CA1313267C - Conversion filtering for digital signalling systems - Google Patents
Conversion filtering for digital signalling systemsInfo
- Publication number
- CA1313267C CA1313267C CA000601202A CA601202A CA1313267C CA 1313267 C CA1313267 C CA 1313267C CA 000601202 A CA000601202 A CA 000601202A CA 601202 A CA601202 A CA 601202A CA 1313267 C CA1313267 C CA 1313267C
- Authority
- CA
- Canada
- Prior art keywords
- sequence
- product
- slowly varying
- encoder
- function
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/25—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM]
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
- H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
- H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
Abstract
TITLE: CONVERSION FILTERING FOR DIGITAL
SIGNALING SYSTEMS
Inventor: Michel T. Fattouche ABSTRACT
One way to increase the bandwidth efficiency of a linear modulation scheme is to increase the number M of possible signaling levels. Such an increase is achieved however at the expense of a smaller minimum distance dmin between the multilevels for a fixed average signal power. The present invention involves the use of a conversion filter as part of a digital signaling system used over a communications channel of limited bandwidth and power. A conventional digital signaling system consists of an encoder, followed by a modulator and a bandpass filter. In the present invention, the digital signaling system consists of an encoder, followed by a modulator, a conversion filter and a bandpass filter. The conversion filter increases the bandwidth efficiency offered by the encoder-modulator combination when the length L of its impulse response extends over several signaling intervals. Such an increase is achieved, however, at the expense of a smaller dmin. By increasing the modulation index h of the conversion filter, it is possible to increase dmin without significantly affecting the bandwidth efficiency. The invention also provides steps for choosing the modulation index h and the cutoff frequency fco of the bandpass filter for a fixed length L of the conversion filing such that dmin is at least locally maximized without significantly affecting the bandwidth efficiency.
SIGNALING SYSTEMS
Inventor: Michel T. Fattouche ABSTRACT
One way to increase the bandwidth efficiency of a linear modulation scheme is to increase the number M of possible signaling levels. Such an increase is achieved however at the expense of a smaller minimum distance dmin between the multilevels for a fixed average signal power. The present invention involves the use of a conversion filter as part of a digital signaling system used over a communications channel of limited bandwidth and power. A conventional digital signaling system consists of an encoder, followed by a modulator and a bandpass filter. In the present invention, the digital signaling system consists of an encoder, followed by a modulator, a conversion filter and a bandpass filter. The conversion filter increases the bandwidth efficiency offered by the encoder-modulator combination when the length L of its impulse response extends over several signaling intervals. Such an increase is achieved, however, at the expense of a smaller dmin. By increasing the modulation index h of the conversion filter, it is possible to increase dmin without significantly affecting the bandwidth efficiency. The invention also provides steps for choosing the modulation index h and the cutoff frequency fco of the bandpass filter for a fixed length L of the conversion filing such that dmin is at least locally maximized without significantly affecting the bandwidth efficiency.
Description
Background of the I~vention This invention relates to the processing of digital data for transmission over a communications channel of limited bandwidth and power, and relates to a method and apparatus for increasing the bandwidth efficiency and power efficiency of the transmission.
One way to increase the bandwidth efficiency of a linear modulation scheme is to increase the number M of possible signaling levels. Such an increase is achieved however at the expense of a smaller minimum distance dmin between the multilevels, for a flxed average signal power.
Csajka et al, U.S. Patent No. 4,077,U21, describes Trellis Coded Modulation (TCM) which combines convolutional coding with linear multilevel modulation schemes in an efficient way. TCM preserves the Bandwidth (BW) efficiency of the modulation schemes while offering 3 to 6 db increase in dmin over multilevel modulation, and is considered the state of the art in the domain of power and Bandwidth (BW) efficient modulation schemes.
The present invention involves the use of a conversion filter and a Bandpass filter (BPF) together with an encoder and a modulator as part of a digital signaling system. The difference between the signaling system involved in the present invention and the signaling system comprising TCM is the conversion filter which allows the signaling system to general schemes that are more BW-efficient than the schemes generated by the encoder-modulator combination. It can be shown that the digital signaling system described in the present invention can generate schemes that have larger ~k dmin/Eb than TCM for comparable BW-efficiency and comparable receiver complexity: Eb being the average energy per trans~itted bit.
Conversion filtering was first introduced in 1969 by Lender, Canadian Patent No. 823,307, in order to generate a signal of near constant envelope. In Lender, the conversion filter is an Infinite Impulse Response tIIR) filter~ constrained to have a specific Power Spectral Density (PSD) and a modulation index h equal to 1/2. Subsequently, conversion iltering was used to generate signals of constant envelope (A.R. Hambley & O.
Tanaka, "Generalized Serial MSK Modulationn, IEEE Trans.
on Commun., Vol. COM-32, pp. 305-308, March 1984 and F.
Amo~oso and J.A. Kivett, "Simplified MSK Signaling Technique~, n IEEE Trans. Commun., Vol. COM -25, pp.
433-441, Apr. 1977). In both cases, the conversion filter is a Finite Impulse Response (FIR) filter, constrained to have a length L equal to 1, a modulation index h equal to 1/2 and whose Lowpass ~LP) equivalent Impulse Response (IR) h(t) is restricted to take the format h(t) = j ~(t) ei~') where ~(t) is a slowly varying function and j= ~.
Summary of the Invention In one aspect, the present invention provides an apparatus for transmitting a digital signal over a communications channel, the apparatus comprising:
_ 4 _ 1 3 1 32 67 at least one encoder for converting digital signals into a sequence of symbols;
: a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a conversion filter electrically connected to the modulator and having a length L and modulation index h for filtering the sequence V to generate a sequence S;
a bandpass filter electrically connected to the conversion filter and having a cut-off frequency fco for filtering the sequence S to generate a sequence R;
for a fixed length ~, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficienc~.
In another aspect, the present invention provides a process for transmitting a digital signal over a communications channel, the process comprising:
encoding the digital signal to generate a sequence of signals modulating the sequence of symbols with a modulator to generate a sequence V, filtering the sequence V with a conversion filter to generate a sequence S, the conversion filter having a length L and modulation index h;
filtering the sequence S with a bandpass filter to generate a sequence R, the bandpass filter having a cut-off frequency fco ,`~ ' ~' . .
~ . ..
'` ,~ ' - . ' ' .
... .. .
~ 5 for a fixed length L, the cut-off frequency fco and the modulation index h being ~hosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
A further summary oE the invention is found in the claims appended to this Patent.
