US RE33056 E Abstract Double side band-quadrature carrier modulation signal points as mapped on the complex plane are drawn from an alphabet consisting of at least 8 points, and are set up in concentric rings each rotated by 45° with respect to adjacent rings. Differential encoding is shown encoding the phase components of the transmitted signals.
Claims(9) 1. A double side band-quadrature carrier modulation system comprising
input means for receiving a sequence of symbols a _{k} at a rate 1/T per second.coding means connected to said input means for providing from said symbbols a sequence of complex valued signal points d _{k} drawn from an alphabet comprising M points arranged in a multiplicity of concentric rings in the complex plane including an innermost ring having four equally spaced points and a plurality of additional rings each having four equally spaced points, each said ring being rotated by 45° with respect to adjacent said rings, andmodulating means connected to said coding means for providing from said signal points a signal in the form ##EQU3## where h(t-kT) represents an impulse response, w _{c} represents a carrier frequency, t represents time, j equals √-1, and k is the index of d_{k} and a_{k} wherein said coding means includes means for effectively providing said signal points arranged in at least four concentric rings in the complex plane. .[.2. The system of claim 1 wherein said coding means includes means for effectively providing said signal points arranged in at least four concentric rings in the complex plane..].
3. The system of claim .[.2.]. .Iadd.1 .Iaddend.wherein said coding means includes means for causing the innermost four said rings to have radii in the ratio √2:3:3√2:5.
4. The system of claim 1 wherein said coding means includes means for causing the phase component of each d
_{k} to depend upon a_{k} and upon the phase component of d.sub.(k-1).5. The system of claim 1 wherein said coding means includes means for causing each said d
_{k} to have integer valued coordinates in the complex plane.6. A double side band-quadrature carrier modulation system comprising
input means for receiving a sequence of symbols a _{k} at a rate 1/T per second,coding means connected to said input means for providing from said symbols a sequence of complex valued signal points d _{k} drawn from an alphabet comprising M points arranged in a multiplicity of concentric rings in the complex plane including an innermost ring having four equally spaced points and .[.a plurality of.]. .Iadd.at least three .Iaddend.additional rings having four equally spaced points, each said ring being rotated by 45° with respect to adjacent said rings, andfiltering means connected to said coding means for providing from said signal points the real and imaginary parts of a complex valued baseband signal in the form ##EQU4## and modulating means connected to said filtering means for providing from said baseband signal a passband signal in the form ##EQU5## where h(t-kT) represents an impulse response, w _{c} represents a carrier frequency, t represents time, j equals √-1, and k is the index of d_{k} and a_{k}.7. A double side band-quadrature carrier modulation method comprising
receiving a sequence of symbols a _{k} at a rate 1/T per secondproviding from said symbols a sequence of complex valued signal points d _{k} drawn from an alphabet comprising M points arranged in a multiplicity of concentric rings in the complex plane including an innermost ring having four equally spaced points and .[.a plurality of.]. .Iadd.at least three .Iaddend.additional rings each having four equally spaced points, each said ring being rotated by 45° with respect to adjacent said rings, andproviding from said signal points a signal in the form ##EQU6## where h(t-kT) represents an impulse response, w _{c} represents a carrier frequency, t represents time, j equals √-1, and k is the index of d_{k} and a_{k}.8. A double side band-quadrature carrier modulation method comprising
receiving a sequence of symbols a _{k} at a rate 1/T per second,providing from said symbols a sequence of complex valued signal points d _{k} drawn from an alphabet comprising M points arranged in a multiplicity of concentric rings in the complex plane including an innermost ring having four equally spaced points and .[.a plurality of.]. .Iadd.at least three .Iaddend.additional rings having four equally spaced points, each said ring being rotated by 45° with respect to adjacent said rings, andproviding from said signal points the real and imaginary parts of a complex valued baseband signal in the form ##EQU7## and providing from said baseband signal a passband signal in the form ##EQU8## where h(t-kT) represents an impulse response, w _{c} represents a carrier frequency, t represents time, j equals √-1, and k is the index of d_{k} and a_{k} wherein said coding means includes means for effectively providing said signal points arranged in at least four concentric rings in the complex plane. .Iadd.9. The system of claim 1 wherein said coding means includes means for providing signal points from an alphabet of sixteen points arranged in exactly four concentric rings in the complex plane. .Iaddend.
