CA2347747A1 - Equalization method especially for offset modulation modes - Google Patents
Equalization method especially for offset modulation modes Download PDFInfo
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- CA2347747A1 CA2347747A1 CA002347747A CA2347747A CA2347747A1 CA 2347747 A1 CA2347747 A1 CA 2347747A1 CA 002347747 A CA002347747 A CA 002347747A CA 2347747 A CA2347747 A CA 2347747A CA 2347747 A1 CA2347747 A1 CA 2347747A1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/01—Equalisers
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
- H04L25/03114—Arrangements for removing intersymbol interference operating in the time domain non-adaptive, i.e. not adjustable, manually adjustable, or adjustable only during the reception of special signals
- H04L25/03146—Arrangements for removing intersymbol interference operating in the time domain non-adaptive, i.e. not adjustable, manually adjustable, or adjustable only during the reception of special signals with a recursive structure
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- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Power Engineering (AREA)
- Digital Transmission Methods That Use Modulated Carrier Waves (AREA)
- Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)
- Filters That Use Time-Delay Elements (AREA)
Abstract
The invention relates to a method for equalizing a receive signal in a digital receiver with the aid of a decision feedback equalizer structure. The receive signal is based on a one dimensional signal constellation (e.g. BPSK, GMSK, OQPSK) or a signal constellation which can be transformed in such a manner.
The coefficients of the DFE are fixed in such a manner that the expected value of the squared real part of the error of the receive signal is minimized. As opposed to prior art, the complex value error is not used as a basis for optimization. Calculation is much more limited to real value. The filter coefficients can also have a real value instead of a complex value. The fundamental aspect of the invention is that it is possible to improve the performance of the DFE structure in a basically simple manner. Even computational complexity can be reduced in comparison with prior art.
The coefficients of the DFE are fixed in such a manner that the expected value of the squared real part of the error of the receive signal is minimized. As opposed to prior art, the complex value error is not used as a basis for optimization. Calculation is much more limited to real value. The filter coefficients can also have a real value instead of a complex value. The fundamental aspect of the invention is that it is possible to improve the performance of the DFE structure in a basically simple manner. Even computational complexity can be reduced in comparison with prior art.
Description
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.
Owner ASCOm Systec AG et al.
- lA-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
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 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 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 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...-.. ~._~.......~._ .. .._... ..~. ......_ .......~...,....~~.._ 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 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.
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 _ 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 ~
_ 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 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:
- ~. 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 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.
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.
Owner ASCOm Systec AG et al.
- lA-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
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 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 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 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...-.. ~._~.......~._ .. .._... ..~. ......_ .......~...,....~~.._ 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 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.
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 _ 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 ~
_ 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 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:
- ~. 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 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.
Claims (4)
1. Method for equalizing a received signal, based on a GMSK or an OQPSK modulation, in a digital receiver with the aid of a DFE (Decision Feedback Equalizer) structure (18), in which the coefficients of the DFE
are fixed so as to minimize the expected value of the quadratic real part of the error in the received signal, characterized in that the samples are rotated (14, 15) in the receiver with a phase j-i, i denoting a sequential index of the sample.
are fixed so as to minimize the expected value of the quadratic real part of the error in the received signal, characterized in that the samples are rotated (14, 15) in the receiver with a phase j-i, i denoting a sequential index of the sample.
2. Circuit arrangement having a DEF (Decision Feedback Equalizer) (18) for equalizing a received signal, based on a GMSK or an OQPSK modulation, in a digital receiver and having first means for calculating the coefficients (17) of the DFE in such a way as to minimize the expected value of the squared real part of the error in the received signal, characterized in that it has second means (14, 15) for rotating the expected values in the receiver a phase j-i, i denoting a sequential index of the sample.
3. Method for equalizing a received signal, based on a BPSK modulation, in a digital receiver with the aid of a DFE (Decision Feedback Equalizer) structure (7), characterized in that the coefficients of the DFE are fixed as follows:
N denoting the length of the channel unit pulse response, M denoting the length of the feedforward filter, h1 R denoting the real part of the channel unit pulse response for 1 ~ i ~ N, h1 I denoting the imaginary part of the channel unit pulse response for 1 ~ i ~ N, f1 R denoting the real part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, f1I
denoting the imaginary part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, g1R
denoting the real part of the filter coefficients of the feedback part of the DFE for 1 ~ i ~ N-1, and .sigma.2 denoting the noise power at the input of the DFE with combined real and imaginary parts of the noise power.
N denoting the length of the channel unit pulse response, M denoting the length of the feedforward filter, h1 R denoting the real part of the channel unit pulse response for 1 ~ i ~ N, h1 I denoting the imaginary part of the channel unit pulse response for 1 ~ i ~ N, f1 R denoting the real part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, f1I
denoting the imaginary part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, g1R
denoting the real part of the filter coefficients of the feedback part of the DFE for 1 ~ i ~ N-1, and .sigma.2 denoting the noise power at the input of the DFE with combined real and imaginary parts of the noise power.