Brief Description of the Figures There will now be described the manner of operation of the invention and preferred embodiments of the invention, with reference to the figures, in which:
Figure 1 is a block diagram of the 4 processing stages of the digital signaling system according to the invention;
Figure 2 illustrates the power spectral density of a signal S(t) derived according to the invention, and normalized to have a maximum of unity, for L - 1, ..., 5,~ = 0 and h/L = 1/4;
Figure 3 illustrates dmin/Eb versus h for L = 5, ..., 8 with ~ = 0:
Figure 4 illustrates the n ( 9 0~ -BW)/21 of S~t) versus h for L = 1, ..., 5 and ~ - 0 where the ~90%-BW~ of S(t) is the frequency band that contains 90~ or more of the average power in S(t);
Figure 5 illustrates the out-of-band power ~O(B) n of S(t) versus B for 0~ = 0, 0.2, ..., 0.6 with L
= 8 and h = 2, where the out-of band power O~B) is the amount of average power in S(t) that exists outside the fre~uency band (fma~ ~ B, fmax B).
Description of the Invention The present invention involves a digltal signaling system which comprises an encoder, a a modulator, a conversion filter and a BP~ as shown in Fig.
1. The encoder receives a sequence C~ of bits intended for transmission and generates a sequence ~ of symbols. The sequence c~ consists of the bits ' ~ i~ C~i 1' ..
which take one of the two values +l and the sequence consists of the symbols - ~
Possible encoders in Fig. 1 are: precoders, channel encoders and source encoders, or any combination thereof.
In the present invention, precoders are used essentially to prevent error propagation, channel encoders are used essentially to achieve a gain in d2in and source encoders are used essentially to achieve a gain in the BW
efficiency. Examples of precoders are differential encoders where ~ i-l ) modulo-M.
Examples of channel encoders are block encoders and convolutional encoders (see Lender, Canadian Patent 823,307 and J.G. Proakis ~igital Communications", McGraw - ~ill, New York, 1983). Examples of source encoders are M-ary mappers followed by a Gray encoder where the real part of ~ i takes one of the M values [+1, _3, ..q +(M-l)] (assuming M even) and where the imaginary part f ~ i takes either the value 0 or one of the ~ values [+1, +3 ... , +(M-l)].
In Fig. 1, the modulator receives the sequence ~ and generates the siynal V(t) which is a function of time "t" and of the sequence ~ . The modulator used ---` 1 3 1 3267 in Fig. 1 consist of either a pulse-shaping filter of impulse response (IR)plt), followed by a single In-phase branch or two parallel branches in Quadrature each with a separate pulse shaping filter of identical impulse response (IR)p(t) where p(t) is a generalized impulse response and may, for example, be any slowly varying function such as a raised cosine function. In both cases, V(t) can be expressed mathematically as:
~/(t) ~ Reg ~ ~i p(t-iT) e~ fc~ ) i where T is the signalling interval of the modulator, f~
is the carrier frequency, assumed to be much greater than l/T and Re denotes the real part of the function in the parentheses. A preferred shaping filter has a rectangular IR defined as:
p(t) = 1 where O T, and O otherwise~
In Fig. 1 the conversion filter receives the signal V(t) and generates the signal S(t). The conversion filter has a LP equivalent IR h(t) defined as h (t) = A (t) ei~("
where the amplitude ~(t) is a slowly varying time function that is nonzero over the interval O ~ t ~ LT and O
elsewhere, the phase ~t) is a slowly varying time function over the interval O < t < LT and constant elsewhere and L is the length of the conversion filter which determines the amount of memory (or equivalently the amount of Intersymbol Interference lISI)) that is contained in the signal S(t). Preferred A(t) is a Raised -Cosine pulse defined as:
l/2(1 - COS ~.~T12 ) < t ~ aLT12, A (t) ~ 1 ~;LTI2 ~ t ~ LT(1~12) - ~ t-LT(1~12) ) LT(l~l2) < t ~ LT
O o~erwise where ~ is the rolloff factor constrained to the range O
~ ~ C 1, which determines the rate of decay of the spectral tail of S(t). Preferred ~ (t) is a linear phase defined as.
O ~ <O
~(t) =~ 2~1LT O < ~ c LT
One way to increase the bandwidth efficiency of a linear modulation scheme is to increase the number M of possible signaling levels. Such an increase is achieved however at the expense of a smaller minimum distance dmin between the multilevels, for a flxed average signal power.
Csajka et al, U.S. Patent No. 4,077,U21, describes Trellis Coded Modulation (TCM) which combines convolutional coding with linear multilevel modulation schemes in an efficient way. TCM preserves the Bandwidth (BW) efficiency of the modulation schemes while offering 3 to 6 db increase in dmin over multilevel modulation, and is considered the state of the art in the domain of power and Bandwidth (BW) efficient modulation schemes.
The present invention involves the use of a conversion filter and a Bandpass filter (BPF) together with an encoder and a modulator as part of a digital signaling system. The difference between the signaling system involved in the present invention and the signaling system comprising TCM is the conversion filter which allows the signaling system to general schemes that are more BW-efficient than the schemes generated by the encoder-modulator combination. It can be shown that the digital signaling system described in the present invention can generate schemes that have larger ~k dmin/Eb than TCM for comparable BW-efficiency and comparable receiver complexity: Eb being the average energy per trans~itted bit.
Conversion filtering was first introduced in 1969 by Lender, Canadian Patent No. 823,307, in order to generate a signal of near constant envelope. In Lender, the conversion filter is an Infinite Impulse Response tIIR) filter~ constrained to have a specific Power Spectral Density (PSD) and a modulation index h equal to 1/2. Subsequently, conversion iltering was used to generate signals of constant envelope (A.R. Hambley & O.
Tanaka, "Generalized Serial MSK Modulationn, IEEE Trans.
on Commun., Vol. COM-32, pp. 305-308, March 1984 and F.
Amo~oso and J.A. Kivett, "Simplified MSK Signaling Technique~, n IEEE Trans. Commun., Vol. COM -25, pp.
433-441, Apr. 1977). In both cases, the conversion filter is a Finite Impulse Response (FIR) filter, constrained to have a length L equal to 1, a modulation index h equal to 1/2 and whose Lowpass ~LP) equivalent Impulse Response (IR) h(t) is restricted to take the format h(t) = j ~(t) ei~') where ~(t) is a slowly varying function and j= ~.
Summary of the Invention In one aspect, the present invention provides an apparatus for transmitting a digital signal over a communications channel, the apparatus comprising:
_ 4 _ 1 3 1 32 67 at least one encoder for converting digital signals into a sequence of symbols;
: a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a conversion filter electrically connected to the modulator and having a length L and modulation index h for filtering the sequence V to generate a sequence S;
a bandpass filter electrically connected to the conversion filter and having a cut-off frequency fco for filtering the sequence S to generate a sequence R;
for a fixed length ~, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficienc~.