Description .Iadd.This application is a continuation of application Ser. No. 144,533, filed Apr. 28, 1980, now abandoned. .Iaddend. This invention relates to double side band-quadrature carrier (DSB-QC) modulation. DSB-QC modulation subsumes a class of modulation techniques such as phase-shift-keying (PSK), quadrature amplitude modulation (QAM), and combined amplitude and phase modulation, such as have long been known in the art. In high-speed data transmission across narrow-bandwidth channels such as the typical voice grade telephone channel, DSB-QC modulation has certain inherent advantages over single-sideband (SSB) and vestigial-sideband (VSB) techniques, such as are used in the majority of high-speed modems today. Against gaussian noise, it is inherently as efficient as SSB or VSB techniques in terms of the signal-to-noise ratios required to support a certain speed of transmission at a certain error rate in a given bandwidth. In addition, a coherent local demodulation carrier can be derived directly from the received data, without requiring transmission of a carrier or pilot tone. Furthermore, DSB-QC systems can be designed to have a much greater insensitivity to phase jitter on the line, or to phase error in the recovered carrier, than is possible with SSB or VSB signals. For modest data rates, well-known modulation schemes such as four-phase modulation provide good margins against both gaussian noise and phase jitter. At higher data rates, more bits of information must be sent per signalling interval, so multi-level signalling structures of greater complexity must be used. The standard schemes mentioned above begin to degrade rapidly aginst either gaussian noise or phase jitter when more signal points are required. It is the principal purpose of the present invention to provide novel signal structures which continue to exhibit near-optimum margins against both gaussian noise and phase jitter as additional points are added. Further advantages of the invention are simplicity of implementation and of detection, suppression of carrier, and 90° symmetry, which allows use of differential phase techniques. In general the invention features a double side band-quadrature carrier modulation system in which the signal points, as mapped on the complex plane, are drawn from an alphabet consisting of at least 8 points, and are set up in concentric rings each rotated by 45° with respect to adjacent rings. Preferred embodiments employ differential encoding of the phase components of the transmitted signals. Other advantages and features of the invention will be apparent from the following description of a preferred embodiment thereof, taken together with the drawings, in which: FIG. 1 is a block diagram of a DSB-QC modulation system; FIGS. 2a-h show several prior art signal structures mapped on the complex plane; FIGS. 3a, b show signal structures of the invention mapped on the complex plane; FIGS. 4a, b are logic diagrams for implementation of the structures of FIGS. 3a, b; FIG. 5 is a block diagram of a differential encoder; and FIG. 6 is a block diagram of a receiver. In DSB-QC modulation the transmitted spectrum X(w) is symmetric about some center (carrier) frequency w A circuit for realizing such a modulation scheme is shown in FIG. 1. A stream of input bits arrives at a rate of n/T bits per second, and is passed through an n-bit storage register 10. The n storage elements in the register are inputs to a combinational logic circuit 12 which forms one of M=2 An aspect of the invention involves the realization that a signal structure can be characterized by the sets of points [S This method of representation permits examination of the effect of distrubances on the modulated waveform x(t). We first consider an ideal case, illustrated in FIG. 6. x(t) enters the receiver and is demodulated by the two locally-generated carriers cos(w
ΣRed and
ΣImd Now suppose that h(t) is a perfect Nyquist waveform, i.e., for some time, τ, h(τ)=1, but h(τ-kT)=0 for integers k>0 or k<0. Then if we sample the two channels every T seconds at the correct times τ+kT, there will be no intersymbol interference, and we simply recover the pair of voltages Rez In a real situation, h(t) will not be a perfect Nyquist waveform, and the channel will introduce additional linear distortion which will lead to intersymbol interference. (At high data rates, it is usually necessary to incorporate an adaptive equalizer to reduce intersymbol interference to an acceptable level such as is described in Proakis and Miller, IEEE Trans. Inf. Theo. Vol. IT-15, No. 4, 1969.) Besides intersymbol interference (which also results when the outputs are not sampled at exactly the right times), real channels introduce other degradations such as noise and nonlinearities. All of these effects tend to perturb the received pair of samples Rez
e then e We define the required signal-to-noise margin S as 10 log Another disturbance of importance on telephone lines is phase jitter. If a transmitted waveform x(t) is subject to phase jitter, the result is (to first order when the phase jitter is slow and channel filtering unimportant)
x'(t)=ReΣ where θ(t) is a random phase process. Typically on telephone lines θ(t) contains frequencies up to 180 Hz, and may have amplitude up to 30° peak-to-peak or more. To some extent the phase jitter can be tracked at the receiver to give the locally-generated carriers cos(w
z where z Table 1 below gives required signal-to-noise ratios and minimum phase separations of points of the same amplitude for the signal structures of FIGS. 2a-h. (The minimum phase separation criterion above is an over-simplified, but still qualitatively indicative, measure of phase jitter immunity, since errors will actually be caused by the combined effects of noise and phase jitter.)