4. Circuit arrangement having a DFE (Decision Feedback Equalizer) (7) for equalizing a received signal, based on a BPSK modulation, in a [illegible]
receiver, characterized in that it has means (6) for calculating the [lacuna] ents of the DFE as follows:
N denoting the length of the channel unit pulse response, M denoting the length of the feedforward filter [lacuna] the real part of the channel unit pulse response for 1 ~ i ~ N, h1I denoting the imaginary part of the channel unit pulse response for 1 ~ i ~ N, f1R
denoting the real part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, f1I
denoting the imaginary part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, g1R
denoting the real part of the filter coefficients of the feedback part of the DFE for 1 ~ i ~ N-1, and .sigma.2 -14a-denoting the noise power at the input of the DFE with combined real and imaginary parts of the noise power.
receiver, characterized in that it has means (6) for calculating the [lacuna] ents of the DFE as follows:
N denoting the length of the channel unit pulse response, M denoting the length of the feedforward filter [lacuna] the real part of the channel unit pulse response for 1 ~ i ~ N, h1I denoting the imaginary part of the channel unit pulse response for 1 ~ i ~ N, f1R
denoting the real part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, f1I
denoting the imaginary part of the filter coefficients of the feedforward part of the DFE for 1 ~ i ~ M, g1R
denoting the real part of the filter coefficients of the feedback part of the DFE for 1 ~ i ~ N-1, and .sigma.2 -14a-denoting the noise power at the input of the DFE with combined real and imaginary parts of the noise power.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| EP98811090.4 | 1998-10-30 | ||
| EP98811090A EP0998083A1 (en) | 1998-10-30 | 1998-10-30 | Equalisation method, particularly for offset modulation types |
| PCT/CH1999/000509 WO2000027083A1 (en) | 1998-10-30 | 1999-10-29 | Equalization method especially for offset modulation modes |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA2347747A1 true CA2347747A1 (en) | 2000-05-11 |
Family
ID=8236418
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002347747A Abandoned CA2347747A1 (en) | 1998-10-30 | 1999-10-29 | Equalization method especially for offset modulation modes |
Country Status (12)
| Country | Link |
|---|---|
| EP (2) | EP0998083A1 (en) |
| JP (1) | JP2002529964A (en) |
| KR (1) | KR20010089314A (en) |
| CN (1) | CN1144430C (en) |
| AU (1) | AU6322599A (en) |
| BR (1) | BR9914950A (en) |
| CA (1) | CA2347747A1 (en) |
| HK (1) | HK1040025A1 (en) |
| ID (1) | ID29202A (en) |
| IL (1) | IL142795A0 (en) |
| NO (1) | NO20012104L (en) |
| WO (1) | WO2000027083A1 (en) |
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| CN101836407B (en) * | 2007-12-10 | 2013-03-27 | 中兴通讯股份有限公司 | A method for optimizing the radio frequency performance of the terminal |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0614627B2 (en) * | 1985-06-04 | 1994-02-23 | 富士通株式会社 | Modem training methods |
| EP0956650A1 (en) * | 1996-10-10 | 1999-11-17 | Statistical Signal Processing, Inc. | Signal processing apparatus employing the spectral property of the signal |
-
1998
- 1998-10-30 EP EP98811090A patent/EP0998083A1/en not_active Withdrawn
-
1999
- 1999-10-29 CN CNB998128473A patent/CN1144430C/en not_active Expired - Fee Related
- 1999-10-29 AU AU63225/99A patent/AU6322599A/en not_active Abandoned
- 1999-10-29 KR KR1020017004859A patent/KR20010089314A/en not_active Application Discontinuation
- 1999-10-29 CA CA002347747A patent/CA2347747A1/en not_active Abandoned
- 1999-10-29 BR BR9914950-8A patent/BR9914950A/en not_active IP Right Cessation
- 1999-10-29 ID IDW00200100934A patent/ID29202A/en unknown
- 1999-10-29 JP JP2000580347A patent/JP2002529964A/en active Pending
- 1999-10-29 WO PCT/CH1999/000509 patent/WO2000027083A1/en not_active Application Discontinuation
- 1999-10-29 IL IL14279599A patent/IL142795A0/en unknown
- 1999-10-29 EP EP99950419A patent/EP1125404A1/en not_active Withdrawn
-
2001
- 2001-04-27 NO NO20012104A patent/NO20012104L/en not_active Application Discontinuation
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2002
- 2002-02-26 HK HK02101468.9A patent/HK1040025A1/en unknown
Also Published As
| Publication number | Publication date |
|---|---|
| EP0998083A1 (en) | 2000-05-03 |
| WO2000027083A1 (en) | 2000-05-11 |
| AU6322599A (en) | 2000-05-22 |
| NO20012104D0 (en) | 2001-04-27 |
| EP1125404A1 (en) | 2001-08-22 |
| JP2002529964A (en) | 2002-09-10 |
| ID29202A (en) | 2001-08-09 |
| NO20012104L (en) | 2001-04-27 |
| CN1144430C (en) | 2004-03-31 |
| BR9914950A (en) | 2001-11-06 |
| KR20010089314A (en) | 2001-09-29 |
| CN1325580A (en) | 2001-12-05 |
| HK1040025A1 (en) | 2002-05-17 |
| IL142795A0 (en) | 2002-03-10 |
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