In another aspect, the present invention provides a process for transmitting a digital signal over a communications channel, the process comprising:
encoding the digital signal to generate a sequence of signals modulating the sequence of symbols with a modulator to generate a sequence V, filtering the sequence V with a conversion filter to generate a sequence S, the conversion filter having a length L and modulation index h;
filtering the sequence S with a bandpass filter to generate a sequence R, the bandpass filter having a cut-off frequency fco ,`~ ' ~' . .
~ . ..
'` ,~ ' - . ' ' .
... .. .
~ 5 for a fixed length L, the cut-off frequency fco and the modulation index h being ~hosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
A further summary oE the invention is found in the claims appended to this Patent.
Brief Description of the Figures There will now be described the manner of operation of the invention and preferred embodiments of the invention, with reference to the figures, in which:
Figure 1 is a block diagram of the 4 processing stages of the digital signaling system according to the invention;
Figure 2 illustrates the power spectral density of a signal S(t) derived according to the invention, and normalized to have a maximum of unity, for L - 1, ..., 5,~ = 0 and h/L = 1/4;
Figure 3 illustrates dmin/Eb versus h for L = 5, ..., 8 with ~ = 0:
Figure 4 illustrates the n ( 9 0~ -BW)/21 of S~t) versus h for L = 1, ..., 5 and ~ - 0 where the ~90%-BW~ of S(t) is the frequency band that contains 90~ or more of the average power in S(t);
Figure 5 illustrates the out-of-band power ~O(B) n of S(t) versus B for 0~ = 0, 0.2, ..., 0.6 with L
= 8 and h = 2, where the out-of band power O~B) is the amount of average power in S(t) that exists outside the fre~uency band (fma~ ~ B, fmax B).
Description of the Invention The present invention involves a digltal signaling system which comprises an encoder, a a modulator, a conversion filter and a BP~ as shown in Fig.
1. The encoder receives a sequence C~ of bits intended for transmission and generates a sequence ~ of symbols. The sequence c~ consists of the bits ' ~ i~ C~i 1' ..
which take one of the two values +l and the sequence consists of the symbols - ~
Possible encoders in Fig. 1 are: precoders, channel encoders and source encoders, or any combination thereof.
In the present invention, precoders are used essentially to prevent error propagation, channel encoders are used essentially to achieve a gain in d2in and source encoders are used essentially to achieve a gain in the BW
efficiency. Examples of precoders are differential encoders where ~ i-l ) modulo-M.
Examples of channel encoders are block encoders and convolutional encoders (see Lender, Canadian Patent 823,307 and J.G. Proakis ~igital Communications", McGraw - ~ill, New York, 1983). Examples of source encoders are M-ary mappers followed by a Gray encoder where the real part of ~ i takes one of the M values [+1, _3, ..q +(M-l)] (assuming M even) and where the imaginary part f ~ i takes either the value 0 or one of the ~ values [+1, +3 ... , +(M-l)].
In Fig. 1, the modulator receives the sequence ~ and generates the siynal V(t) which is a function of time "t" and of the sequence ~ . The modulator used ---` 1 3 1 3267 in Fig. 1 consist of either a pulse-shaping filter of impulse response (IR)plt), followed by a single In-phase branch or two parallel branches in Quadrature each with a separate pulse shaping filter of identical impulse response (IR)p(t) where p(t) is a generalized impulse response and may, for example, be any slowly varying function such as a raised cosine function. In both cases, V(t) can be expressed mathematically as:
~/(t) ~ Reg ~ ~i p(t-iT) e~ fc~ ) i where T is the signalling interval of the modulator, f~
is the carrier frequency, assumed to be much greater than l/T and Re denotes the real part of the function in the parentheses. A preferred shaping filter has a rectangular IR defined as:
p(t) = 1 where O T, and O otherwise~
In Fig. 1 the conversion filter receives the signal V(t) and generates the signal S(t). The conversion filter has a LP equivalent IR h(t) defined as h (t) = A (t) ei~("
where the amplitude ~(t) is a slowly varying time function that is nonzero over the interval O ~ t ~ LT and O
elsewhere, the phase ~t) is a slowly varying time function over the interval O < t < LT and constant elsewhere and L is the length of the conversion filter which determines the amount of memory (or equivalently the amount of Intersymbol Interference lISI)) that is contained in the signal S(t). Preferred A(t) is a Raised -Cosine pulse defined as:
l/2(1 - COS ~.~T12 ) < t ~ aLT12, A (t) ~ 1 ~;LTI2 ~ t ~ LT(1~12) - ~ t-LT(1~12) ) LT(l~l2) < t ~ LT
O o~erwise where ~ is the rolloff factor constrained to the range O
~ ~ C 1, which determines the rate of decay of the spectral tail of S(t). Preferred ~ (t) is a linear phase defined as.
O ~ <O
~(t) =~ 2~1LT O < ~ c LT
2~ LT < ~
where h is the modulation index which determines the frequency by which the conversion filter is offset from the carrier frequency fc.
While a preferred manner of applying the conversion filter has been described, in general, the conversion filter has the effect of applying the following relation to the sequence ~ :
S~l~, Rc~ . ~i ( p(~ h(~) ) ej2~'f'l ) where n*n denotes a convolution operation. This equation could he appliedy for example, as a lookup table.
Finally, in Fig. 1, the BPF receives the signal S~t) and generates the signal R(t) which is ready to undergo amplification and transmission over a communications channel. The amplification is assumed linear, otherwise, the conversion filter will have to be predistorted in order to compensate for distortion inflicted on R(t) due to nonlinear amplification. The ~PF
has a nonzero flat response over the frequency range [fmax fco,fmax+fco] where fmax corresponds to the positive frequency where the PSD of V(t) reaches its maximum and fco is the cutoff fre~uency of the BPF.
Explanation of the Invention The following explanation is in rela~ion to the digital signaling system in ~ig. 1. The encoder~modulator combination offers an initial BW efficiency and an initial dmin/Eb. The digital signaling system offers a final BW efficiency and a final dmin/Eb. Fig. 2 illustrates the Power Spectral Density (PSD) of the signal S(t) (normalized to have a maximum of unity) for L=l, ...,5 with ~ =0 and h/L = 1/4, and whicn shows that by increasing L, the main lobe of the PSD of S(t) is decreased. In other words, by increasing the length L of the conversion filter, the final efficiency is increased compared to the initial efficiency.