TABLE I______________________________________ 2a 2b 2c 2d 2e 2f 2g 2h______________________________________Required Signal-to-Noise Ratio (dB) 3 8.3 14.1 3 10 8.4 13.9 11.5Phase Separation 90° 45° 22.5° 90° 37° 90° 90° 45°______________________________________ Experience has shown that on telephone lines a minimum phase separation of 45° may be insufficient to guarantee low error rates when phase jitter is severe. For M=8 or 16, this means that only the 4-phase, 2- or 4-amplitude structures of FIGS. 2f and 2g can be used. But these structures are rather inefficient in their use of power, as is shown by their values of required signal-to-noise margin in Table I. The signal structures of the present invention retain the full 90° phase separations of the 4-phase structures, as well as their four-phase symmetry, while substantially reducing the required signal-to-noise margin over the structures of FIGS. 2f and 2g. FIG. 3a illustrates a structure according to the invention for the case M=8, and FIG. 3b, a structure for M=16. In the former case the points are at (1+j)j Table II below gives required signal-to-noise ratios and minimum phase separations for the structure of FIGS. 3a and 3b. The savings over FIGS. 2f and 2g are 1 dB and 2.6 dB, respectively. In fact FIG. 3b is only 1.3 dB worse than the optimal FIG. 2e for M=16, but has greatly enhanced protection against phase errors.
TABLE II______________________________________ 3a 3b______________________________________Required Signal-toNoise Ratio (dB) 7.4 11.3Phase Separation 90° 90°______________________________________ In general, the class of structures according to the invention may be described as follows. Interest is confined to M-point structures for M≧8, since the simple 4-phase structure of FIG. 2a is entirely satisfactory for M=4. M is assumed to be a multiple of 4, as it will be if it is a power of 2. Then, m=M/4 rings of radii r Implementation of the invention is straight-forward. The circuit of FIG. 1 can be used with appropriate combinational logic to generate the integers 0, +1, +3, or +5 in ordinary two's-complement form, which can then drive standard 3- or 4-bit D/A converters. FIG. 4a gives appropriate logic for the signal structure of FIG. 3a, where (B1, B2, B3) are the three input bits, (XS, X1, X2) and (YS, Y1, Y2) are two's-complement representations of the real and imaginary parts of the signal points, and the correspondence is according to the three-bit numbers associated with each signal point on the diagram of FIG. 3a. (In this correspondence B1 is in effect an amplitude variable denoting inner or outer ring, whereas B2 and B3 select one of the four phases.) Similarly FIG. 4b gives logic for FIG. 3b, where (B1, B2, B3, B4) are the four input bits and (XS, X1, X2, X3) and (YS, Y1, Y2, Y3) are the coordinates of the signal points in two's-complement form, coded according to the diagram of FIG. 3b (where B1 and B2 select one of the four rings, and B3 and B4 select the phase on the ring). Because of the four-phase symmetry of these structures, the carrier is suppressed--i.e., there is no carrier power at the frequency w
d where d(0)=(1+j) and d(1)=3, while θ(0,0)=0, θ(0, 1)=π/2, θ(1,1)=π, and θ(1,0)=3π/2, and B1
θ
d Then at the receiver the phase θ(B2 FIG. 5 illustrates the implementation of differential encoding. The phase bits B2 and B3 are Gray-coded into a 2-bit integer which is added to the stored 2-bit integer (θ1 Other embodiments are within the following claims: Patent Citations
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