WO1999034567A1

WO1999034567A1 - Demodulation method and demodulator

Info

Publication number: WO1999034567A1
Application number: PCT/FI1998/000975
Authority: WO
Inventors: Olli Piirainen; Kari NIEMELÄ
Original assignee: Nokia Telecommunications Oy
Priority date: 1997-12-12
Filing date: 1998-12-11
Publication date: 1999-07-08
Also published as: AU1565499A; FI974506A0

Abstract

The invention relates to a demodulator applying a demodulation method of the invention. Samples of a signal having a constant envelope and being modulated by continuous phase frequency modulation are applied to the demodulator. The modulation index h of the signal is 1/(2m), where m ⊂ {2, 3, ... }. The samples have a phase value (Ζ) that depends on the modulation. In order to detect the signal, the phase values (Ζ) of the samples of the received signal are multiplied in a multiplier (34) by m.

Description

DEMODULATION METHOD AND DEMODULATOR

FIELD OF THE INVENTION

The invention relates to a demodulation method in which a signal having a constant envelope and being modulated by continuous phase fre- quency modulation is received, the signal having a modulation index h of 1/(2m), where m e {2, 3, ..., ∞}, and in which method samples are taken from the received signal, the samples having a phase value that depends on the modulation.

The invention also relates to a demodulator arranged to receive a signal having a constant envelope and being modulated by continuous phase frequency modulation, the signal having a modulation index 1/(2m) where m e

{2, 3, ..., oo} and comprising samples with a phase value that depends on the modulation.

BACKGROUND OF THE INVENTION A demodulation method is an important step in the development of new data transmission methods. Because of losses occurring on a transmission path and because of transmission path capacity, data symbols to be transmitted cannot be transmitted over the transmission path as such, but the symbols must be modulated by means of a suitable method so as to obtain good transmission path capacity and transmission quality. The success of data transmission depends to a large extent on the demodulator of a receiver.

Phase modulation or frequency modulation may have a discontinuous or a continuous phase. As the phase of a carrier is constrained to be continuous, the continuous phase modulation method includes a memory,. How- ever, the memory feature can be ignored in the receiver when data is differentially encoded. A typical receiver used in radio systems comprises a correlator and an MLS detector (Maximum-Likelihood Sequence) searching through the state trellis for paths having the shortest Euclidean distance. Instead of the correlator, a matched filter can also be used. In the search through the trellis for the shortest paths, the Viterbi algorithm is typically used.

There are a number of various CPM modulation methods having a continuous envelope, including Minimum Shift Keying MSK, Gaussian Minimum Shift Keying GMSK, Tamed Frequency Modulation TMF and Continuous Phase Frequency Shift Keying CPFSK. The GMSK method is used in the GSM cellular radio system. The phase Φ(t;l) of a CPFSK-modulated (Continuous Phase Frequency Shift Keying) carrier signal is of the form

(1 ) {t;\) = θ_n +2π}ιI_nq{t -nT) , where θ_n corresponds to the effect (memory) of symbols up to a time instant (n-1 )T and h stands for a modulation index. When the modulation index h is h = >2, Minimum Shift Keying MSK is used. The difference between the two frequencies used in the modulation is as small as possible so as to guarantee the orthogonality of the frequencies. For example, the GSM radio system uses this kind of modulation which, furthermore, filters the frequency band of the data with a Gaussian filter. When a modulation index is decreased below h = !4, orthogonality is lost and a conventional MSK demodulator can thus no longer be used. However, it is possible to increase data transmission rate, since reducing the modulation index results in a reduced bandwidth. In prior art solutions, reducing the modulation index h below h =

involves extensive modifications in the demodulator and radio frequency parts of the receiver, since a demodulator of the MSK type cannot any longer be used as such.

BRIEF DESCRIPTION OF THE INVENTION An object of the invention is thus to provide a method and equipment implementing the method to solve the above-mentioned problems. No changes are then required in the RF parts of a receiver and, as compared with the prior art, a demodulator can be realized with small changes without a substantial loss of performance. This is achieved by the method of the type presented in the introduction, which is characterized by multiplying the phase values of the samples of the received signal by m to detect the signal.

The invention also relates to a demodulator which is characterized in that the demodulator comprises a means for multiplying the phase values of the samples of the received signal by m.

The method and system of the invention provide many advantages. Not many changes are required in the prior art demodulator solution of the MSK type, even though a modulation index smaller than h = V-≥ was used in the modulation of the transmitted signal. BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the invention will be described in more detail by means of preferred embodiments with reference to the accompanying drawings, in which Figure 1 shows a set of dots in a signal space, formed of DBCPM signal bits,

Figure 2 shows a block diagram of a demodulator, and

Figure 3 shows a block diagram of a converter.