Fig. 2 also shows that S(t) is not a bandlimited signal. To bandlimit S(t), S(t) must be filtered using a bandpass filter as shown in Fig. 1. In this case, the bandpass filter has to be centered in the frequency domain around fmax and the cutoff frequency fco has to be chosen large enough to pass essentially about 90% or more of the average power in the signal S(t).
Another parameter that controls the final BW
efficiency, in addition to L, is the rolloff factor o~ of lo - 1 31 3267 the amplitude A(t) of the LP equivalent IR of the conversion filter. Fig. 5 illustrates the out-of-band power "O(B)" of S(t) versus B for o~ = 0, 0.2, ..., 0~6 with L = 8 and h = 2, where the out-of-band power O(B) is the amount of average power in S(t) that exists outside the frequency band (fmaX-B, fmaX+B). Fig. 5 shows an increase in the rate of decay of the tail of O(B) as 0~ is increased and a simultaneous increase in the width of O(B) around B = O. In other words, a small ~ is necessary when O(B) ~ -11.5 db (corresponding to a bandpass filter that allows 93~ or less of the average power in S(t)), while a large ~ is necessary when 0(3) ~ -11.5 db (corresponding to a bandpass filter that allows more than 93% of the average power in S(t)), under the constraint that O ~ ~ ~
1. The role of ~ is however of secondary importance compared to the role played by L in controlling the BW
efficiency, since L is chosen first according to the desired final BW efficiency, then ~ is chosen according to L such that the final BW efficiency is maximized.
B~ increasing the length L of the conversion filter, memory is added into S(t). In other words, the amount of ISI that exists in S(t) is directly proportional to L. Such an ISI can in turn decrease the value of the final dmin/Eb compared to the initial dmin/Eb. Nonetheless, ranges of the modulation index h of the conversion filter exist where dmin/Eb is increased by varying h as shown in Fig.
where h is the modulation index which determines the frequency by which the conversion filter is offset from the carrier frequency fc.
While a preferred manner of applying the conversion filter has been described, in general, the conversion filter has the effect of applying the following relation to the sequence ~ :
S~l~, Rc~ . ~i ( p(~ h(~) ) ej2~'f'l ) where n*n denotes a convolution operation. This equation could he appliedy for example, as a lookup table.
Finally, in Fig. 1, the BPF receives the signal S~t) and generates the signal R(t) which is ready to undergo amplification and transmission over a communications channel. The amplification is assumed linear, otherwise, the conversion filter will have to be predistorted in order to compensate for distortion inflicted on R(t) due to nonlinear amplification. The ~PF
has a nonzero flat response over the frequency range [fmax fco,fmax+fco] where fmax corresponds to the positive frequency where the PSD of V(t) reaches its maximum and fco is the cutoff fre~uency of the BPF.
Explanation of the Invention The following explanation is in rela~ion to the digital signaling system in ~ig. 1. The encoder~modulator combination offers an initial BW efficiency and an initial dmin/Eb. The digital signaling system offers a final BW efficiency and a final dmin/Eb. Fig. 2 illustrates the Power Spectral Density (PSD) of the signal S(t) (normalized to have a maximum of unity) for L=l, ...,5 with ~ =0 and h/L = 1/4, and whicn shows that by increasing L, the main lobe of the PSD of S(t) is decreased. In other words, by increasing the length L of the conversion filter, the final efficiency is increased compared to the initial efficiency.
Fig. 2 also shows that S(t) is not a bandlimited signal. To bandlimit S(t), S(t) must be filtered using a bandpass filter as shown in Fig. 1. In this case, the bandpass filter has to be centered in the frequency domain around fmax and the cutoff frequency fco has to be chosen large enough to pass essentially about 90% or more of the average power in the signal S(t).
Another parameter that controls the final BW
efficiency, in addition to L, is the rolloff factor o~ of lo - 1 31 3267 the amplitude A(t) of the LP equivalent IR of the conversion filter. Fig. 5 illustrates the out-of-band power "O(B)" of S(t) versus B for o~ = 0, 0.2, ..., 0~6 with L = 8 and h = 2, where the out-of-band power O(B) is the amount of average power in S(t) that exists outside the frequency band (fmaX-B, fmaX+B). Fig. 5 shows an increase in the rate of decay of the tail of O(B) as 0~ is increased and a simultaneous increase in the width of O(B) around B = O. In other words, a small ~ is necessary when O(B) ~ -11.5 db (corresponding to a bandpass filter that allows 93~ or less of the average power in S(t)), while a large ~ is necessary when 0(3) ~ -11.5 db (corresponding to a bandpass filter that allows more than 93% of the average power in S(t)), under the constraint that O ~ ~ ~
1. The role of ~ is however of secondary importance compared to the role played by L in controlling the BW
efficiency, since L is chosen first according to the desired final BW efficiency, then ~ is chosen according to L such that the final BW efficiency is maximized.
B~ increasing the length L of the conversion filter, memory is added into S(t). In other words, the amount of ISI that exists in S(t) is directly proportional to L. Such an ISI can in turn decrease the value of the final dmin/Eb compared to the initial dmin/Eb. Nonetheless, ranges of the modulation index h of the conversion filter exist where dmin/Eb is increased by varying h as shown in Fig.
3 which illustrates dmin/Eb versus h for L =5, ...,8 with oC =0. On the other hand, if h is increased, it may affect the overall bandwidth efficiency. Fig. 4 illustrates the "(90%-BW)/2" of S(t) versus h for L = 1, ..., 5 and ~ = 0 where the l90~-BW~ of S(t) is the frequency band that contains 90~ or more of the average power in S(t). From comparing Fig. 4 with Fig. 3, there is a range of values of h where it is possible to locally maximize dmin/Eb without significantly affecting the overall BW efficiency.
The present invention describes a transmission process and apparatus which is, of course, only one end of the transmitter/receiver pair. Receivers that would have practical utility with the present invention are well known in the art, as described, for example, in J.G.
Proakis "Digital Communications~, McGraw-Hill, New York, 1983, and would include the ~ollowing parts: a coherent demodulator, followed by a filter matched to ~p[t)*h(t)n, possibly an equalizer to remove part of the ~SI introduced by the BP~ and finally a Viterbi Algarhythm (VA) with ~L
states. However, sub-optimal receivers can also be used at the expense of a poorer performance of the receiver.
Examples of sub-optimal receivers are, for example, as described in the last mentioned reference, non-coherent receivers (such as differential detectors or frequency discriminators to be used when coherent detection is not possible) and symbol-by~symbol receivers (such as linear mean square equalizers or decision feed-back equalizers to be used when low complexity r~ceivers are desirable).
With a given encoder and modulator, the various perameters of the conversion filter and of the bandpass filter may be chosen as follows:
1. The initial dmin/Eb and the initial BW
efficiency offered by the encoder-modulator combinatlon are calculated.
