at the same time by comparison with the known
DFE in accordance with the prior art.
Patentanwalte AG
RS/mg-13842 AMENDED SHEET xeller s Partner
09.10.00
CA 02347747 2001-04-19
- 2 -
The features of Claim 1 define the achievement
of the object. In accordance with the invention, the
coefficient of the DFE are fixed so as to minimize the
expected value of the squared real part of the error.
By contrast with the prior art, the error,
which is a complex value per se, is not used as a basis
for optimization. However, calculation is limited to
the real value. The filter coefficients of the feedback
filter are not complex, only those of the feedforward
filter being so in general. The essential point is that
the performance of the DFE structure can be improved in
this basically simple way, it even being possible to
reduce the computational outlay in comparison with the
prior art.
In the case of a binary BPSK signal the
coefficients are preferably calculated in accordance
with the formulas (I) and (II) specified further below.
The invention is suitable not only for BPSK
(BPSI [sic] - Binary Phase Shift Keying) signals, but
also for GMSK and OQPSK modulation methods (GMSK -
Gaussian Minimum Shift Keying, OQPSK - Offset
Quadrature Phase Shift Keying) . Also t:o be regarded as
one-dimensional modulation methods are, therefore,
those which although having a two-dimensional signal
constellation can be transformed (with the aid of a
suitable transformation) into an (at least
approximately) equivalent one-dimensional represent-
ation.
The circuitry for implementing the method
according to the invention poses no special
difficulties. The calculation is typically programmed
in a processor or ASIC.
The invention is suitable, for example, for a
HIPERLAN system. (Such an advantageous system structure
follows, for example, from EP 0 795 976 A2, Ascom Tech
CA 02347747 2001-04-19
- 3 -
AG). The so-called European Telecommunications Standard
(ETS) defines the technical characteristics of a
wireless local high performance network (HIPERLAN).
HIPERLAN is a short range communications subsystem with
a high data rate (compare in this regard ETSI 1995,
ETS 300 652, UDC: 621 396). The ETS-HIPERLAN standard
is provided for the frequency band 5.15 to 5.30 GHz.
Further advantageous embodiments and
combinations of features of the invention result from
the following detailed description and the totality of
the patent claims.
Brief description
of the drawings
In the drawings used to explain the exemplary
embodiment:
Figure 1 shows a diagrammatic illustration of a
DFE;
Figure 2 shows a diagrammatic illustration of an
exemplary embodiment;
Figure 3 shows a representation of the
performance of the method according to
the invention by comparison with the
prior art;
Figures 4a-c show a comparison of the error behavior
in the prior art and with the invention;
Figure 5 shows a diagrammatic illustration of a
BPSK receiver;
Figure 6 shows a diagrammatic illustration of a
GMSK receiver.
Ways of implementing the invention
The principle of the invention is to be stated
below by a comparison with the prior art.
Figure 1 shows a block structure, known per se,
of a DFE. The received signal I downwardly modulated by
the carrier is entered into a feedforward filter FF of
the DFE. Thereafter, it is combined (adder) with the
estimated signal I fed back by the decision devide DD
via the feedback filter FB. The signal I is therefore
CA 02347747 2001-04-19
present at the input of the decision device DD. The
coefficients f and g (which are understood in the
present as vectors with a plurality of coefficient
components) are calculated as follows in accordance
with the prior art:
Inin E ~I - ,III ( ) ..
JrJ:
In contrast therewith, the invention carries
out the following optimization:
min.~~Re~l -I~~2 (B)
a~,,,,
The difference from the prior art therefore
consists in the type of calculation of the filter
coefficients. The remaining structure of the DFE is
maintained without change. This is explained in detail
below with the aid of exemplary embodiments.
Figure 2 shows a concrete example of a DFE . As
is usual for modern coherent digital receivers, the
signal processed by it is represented by complex
numbers. The real part stands in this case for the in
phase component, and the imaginary part stands for the
quadrature component. In accordance with the generally
current understanding, the DFE shown in Figure 2 has
complex coefficients and complex data.
