Complex Carrier Modulation for Spectrum Utilization
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Solution Overview
Problem
Current real carrier modulation methods waste frequency spectrum resources and lose signal energy due to the neglect of negative frequencies and improper use of complex signals, leading to ambiguity in frequency bands and energy loss during demodulation.
Innovation Solution
Implementing complex carrier modulation using complex signals e−iωt or eiωt as carrier signals to modulate and demodulate signals, allowing independent use of left and right frequency bands and maintaining signal energy by transmitting and receiving both the real and imaginary parts of the complex signal.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of energy
If real carrier modulation is used to transmit signals, then the modulation process is simple and compatible with real signal processing, but frequency spectrum resources are wasted and signal energy is lost due to neglecting negative frequencies
Solution Approach 1:
The patent transitions from real signal modulation to complex signal modulation, adding the imaginary dimension to the signal space. By using complex carrier signals e^(jωt) instead of real carrier signals cos(ωt), the system can independently utilize both positive and negative frequency components, thereby recovering the wasted signal energy while maintaining manageable modulation complexity through established complex signal processing techniques.
Solution Approach 2:
The patent changes the fundamental parameter of the carrier signal from real-valued to complex-valued. By using complex exponential functions e^(jωt) with both positive and negative frequencies instead of real cosine functions, the system recovers the energy previously lost in the negative frequency components, while the complexity increase is offset by the mathematical elegance of complex signal processing.
2Productivity
If only positive frequency bands are used for communication, then the modulation and demodulation processes are straightforward, but spectrum utilization is halved due to abandonment of negative frequency resources
Solution Approach 1:
The patent utilizes the complex plane as an additional dimension to distinguish between positive and negative frequency components. By representing signals as complex exponentials e^(jωt) where the sign of ω indicates rotation direction in the complex plane, the system can independently address both positive and negative frequency bands, effectively doubling spectrum utilization while maintaining clear frequency band distinction through the complex signal representation.
Solution Approach 2:
The patent applies asymmetric treatment to positive and negative frequency components by using complex exponential functions with distinct signs. The complex signal e^(jωt) with ω>0 represents counter-clockwise rotation while e^(-jωt) with ω<0 represents clockwise rotation, creating an asymmetric but distinguishable representation that enables independent utilization of both frequency bands without confusion.
3Loss of information
If real signals are transmitted instead of complex signals, then the transmission system is simpler and compatible with conventional receivers, but information completeness is reduced due to inability to distinguish left and right rotating frequency signals
Solution Approach 1:
The patent restores information completeness by transmitting complex signals that preserve both the real and imaginary components. The complex signal representation e^(jωt) contains complete information about both magnitude and phase, as well as the direction of rotation (positive or negative frequency), eliminating the information loss inherent in real signal transmission while keeping the processing complexity manageable through standard complex arithmetic operations.
Solution Approach 2:
The patent uses complex exponential functions as a mathematical copy that preserves complete signal information. The complex signal e^(jωt) serves as a complete representation that encapsulates both the amplitude and phase information, as well as the rotational direction, providing a full-information copy of the signal characteristics that cannot be obtained from real signals alone.
Data Source
AI summary
A method, device and system for complex carrier modulation are provided in the disclosure, wherein e−iωt or eiωt is used as a carrier frequency to perform carrier modulation on a to-be-carried signal. The modulated signal transmitted in a medium is a rotating complex signal. The method can enable right and left frequency bands to carry independent information. Therefore the spectrum utility ratio is improved. Employing the method for complex carrier modulation provided in the disclosure can use the right and left frequency spectrum resources adequately, and the loss of signal energy is small, therefore the capacity of a channel is improved greatly.