2. The length L of the conversion filter is chosen according to the final BW efficiency with fco chosen such that about 90~ or more of the average - 12 - . 1 3 1 3267 power in the signal S(t) output from the conversion filter is allowed through the BPF.
3. The rolloff factor is chosen according to L and to fco such that the final BW efficiency is maximized.
The present invention describes a transmission process and apparatus which is, of course, only one end of the transmitter/receiver pair. Receivers that would have practical utility with the present invention are well known in the art, as described, for example, in J.G.
Proakis "Digital Communications~, McGraw-Hill, New York, 1983, and would include the ~ollowing parts: a coherent demodulator, followed by a filter matched to ~p[t)*h(t)n, possibly an equalizer to remove part of the ~SI introduced by the BP~ and finally a Viterbi Algarhythm (VA) with ~L
states. However, sub-optimal receivers can also be used at the expense of a poorer performance of the receiver.
Examples of sub-optimal receivers are, for example, as described in the last mentioned reference, non-coherent receivers (such as differential detectors or frequency discriminators to be used when coherent detection is not possible) and symbol-by~symbol receivers (such as linear mean square equalizers or decision feed-back equalizers to be used when low complexity r~ceivers are desirable).
With a given encoder and modulator, the various perameters of the conversion filter and of the bandpass filter may be chosen as follows:
1. The initial dmin/Eb and the initial BW
efficiency offered by the encoder-modulator combinatlon are calculated.
2. The length L of the conversion filter is chosen according to the final BW efficiency with fco chosen such that about 90~ or more of the average - 12 - . 1 3 1 3267 power in the signal S(t) output from the conversion filter is allowed through the BPF.
3. The rolloff factor is chosen according to L and to fco such that the final BW efficiency is maximized.
4. Finally, the modulation index h is chosen according to L such that dmin/Eb reaches a local maximum without affecting the final BW
efficiency significantly (essentially a reduction of the final BW efficiency of about 10~ or less is acceptable although lower values such as 5% or 2% are more desirable).
Examples of the Preferred Parameters The following examples demonstrate the preferred values for the parameters L, ~ , h and fco according to the steps mentioned in the previous section, together with the corresponding final dmin/Eb and final BW
efficiency. When a Viterbi Algorithm (VA) is used in the receiver, its preferred number of states is also shown in the following examples.
Example I
The encoder consists of an M-ary mapper, î.e.
is a sequence o~ symbols that take one of the M values:
[+1~ ~3r ~ ~ ~ +(M-l)]~ followed by a Gray encoder. The modulator consists of a rectangular shaping filter followed by a single In-phase branch. Table I summarizes the preferred values of OC, h and fco for L=l, ..., 8 and M=2 and 4 ~ together with the corresponding dmin/Eb~ BW efficiency and the number of states re~uired in VA.
T~BLE I
M L h c~ fCoT d2min/Eb BW ~ of VA
efficiency states -.
2 1 0~5 0~00 O~S00 4~00 1~000 0 2 2 0~5 0~00 0~360 4~00 1~388 4 2 3 0~75 0~16 0~309 4~00 1~618 S
2 4 0~85 0~28 0~252 4~00 1~984 16 2 5 1~15 0~40 0~213 3~861 2~347 32 2 6 1 o25 0 ~44 0.180 3~ 487 2~777 6~
2 7 1~45 0~44 1~56 2~989 3~205 128 2 8 1~70 0~44 0~141 2~858 3~546 256 ~ 1 0~5 0~00 0~500 1~60 2~000 0 2 2 0~5 0~00 0~360 1~60 2~776 4 2 3 0~75 0~16 0~309 1~60 3~236 8 2 4 0~85 0~28 0~252 1~60 3~968 16 2 5 1~15 0~40 0~213 1~544 4~694 32 2 6 1~25 0~44 0~180 1~395 5~554 64 2 7 1~45 0~44 1~56 1~196 6~10 128 2 8 1~70 0~44 0~141 1~143 7~092 256 Example II
Once a~ain, the encoder consists of an M-ary mapper and a Gray encoder. In this case, however, the modulator consists of a rectangular shaping filter followed by two parallel branches in Quadrature. Table II
summarizes the preferred values of o~ , h and fco for L=l, ..., 4 and M=2 and 4, together with the corresponding dmin/Eb, the final BW efficiency and the number of states required in VA.
TABLE II
M L h ~ fcoT d2min/Eb BW # of VA
efficiency states 2 1 0.5 0.00 0.500 4.000 2.000 4 2 2 0O4 0.00 0.354 3~687 2.82S 16 2 3 0.6 0.08 0.297 2.524 3.367 6~
2 4 0.8 0.28 0.252 2.000 3.968 256 4 1 0.5 0.00 0.500 1.600 4.000 4 4 2 0.~ 0.00 0.354 1.475 5.650 16 4 3 0.6 0.08 0.297 1.010 6.734 64 4 4 0.8 0.28 0.252 0.800 7~936 256 Ex~mpl~ III
The encoder consists of the binary convolutional encoder of rate 1/2 and of constraint length v, with generators: gl and g2 followed by an M-ary mapper and a Gray encoder. The modulator consists of a rectangular shaping filter followed by a single In-phase branch.
Table III summarizes the preferred values of ~ , h and fco for L=l r . . . ~ 4 and M=2, v=2 & 3, together with the corresponding dmin/Eb, the final BW efficiency and the number of states required in a VA.
TABLE III
M L v Yl g2 h O~ fcoT d2mint BW # of VA
- Eb efficiency states _ 2 1 2 3 1 0.50.00 0.500 6.000 0.500 2 2 1 3 5 7 0.50.00 0.50010.000 0.500 2 2 2 3 1 0.60.00 0.354 5.532 0.672 4 2 2 3 5 7 0/60.00 0.354 9.043 0.672 8 2 3 2 3 1 0.80.24 0.297 4.457 0.801 8 2 3 3 5 7 0.80.24 0.297 6.841 0.80116 2 4 2 3 1 1.050.4 0.252 3.830 0.98016 2 4 3 5 7 1.050.4 0.252 5.615 0.98032 ~` 1 3 1 3267 ILLUSTRATION OF THE EFFECT ON POWER EFFICIENCY
OF V~RIATION IN THE PARAMETERS
In Fig. 2, which illustrates the Power Spectral Density (PSD) of the signal S(t) generated according to the process described in this patent (and normalized to have a maximum of unity) for L = 1, ..., 5 with ~ = 0 and h/L = 1/4, it may be seen that by increasing L, the main lobe of the PSD of S(t) is decreased. ~fmax in Fig~ 2 corresponds to the positive frequency where the PSD of
efficiency significantly (essentially a reduction of the final BW efficiency of about 10~ or less is acceptable although lower values such as 5% or 2% are more desirable).