If only the real part of the error is optimized
according to the MMSE (MMSE - Minimum Mean Square
Error) criterion, the feedforward filter coefficients
are given by the following system of equations:
~a ,~.r A.r
fx"~~~.~t~~n hlc _~ ~'l~hr, _ y
Mi-I-I '- 2 I L.. m G~ ml-i ntl-.u Jur na~l i ntl-m
m-l n_1 m-I ~r-I
I a;~ M A~l l .A.! l I
I
- hMYt-I =. 2 -. ~ f,H ~ hl,.,~-I hr~ ~-lu + ~ fnr ~ ~rr~I~1-I hrr~rl-rn
n~::l n=t rn=~ r~ol
.. . .. _...4.._.-w...~w.m..~,...,~.."..,.~-,.. ~~-..wv..~.~.. ~_.. ., . ..
..,.. .. ...ut...-.. ~._~.......~._ .. .._... ..~. ......_
.......~...,....~~.._
CA 02347747 2001-04-19
- 5 -
These are 2M real equations (1 5 i < M).
Coefficients whose indices are too great or too small
are to be taken as 0 in this case. The indices run from
1 to L for vectors of length L. The values of the
filter coefficients can be obtained a sing methods known
per se for solving systems of linear equations. There
is no need to go into these standard methods in more
detail.
The feedback filter coefficients are determined
by the following equations:
M
__ _~ ~rrh rr
111 I~f~"'fJl Irr t+~~f)7
llfw
These are N-1 equations, because M + 1 < i < M + N - 1.
Formulae (I) and (II) are based on the
following conventions:
N length of the channel unit pulse response;
M length of the feedforward filter;
h1R real part of the channel unit pulse response,
1 < i < N.
hli imaginary part of the channel unit pulse response,
1 < i < N.
f1R real part of the filter coefficients of the
feedforward part of the DFE, 1 S i S M,
z
fl imaginary part of_ the filter coefficients of the
feedforward part of the DFE, 1 5 i S M,
giR real part of the filter coefficients of the
feedforward part of the DFE, 1 S i < N-l,
noise power at the input of the DFE (real part and
imaginary part of the noise power combined). If
this value is nct known, it can be set to be
constant without substantially reducing the
performance.
Mostly, M = N. It is no advantage to have
N < M. The complexity can be reduced at the expense of
the performance if N > M. However, the calculation
CA 02347747 2001-04-19
- 6 -
according to the invention nevertheless supplies the
optimum filter coefficients with reference to the mean
quadratic error.
The length of the feedback filter is equal to
or one shorter than the length of the channel unit
pulse response (that is to say N-1). Were the length
selected to be larger, the coefficients of the
additional taps would all be 0. A shorter length would
lead to intersymbol interference at the input of the
decision device. Because the addition of taps to the
feedback filter does not substantially increase the
overall complexity, the full length is used as a rule.
The coefficients of the feedback filter have no
imaginary part. The reason for this is that the input
to the feedback filter is real, as is its output. (The
imaginary part of the input of the decision device is
not considered.)
The calculation according to the invention of
the filter coefficients is suitable for different
applications. It is shown below how the performance of
a HIPERLAN receiver can be improved. In this case, the
known complex MMSE method is contrasted with the real
MMSE method according to the invention. It is
presupposed, furthermore, that the receivers carry out
a 3-antenna selection diversity. Simulation of the
appropriate receivers permits the packet error rate to
be estimated.
It is assumed that the parameter a2 lies 10 dB
and [sicJ the received signal power in the receiver.
Furthermore, the starting point is radio channels with
a delay spread of 45 ns or 75 ns. The DFE has a 8
feedforward taps and 7 feedback tabs.
The results displayed in Figure 3 show a
significant improvement in both applications of the
calculating method according to the invention. The
error rate is higher for large delay spreads (75 ns).
Error rates below the threshold of measureability are
established at 20 dB signal-to-noise and 45 ns delay
spread.
CA 02347747 2001-04-19
The effect of the method according to the
invention can be illustrated with the aid of Figures 4a
to 4c. If QPSK [sic] is used as modulation method, the
decision device outputs one of the four complex values
1 + j, 1 - j, -1 + j, -1 - j as a function of which of
them comes closest to the input value of the decision
device. The input value is distorted by the noise and
the non-eliminated residual intersymbol interference.
This is expressed in Figures 4a-c by the cloud-like
distributions.