DETAILED DESCRIPTION OF THE INVENTION The solution of the invention is suitable for use particularly in the

GSM radio system without, however, restricting to it. Although the manner a signal to be received is generated at the transmitting end is irrelevant to the solution of the invention, the signal to be received has to be a phase/frequency-modulated signal with a continuous phase and a constant envelope. Both phase modulation and frequency modulation can be used, since frequency modulation can be presented as a derivative of phase modulation, and a receiver detects the received bits with the help of phase differences, as it is obvious to those skilled in the art.

Let us first study the basic theory of the inventive solution by ex- amining modulation. Let us first define a modulating bit frequency f^ = 1/T, where T is the duration of a data bit. For the demodulation of the invention, transmission is differentially modulated, which enables modulation without memory. In transmission, every bit dj = [0,1] is differentially encoded. The output of a differential encoder d_{ is:

where ® denotes modulo 2 addition. The bits are mapped from a set {0, 1} to

where otj e {-1 , 1}. The data values ct_j so formed, which correspond to the Di- rac delta function representing an impulse, are filtered with a linear filter having an impulse response of: g(t) = h(t) *rect

(4) r,

where a rectangular pulse rect(t/T) is defined by:

rectl — 1 = 0, otherwise and ^* stands for convolution. If Gaussian filtered modulation is involved, a function h(t) is a Gaussian filter having an impulse response of the form:

^{(5) t) =}

' ^{and BT = β} where B stands for a 3-dB bandwidth of the Gaussian filter. The phase of the modulated signal so formed is:

(6) <z>(/' ) (u)du

where the modulation index h of the invention is 1/(2m), where m is 1 , 2, 3, .... oo, f is a time reference t' = 0, starting from bit 0. As compared with prior art solutions, it can be emphasized that the modulation index h is not an arbitrary rational fraction, but the denominator of the modulation index h comprises only even numbers. A radio-frequency carrier so modulated can be presented in the form of:

\2E_r (7) ^χ(?) = J—r cos(2rf₀t'+φ(t') + <p₀) ,

where E_c is the energy of a modulating bit, f₀ is a centre frequency and φ₀ is a random phase arising from noise.

Let us next study the demodulation of this kind of a signal in more detail. When samples are taken at a bit frequency, an MSK signal is demodulated as follows. The sampled signal is of the form:

The representation of the demodulated MSK signal is:

It can be seen from the formula (9) that in a demodulator, the MSK-modulated signal whose modulation index h is Y. obtains values at π/2 intervals. If the signal is binary coded and has a constant envelope (defined | s(n)l = 1 ), and if the arguments, or the angle values, of the signal obtain values ±π, then the dot pattern in a complex signal space is 1 , j, -1 , -j. In the demodulation, a signal having different modulation indices h can be made to correspond to the MSK modulated signal in the following way:

(10) pin) =

, where m = — ,

where the phase is multiplied by m. The phase is multiplied by m because in the modulation, a phase function is divided by m, as it is found in the formula (6). In a general case, the signal can also be denoted in the following way:

In other words, on the basis of the formula (11 ), it is possible to establish a general mapping by means of which particularly a binary-coded sig- nal can be restored to the modulation of the MSK type, the signal having a modulation index h of the form h = 1/(2m), where m is m = {2,3, ..., ∞}. The general form is such that the phase values arg(s(n)) = Φ (t;l) of the samples s(n) of a signal that is received so as to detect the signal are multiplied by m. When the signal is again of the MSK type, prior art detectors, such as a BSK detector (Binary Phase Shift Keying), can be used . For example, when quarterly encoding is used, the mapping restores the signal in order to be detected with a prior art QFSK detector (Quarterly Frequency Shift Keying). The formula (11 ) can also be presented as a mapping from a complex z space to a complex w space in the following way

.m (12) w- \m-\ where z is the sample s(n) of the received signal and m depends on the modulation index h so that m = 1/(2h).

Let us next study the inventive idea by means of Figure 1. In the case of A in Figure 1 , a signal whose modulation index h is h = V₄ is received. As in a prior art demodulator, the samples of the received signal are multiplied π ±j— in a known manner in order to shift the phase values by a factor e . The phase values of the samples are thus shifted π/4, and there are now four dots instead of eight on the circle. Phase value shift can also take place after the inventive mapping. However, the phase values are then shifted double the π ±_j — amount, i.e. by a factor e ² . In a general case, the phase values are shifted π ±j before the inventive mapping operation by e ^2m , or after the inventive map- π typing operation by e ^m . Values corresponding to a binary-coded signal value

"1" are located at points ±j, and values corresponding to "0" are located at points ±1. The binary values "1" and "0" can be changed without changing the course of the inventive solution. When the points ±j and ±1 are presented by the inventive method according to the formula (12), a case similar to the case of B in Figure 1 is obtained, where the point -1 corresponds to bit "1" and the point 1 corresponds to bit "0". A case is presented at B in which a prior art detector, such as a BPSK detector, can detect the received signal.