Examples of the Preferred Parameters The following examples demonstrate the preferred values for the parameters L, ~ , h and fco according to the steps mentioned in the previous section, together with the corresponding final dmin/Eb and final BW
efficiency. When a Viterbi Algorithm (VA) is used in the receiver, its preferred number of states is also shown in the following examples.
Example I
The encoder consists of an M-ary mapper, î.e.
is a sequence o~ symbols that take one of the M values:
[+1~ ~3r ~ ~ ~ +(M-l)]~ followed by a Gray encoder. The modulator consists of a rectangular shaping filter followed by a single In-phase branch. Table I summarizes the preferred values of OC, h and fco for L=l, ..., 8 and M=2 and 4 ~ together with the corresponding dmin/Eb~ BW efficiency and the number of states re~uired in VA.
T~BLE I
M L h c~ fCoT d2min/Eb BW ~ of VA
efficiency states -.
2 1 0~5 0~00 O~S00 4~00 1~000 0 2 2 0~5 0~00 0~360 4~00 1~388 4 2 3 0~75 0~16 0~309 4~00 1~618 S
2 4 0~85 0~28 0~252 4~00 1~984 16 2 5 1~15 0~40 0~213 3~861 2~347 32 2 6 1 o25 0 ~44 0.180 3~ 487 2~777 6~
2 7 1~45 0~44 1~56 2~989 3~205 128 2 8 1~70 0~44 0~141 2~858 3~546 256 ~ 1 0~5 0~00 0~500 1~60 2~000 0 2 2 0~5 0~00 0~360 1~60 2~776 4 2 3 0~75 0~16 0~309 1~60 3~236 8 2 4 0~85 0~28 0~252 1~60 3~968 16 2 5 1~15 0~40 0~213 1~544 4~694 32 2 6 1~25 0~44 0~180 1~395 5~554 64 2 7 1~45 0~44 1~56 1~196 6~10 128 2 8 1~70 0~44 0~141 1~143 7~092 256 Example II
Once a~ain, the encoder consists of an M-ary mapper and a Gray encoder. In this case, however, the modulator consists of a rectangular shaping filter followed by two parallel branches in Quadrature. Table II
summarizes the preferred values of o~ , h and fco for L=l, ..., 4 and M=2 and 4, together with the corresponding dmin/Eb, the final BW efficiency and the number of states required in VA.
TABLE II
M L h ~ fcoT d2min/Eb BW # of VA
efficiency states 2 1 0.5 0.00 0.500 4.000 2.000 4 2 2 0O4 0.00 0.354 3~687 2.82S 16 2 3 0.6 0.08 0.297 2.524 3.367 6~
2 4 0.8 0.28 0.252 2.000 3.968 256 4 1 0.5 0.00 0.500 1.600 4.000 4 4 2 0.~ 0.00 0.354 1.475 5.650 16 4 3 0.6 0.08 0.297 1.010 6.734 64 4 4 0.8 0.28 0.252 0.800 7~936 256 Ex~mpl~ III
The encoder consists of the binary convolutional encoder of rate 1/2 and of constraint length v, with generators: gl and g2 followed by an M-ary mapper and a Gray encoder. The modulator consists of a rectangular shaping filter followed by a single In-phase branch.
Table III summarizes the preferred values of ~ , h and fco for L=l r . . . ~ 4 and M=2, v=2 & 3, together with the corresponding dmin/Eb, the final BW efficiency and the number of states required in a VA.
TABLE III
M L v Yl g2 h O~ fcoT d2mint BW # of VA
- Eb efficiency states _ 2 1 2 3 1 0.50.00 0.500 6.000 0.500 2 2 1 3 5 7 0.50.00 0.50010.000 0.500 2 2 2 3 1 0.60.00 0.354 5.532 0.672 4 2 2 3 5 7 0/60.00 0.354 9.043 0.672 8 2 3 2 3 1 0.80.24 0.297 4.457 0.801 8 2 3 3 5 7 0.80.24 0.297 6.841 0.80116 2 4 2 3 1 1.050.4 0.252 3.830 0.98016 2 4 3 5 7 1.050.4 0.252 5.615 0.98032 ~` 1 3 1 3267 ILLUSTRATION OF THE EFFECT ON POWER EFFICIENCY
OF V~RIATION IN THE PARAMETERS
In Fig. 2, which illustrates the Power Spectral Density (PSD) of the signal S(t) generated according to the process described in this patent (and normalized to have a maximum of unity) for L = 1, ..., 5 with ~ = 0 and h/L = 1/4, it may be seen that by increasing L, the main lobe of the PSD of S(t) is decreased. ~fmax in Fig~ 2 corresponds to the positive frequency where the PSD of
5(t) reaches its maximum). Fig. 2 also shows that S(t) is not a bandlimited signal. To bandlimit S(t), filter S(t) must be filtered using a bandpass filter as shown on Fig.
1. In this case, the bandpass filter has to be centered in the frequency domain around fmax.
The increase in L is expected to aEfect ~min/Eb since by increasing L, the intersymbol interference in V(t) is increased. Fig. 3 however, illustrates dmin/Eb versus h for L = 5, ..., 8 with = 0, and shows that dmin/Eb can be increased by increasing h. Thus, if h is increased, it may affect the overall bandwidth efficiency. Fig. 4 illustrates the "(90~-BW)/2" of S(t) versus h for L = 1, ..., 5 and OC= 0 where the 190%-BW" of S(t) is the frequency band that contains 90% or more of the average power in S(t). From comparing Fig. 4 with Fig. 3, there is a range of values of h where it is possible to increase dmin/Eb without significantly affecting the overall BW efficiency.
Fig. 5 illustrates the out-of-band power RO(B)"
of S(t) versus B for ~= 0, 0.2, ..., 0.6 with L = 8 and h = 2, where the out-of-band power O(B) is the amount of average power in S(t) that exists outside the frequency band (fmaX-B EmaX+B). Fig. 5 shows an increase in the rate of decay oE the tail of O(B) as G~ is increased and a simultaneous increase in the width of O(B) around B = O.
In other words, a small ~ is necessary when O(B) 1 -11.5 db (corresponding to a bandpass filter that allows 93% or less of the average power in S(t)), while a large ~ is necessary when O(B) ~ -1.1.5 db (corresponding to a bandpass filter that allows more than 93% of the average power in S(t)), under the constraint that O ~ ~ C 1.