The minimization of the complex quadratic error
leads to a distribution resembling a circular disk
around each constellation point, as is shown in Figures
4a and 4b. By contrast therewith, the minimization
according to the invention of the real part of the
quadratic errors leads to an oval distribution (Figure
4c) which is, as it were, squashed. Viewed in the
complex plain, the mean value of the (complex)
quadratic error is greater than in the case of the
prior art (Figures 4a, b). However, the error is
shifted onto the imaginary axis. On the real axis, it
is smaller than in the case of the prior art. However,
since the output of the decision device can only be
real, the increased error plays no role on the
imaginary axis.
Figure 5 shows how the invention is integrated
in a BPSK receiver. The data 1 are modulated onto a
carrier wave in a transmitter by a BPSK modulator 2. In
a receiver, a demodulator 3 ensures the received signal
is converted into the frequency baseband, and ensures
the appropriate filtering. Thereafter, the signal is
sampled at the symbol rate (sampler 4). The output of
the sampler is processed by the channel estimator 5, on
the one hand, and by the DFE 7, on the other hand. The
calculation of the coefficients in accordance with the
invention takes place in the coefficient computer 6.
The transmitted data 8 are present at the output of the
DFE 7. The structure of the receiver is known per se.
What is new is the way described further above in which
CA 02347747 2001-04-19
_ g _
the coefficients are determined in the coefficient
computer 6.
Fundamentally, the invention can also be used
for a QPSK [sic] method (the modulators/demodulators
requiring to be appropriately designed). By contrast
with the BPSK receiver, it is then necessary for the
DFE to operate in each case with complex numbers.
The general layout of the GMSK transmission
method is shown in Figure 6. The data ~~ are precoded in
a known way on the transmitter side in a precoder 10
and modulated onto a carrier way with t:he aid of a GMSK
modulator 11. A demodulator 12 in a receiver ensures
conversion of the received signal into the frequency
baseband, and ensures appropriate filtering.
Thereafter, the signal is sampled (sampler 13) at the
symbol rate. The output of the sampler is multiplied by
a phase factor jl (phase shifter 14, multiplier 15) and
thereafter processed by the channel estimator 16, on
the one hand, and by the DFE 18, on the other hand. The
calculation of the coefficients takes place according
to the invention in the coefficient computer 17. The
transmitted data 19 are present at the output of the
DFE 18. Here, as well, the structure of the receiver is
known per se. What is new is the way in which the
coefficients are determined in the coefficient
computer 6.
The aim below is to explain how the invention
can be used for GMSK and OQPSK modulation methods,
which seem at first glance to have a two-dimensional
signal constallation.
It is known that the GMSK modulated signal
represented in the complex baseband can be specified as
follows by a binary bit stream with the symbols
bk E[-l, + 1], k = ...-1, 0, l, 2...:
~-r~~
( I I I ) s~ ~t ~ = A exp '~ ~ ~ b~ ~g (t )d r + ~"
2 ~
CA 02347747 2001-04-19
_ g _
A and ~o denote the amplitude and the initial
carrier phase; g(i) is the (Gaussian partial response)
pulse, which defines the phase modulation, and T is the
symbol or bit duration.
The modulated signal can be approximated
effectively by the following linear partial response
QAM signal, as a function of the pulse g(i):
s"~I~=' ~ exP(,'~"~~a~~~t-k~'~
k
In this case, the terms ak are complex data
symbols which depend only on the symbols bk and have
the value range [+ 1, -1, + j, -j] , g (t) is a partial-
response pulse shaping function. It holds that:
. ., ?C k ,
ax ~ e~, ~..._ ~ b~
2 '
!~ c-co
It is known (Baier, A. et al., "Bit
Synchromization and Timing sensitivity in Adaptive
Viterbi Equalizers for Narrowband-TDMA Digital Mobile
Radio Systems", IEEE 1988, CH 2622-9/9/0000-0377] that
the above approximation can be very good for GMSK
modulation with the aid of a time/bandwidth product of
0.3 as used in GSM and HIPERLAN.
This approximation corresponds precisely to a
linear QAM modulation with the aid of data symbols from
the value range [+l, -l, +j, -j]. The sum
k
~n
l1 ~ ~a0
is alternately even and odd, so that transmitted
symbols a.k are alternately real and imaginary. This
modulation is known under the designation of OQPSK
(offset quadrature phase shift keying). The transition
CA 02347747 2001-04-19
- 10 -
between the symbols ak and bk is very simple. It may be
pointed out that the transition from a~ to bk is robust
against errors, whereas it is not so for the inverse
transition. A single error in the sequence bk will
entail very many (possibly infinitely many) errors in
the derived sequence of the symbols ak.