Figure 2 shows a block diagram of a demodulator of the invention. The demodulator comprises means 20 for shifting phase values, a converter 22 and a detector 24. The means 20 shift the phase values of a received signal in a known manner. The means 20 can be located before the inventive converter 22, which is the case in Figure 2, or between the converter 22 and the detector 24. The inventive converter 22 maps the phase values of the samples of the signal by multiplying the phase values by m, m € {2, 3, ..., ∞}. In the binary case, the detector 24 is a prior art BPSK detector, for instance. A dashed line in Figure 2 presents a prior art solution. In the prior art solution, the received signal propagates through a phase shifter 20, in this case a demodulator, directly to the detector 24. A typical CPM receiver (Continuous Phase Modulation) comprises a correlator acting as the above-mentioned phase shifter, and an MLS detector (Maximum-Likelihood Sequence) searching through the state trellis for the paths with the shortest Euclidian distance. Instead of the correlator, a matched filter can also be used to shift the phases. Typically, the Vitebri algorithm, for instance, is used to search through the trel- lis for the shortest paths.

Figure 3 presents a way of implementing the inventive converter 22. When the samples of the received signal are in the cartesian form as x,y values, a coordinates converter 32 converts the cartesian values x.y into the polar form A and Φ. Typically, the value A is formed by A = ^j(x² +y²) and the value Φ is typically formed by Φ = αrctanl — J . In a multiplier 34, the phase va¬

lue Φ is multiplied by m. Next, the values A and Φ are converted back into the cartesian form in a converter 36. In that case, x is formed by x = A cos(Φ) and y = A sin(Φ), for instance. The actual multiplication and conversions of coordi- nates can be replaced by tables, for example.

The solutions of the invention can be implemented particularly for digital signal processing with ASIC and/or VLSI circuits, for instance. The operations to be executed are preferably implemented by software based on microprocessor technology. Although the invention is described above with reference to the example according to the accompanying drawings, it is obvious that the invention is not restricted thereto, but it can be modified in a variety of ways within the scope of the inventive idea disclosed in the attached claims.

Claims

1. A demodulation method in which a signal having a constant envelope and being modulated by continuous phase frequency modulation is received, the signal having a modulation index h of 1/(2m), where m e {2, 3, ..., co}, and in which method samples are taken from the received signal, the samples having a phase value (╬ª) that depends on the modulation, characterized by multiplying the phase values (╬ª) of the samples of the received signal by m to detect the signal.

2. A method as claimed in claim ^characterized in that the received signal is binary coded, whereby the phase values (╬ª) of the samples of the received signal are shifted by ╧Ç/(k-m), multiplied by m and for the detection, a detection method of an MSK type is used, where k = 2 when the phase values (╬ª) are shifted before the phase values (╬ª) of the samples are multiplied by m, and k = 1 when the phase values (╬ª) are shifted after the phase values (╬ª) of the samples are multiplied.

3. A method as claimed in claim 1, characterized in that when the modulation index of the received signal changes, the phase values (╬ª) of the samples are also multiplied in a corresponding manner by the changed m.

4. A method as claimed in claim 1, characterized in that the received signal to be demodulated is differentially encoded.

5. A demodulator arranged to receive a signal having a constant envelope and being modulated by continuous phase frequency modulation, the signal having a modulation index 1/(2m) where m e {2, 3 Γê₧} and com- prising samples with a phase value (╬ª) that depends on the modulation, characterized in that the demodulator comprises a means (22, 34) for multiplying the phase differences (╬ª) of the samples of the received signal by m.

6. A demodulator as claimed in claim 5, characterized in that the received signal is binary coded, the demodulator comprises means

(20) for shifting the phase of the phase values (╬ª) of the samples of the signals by ╧Ç/(km), means (22, 34) for multiplying the phase values (╬ª) of the samples by m, and a detector (24) of an MSK type where k = 2 when the means (20) for shifting the phase values of the samples are located before the means for multiplying by m, and k = 1 when the means (20) for shifting the phase values of the samples are located after the means (22, 34) for multiplying.

7. A demodulator as claimed in claim 5, characterized in that when the modulation index of the received signal has changed, the means (22, 34) of the demodulator are arranged to multiply the phase values (╬ª) of the samples of the received signal by the changed m.

8. A demodulator as claimed in claim 5, characterized in that the received signal to be demodulated is differentially encoded.