It will be understood that whiie preferred embodiments of the invention have been described, immaterial modifications may be made to the invention without departing from its substance and these are intended to be covered by the scope of the claims that follow.
1. In this case, the bandpass filter has to be centered in the frequency domain around fmax.
The increase in L is expected to aEfect ~min/Eb since by increasing L, the intersymbol interference in V(t) is increased. Fig. 3 however, illustrates dmin/Eb versus h for L = 5, ..., 8 with = 0, and shows that dmin/Eb can be increased by increasing h. Thus, if h is increased, it may affect the overall bandwidth efficiency. Fig. 4 illustrates the "(90~-BW)/2" of S(t) versus h for L = 1, ..., 5 and OC= 0 where the 190%-BW" of S(t) is the frequency band that contains 90% or more of the average power in S(t). From comparing Fig. 4 with Fig. 3, there is a range of values of h where it is possible to increase dmin/Eb without significantly affecting the overall BW efficiency.
Fig. 5 illustrates the out-of-band power RO(B)"
of S(t) versus B for ~= 0, 0.2, ..., 0.6 with L = 8 and h = 2, where the out-of-band power O(B) is the amount of average power in S(t) that exists outside the frequency band (fmaX-B EmaX+B). Fig. 5 shows an increase in the rate of decay oE the tail of O(B) as G~ is increased and a simultaneous increase in the width of O(B) around B = O.
In other words, a small ~ is necessary when O(B) 1 -11.5 db (corresponding to a bandpass filter that allows 93% or less of the average power in S(t)), while a large ~ is necessary when O(B) ~ -1.1.5 db (corresponding to a bandpass filter that allows more than 93% of the average power in S(t)), under the constraint that O ~ ~ C 1.
It will be understood that whiie preferred embodiments of the invention have been described, immaterial modifications may be made to the invention without departing from its substance and these are intended to be covered by the scope of the claims that follow.
Claims (20)
1. Apparatus for transmitting a digital signal over a communications channel, the apparatus comprising:
at least one encoder for converting digital signals into a sequence of symbols;
a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a conversion filter electrically connected to the modulator and having a length L and modulation index h for filtering the sequence V to generate a sequence S, a bandpass filter electrically connected to the conversion filter and having a cut-off frequency for filtering the sequence S to generate a sequence R;
for a fixed length L, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
at least one encoder for converting digital signals into a sequence of symbols;
a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a conversion filter electrically connected to the modulator and having a length L and modulation index h for filtering the sequence V to generate a sequence S, a bandpass filter electrically connected to the conversion filter and having a cut-off frequency for filtering the sequence S to generate a sequence R;
for a fixed length L, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
2. Apparatus for transmitting a digital signal over a communications channel, the apparatus comprising:
at least one encoder for converting digital signals into a sequence of symbols;
a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a finite impulse response conversion filter electrically connected to the modulator and having a length L greater than 1 and modulation index h for filtering the sequence V to generate a sequence S; and a bandpass filter electrically connected to the conversion filter and having a cut-off frequency fco for filtering the sequence S to generate a sequence R.
at least one encoder for converting digital signals into a sequence of symbols;
a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a finite impulse response conversion filter electrically connected to the modulator and having a length L greater than 1 and modulation index h for filtering the sequence V to generate a sequence S; and a bandpass filter electrically connected to the conversion filter and having a cut-off frequency fco for filtering the sequence S to generate a sequence R.
3. Apparatus for transmitting a digital signal over a communications channel, the apparatus comprising:
at least one encoder for converting digital signals into a sequence of symbols;
a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a conversion filter electrically connected to the modulator and having a length L and modulation index h for filtering the sequence V to generate a sequence S;
a bandpass filter electrically connected to the conversion filter, centred in the frequency domain around the positive frequency, fmax, where the sequence S has its maximum power spectral density and having a cut-off frequency fco for filtering the a sequence S to generate a sequence R; and for a fixed length L, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
at least one encoder for converting digital signals into a sequence of symbols;
a modulator electrically connected to the encoder for modulating the sequence of symbols to generate a sequence V;
a conversion filter electrically connected to the modulator and having a length L and modulation index h for filtering the sequence V to generate a sequence S;
a bandpass filter electrically connected to the conversion filter, centred in the frequency domain around the positive frequency, fmax, where the sequence S has its maximum power spectral density and having a cut-off frequency fco for filtering the a sequence S to generate a sequence R; and for a fixed length L, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
4. The apparatus of Claim 1, 2 or 3 in which L and the cut-off frequency are chosen so that greater than 90%
of the average power in R is allowed through the bandpass filter, and the modulation index is chosen to at least locally maximize the power efficiency while maximizing the bandwidth efficiency.
of the average power in R is allowed through the bandpass filter, and the modulation index is chosen to at least locally maximize the power efficiency while maximizing the bandwidth efficiency.
5. The apparatus of Claim 1, 2 or 3 in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T where T is the signaling interval.
6. The apparatus of Claim 3 in which the bandpass filter has a nonzero flat response over the frequency range defined by fmax - fco and fmax + fco-
7. The apparatus of Claim 1, 2 or 3 in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ? chosen to maximize the final bandwidth efficiency.
8. The apparatus of Claim 1, 2 or 3 in which the encoder is an M-ary mapper followed by a Gray encoder, and the modulator is a rectangular shaping filter followed by a single In-phase branch, in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
9. The apparatus of Claim 1, 2 or 3 in which the encoder is an M-ary mapper and a Gray encoder, and the modulator is a rectangular shaping filter followed by two parallel branches in Quadrature, in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ? , and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ? , and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
10. The apparatus of Claim 1, 2 or 3 in which the encoder is a binary convolution encoder of rate 1/2 and of constraint length v, with generators: g1 and g2 followed by a M-ary mapper and a Gray encoder, and the modulator is a rectangular shaping filter followed by a single In-phase branch, in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
11. A process for transmitting a digital signal over a communications channel, the process comprising:
encoding the digital signal to generate a sequence of signals;
modulating the sequence of symbols with a modulator to generate a sequence V;
filtering the sequence V with a conversion filter to generate a sequence S, the conversion filter having a length L and modulation index h, filtering the sequence S with a bandpass filter to generate a sequence R, the bandpass filter having a cut-off frequency fco;
for a fixed length L, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
encoding the digital signal to generate a sequence of signals;
modulating the sequence of symbols with a modulator to generate a sequence V;
filtering the sequence V with a conversion filter to generate a sequence S, the conversion filter having a length L and modulation index h, filtering the sequence S with a bandpass filter to generate a sequence R, the bandpass filter having a cut-off frequency fco;
for a fixed length L, the cut-off frequency fco and the modulation index h being chosen so that the power efficiency is at least locally maximized without a significant loss of bandwidth efficiency.