The transmitted symbols ak must be recovered in
the receiver. It is assumed below that the same frame
synchronization is available in the transmitter and in
the receiver. It is known of the first symbol ao that
it is real (specifically either +1 or -1). If the first
symbol is imaginary, a slight adaptation of the
subsequent formalism is required. The transmitted
signal is so(t) and the received signal is r(t), which
constitutes a convolution with the channel unit pulse
response and the analog filters of the receiver:
tip r~t~ ~ A~~k j~~t ._ kT~
k
h(t) being the convolution of the transmission signal
with g'(t), the initial phase shift, the channel unit
pulse response and the pulse response of the totality
of the filters on the receiver side.
The complex baseband signal is sampled in the
receiver in accordance with the channel symbol rate so
as to generate a time-discrete signal. This can be
described as follows:
~VI I) ~, _ ~~ ax h(iT + ~. - k~'~
x
A sampling phase ~, was adopted. ~,=0 can be set
without limitation of generality, because a time delay
can always be included in the channel unit pulse
response.
The signal is multiplied by the phase j-1 before
being fed to the DFE:
CA 02347747 2001-04-19
- ~. 1 -
r, = , j J' ~I~ ak h(i ~'' __ l~")
k
(VIII) r, = A~.j-kak~ ~I ~'~hC~I-~~~
K
rl =~~'~h~~'"k~'~
x
ck is the ak. Note
data sequence
derived
from
that the phase only [+l, -1,
j-1 can the
assume values
+j, -j), It very multiply
is therefore easy
to
that [sic] received by (compare
signal this
phase
multiplier
14 in
Figure
6).
l l l-1.+1
(IX) ct =~-'ak ~=exp ~, s111
=expCr ~-k+ E,
Z ~exp~ ~b~~~ E~~-~,fi)~
2 ~b"
2 f .,
One of these cases can be avoided if a frame
synchronization is available. The second possibility is
therefore ignored. It can therefore be detected that
the signal values sampled on the receiver side is [sic)
a convolution of the exclusively real data sequence ck
with the specific function h(t) which includes:
~ the pulse shaping of the modulation,
~ the channel unit pulse response,
~ the initial phase of the carrier signal,
~ the time offset of the sampling, and
~ the rotation with the phase j-1 in the receiver.
The function can be determined, for example, with the
aid of a training sequence and a correlation
calculation in the receiver. This is the function which
is used in the receiver to calculate the filter
coefficients of the DFE. The DFE must generate only a
real output, because the basic data are exclusively
real (ck). Finally, it. is possible (given knowledge of
the index k) to determine the original data symbols ak.
As mentioned further above, the GMSK modulation
can be approximated very well by the OQPSK modulation
(with the precondition that the time/bandwidth product
CA 02347747 2001-04-19
- 12 -
is known and the transformation of the data stream is
performed between ak and bk). It is possible in this way
to use the DFE according to the invention for GMSK and
OQPSK as well. Only one additional, but simple and
robust transformation of the data is required. An
additional simplification is achieved if precoding is
used in the transmitter before the GMSK modulation.
Given an unfavorable time/bandwidth product,
the equalizing of C;MSK in a way according to the
invention can lead to a slightly worse performance than
in the case of OQPSK, because despite everything GMSK
is not exactly linear after the data transformation.
However, the instances of worsening can be neglected if
the time/bandwidth product is of the usual order of
magnitude.
It may be stated in summary that it is possible
to improve the equalization with the aid of the
invention in the case of the in practice very greatly
widespread one-dimensional modulation methods and with
the use of the advantageous DFB structure. The
evaluation in the feedback filter can be performed
using real values instead of complex ones. Again, the
output of the feedforward filter need only be real.
Consequently, all that need be carried out in this
filter is those calculations which contribute to the
real value of the output. Receivers according to the
invention can, for example, be used in the case of GSM
telephones or cordless DECT telephone sets, or in the
case of data communication between computers on the
basis of HIPERLAN.