12. A process for transmitting a digital signal over a communications channel, the process comprising:
encoding the digital signal to generate a sequence of signals;
modulating the sequence of symbols with a modulator to generate a sequence V;
filtering the sequence V with a finite impulse response conversion filter to generate a sequence S, the conversion filter having a length L > 1 and a modulation index h;
filtering the sequence S with a bandpass filter to generate a sequence R, the bandpass filter having a cut-off frequency fco.
encoding the digital signal to generate a sequence of signals;
modulating the sequence of symbols with a modulator to generate a sequence V;
filtering the sequence V with a finite impulse response conversion filter to generate a sequence S, the conversion filter having a length L > 1 and a modulation index h;
filtering the sequence S with a bandpass filter to generate a sequence R, the bandpass filter having a cut-off frequency fco.
13. A process for transmitting a digital signal over a communications channel, the process comprising:
encoding the digital signal to generate a sequence of signals, modulating the sequence of symbols with a modulator to generate a sequence V, filtering the sequence V with a conversion filter to generate a sequence S, the conversion filter having a length L and modulation index h:
filtering the sequence S with a bandpass filter, centered in the frequency domain around the positive frequency, fmax, where the sequence 5 has its maximum power spectual density, and having a cut off frequency fco for filtering the sequence S to generate a sequence R.
encoding the digital signal to generate a sequence of signals, modulating the sequence of symbols with a modulator to generate a sequence V, filtering the sequence V with a conversion filter to generate a sequence S, the conversion filter having a length L and modulation index h:
filtering the sequence S with a bandpass filter, centered in the frequency domain around the positive frequency, fmax, where the sequence 5 has its maximum power spectual density, and having a cut off frequency fco for filtering the sequence S to generate a sequence R.
14. The process of Claim 11, 12 or 13 in which L and the cut-off frequency are chosen so that greater than 90%
of the average power in R is allowed through the bandpass filter, and the modulation index is chosen to at least locally maximize the power efficiency while maximizing the bandwidth efficiency.
of the average power in R is allowed through the bandpass filter, and the modulation index is chosen to at least locally maximize the power efficiency while maximizing the bandwidth efficiency.
15. The process of Claim 11, 12 or 13 in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T where T is the signaling interval.
16. The process of Claim 13 in which the bandpass filter has a nonzero flat response over the frequency range defined by fmax - fco and fmax + fco.
17. The process of Claim 11, 12 or 13 in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ? chosen to maximize the final bandwidth efficiency.
18. The process of Claim 11, 12 or 13 in which the encoder is an M-ary mapper followed by a Gray encoder, and the modulator is a rectangular shaping filter followed by a single In-phase branch, in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
19. The process of Claim 11, 12 or 13 in which the encoder is an M-ary mapper and a Gray encoder, and the modulator is a rectangular shaping filter followed by two parallel branches in Quadrature, in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
20. The process of Claim 11, 12 or 13 in which the encoder is a binary convolution encoder of rate 1/2 and of constraint length v, with generators: g1 and g2 followed by a M-ary mapper and a Gray encoder, and the modulator is a rectangular shaping filter followed by a single In-phase branch, in which the conversion filter is defined by the product of a slowly varying time function A(t) and a slowly varying phase function that are both nonzero between 0 and the product of L and T, where T is the signalling interval, and in which the slowly varying function A(t) is a raised cosine function having a roll-off factor ?, and L, H, ? and the product of T and fco having values about as shown in the rows of the following table:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA000601202A CA1313267C (en) | 1989-05-30 | 1989-05-30 | Conversion filtering for digital signalling systems |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA000601202A CA1313267C (en) | 1989-05-30 | 1989-05-30 | Conversion filtering for digital signalling systems |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1313267C true CA1313267C (en) | 1993-01-26 |
Family
ID=4140128
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000601202A Expired - Fee Related CA1313267C (en) | 1989-05-30 | 1989-05-30 | Conversion filtering for digital signalling systems |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1313267C (en) |
-
1989
- 1989-05-30 CA CA000601202A patent/CA1313267C/en not_active Expired - Fee Related
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US7079584B2 (en) | OFDM, CDMA, spread spectrum, TDMA, cross-correlated and filtered modulation | |
| US6665348B1 (en) | System and method for interoperable multiple-standard modulation and code selectable Feher's GMSK, enhanced GSM, CSMA, TDMA, OFDM, and third-generation CDMA, W-CDMA and B-CDMA | |
| US7110433B2 (en) | Spread spectrum, cross-correlated and filtered modulated systems | |
| US5642384A (en) | Trellis coded modulation scheme with low envelope variation for mobile radio by constraining a maximum modulus of a differential phase angle | |
| US7440488B2 (en) | TDMA, spread spectrum RF agile filtered signal transmission | |
| US8259832B2 (en) | QAM and GMSK modulation methods | |
| US6757334B1 (en) | Bit rate agile third-generation wireless CDMA, GSM, TDMA and OFDM system | |
| US5640423A (en) | Method for signal transmission using spectrally efficient orthogonal modulation | |
| CA2155267C (en) | Pre-compensated frequency modulation (pfm) | |
| US20080031126A1 (en) | Mis-Matched Modulation-Demodulation Format Selectable Filters | |
| US5600676A (en) | Modulation scheme with low envelope variation for mobile radio by constraining a maximum modulus of a differential phase angle | |
| JPH08195782A (en) | Circuit and method of transmitting and receiving numerical signal and being compatible with conventional coding tech-nique and decreasing peak power of filter-processed andtransmitted signal | |
| Seo et al. | Bandwidth compressive 16-state SQAM modems through saturated amplifiers | |
| US7272195B2 (en) | Method and circuit for controlling the peak power of a filtered signal in a single carrier data transmission system | |
| CA1313267C (en) | Conversion filtering for digital signalling systems | |
| WO1997029576A1 (en) | Coherent modulation of cpm signals | |
| US5127024A (en) | Conversion filtering for digital signaling systems | |
| WO2003105373A1 (en) | Methods for transmitting and receiving laser signals, as well as transmitter and receiver which carry out said methods | |
| Reddy | Voice-band modem: A device to transmit data over telephone networks: Advanced ideas which made high data rates possible | |
| Fattouche | Linearized continuous phase modulation | |
| CN113541798A (en) | Multi-band optical transmission system based on super-Nyquist transmission technology | |
| Balachandran et al. | Use of the M-algorithm to decode filtered CPM signals | |
| Hashem et al. | New GMSK transmitter structure for mobile radio systems | |
| CA2200531A1 (en) | Pre-compensated frequency modulation (pfm) |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| MKLA | Lapsed |