Carrier Frequency Estimation for Probabilistically Shaped Signals
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Solution Overview
Problem
Probabilistically shaped quadrature amplitude modulation (PS-QAM) signals reduce the frequency of corner symbols in constellations, impairing the performance of standard carrier frequency estimation (CFE) and carrier phase estimation (CPE) methods in digital signal processing (DSP) systems.
Innovation Solution
The method involves normalizing the fourth power of received symbols in CFE and using the coordinate rotation digital computer (CORDIC) algorithm to efficiently compute the complex number representing the normalized fourth power, thereby reducing noise in carrier frequency estimation and avoiding division operations that hinder real-time processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard CFE and CPE methods are used with PS-QAM signals, then the corner symbols are expected to provide sufficient estimation data, but the low occurrence of corner symbols in PS-QAM signals impairs estimation performance
Solution Approach 1:
The patent changes the parameter being measured from the original symbol values to the fourth power of the symbol values. This transformation causes symbols from different constellation regions (including non-corner symbols) to map to the same values, effectively increasing the occurrence of usable estimation data points without changing the physical signal characteristics.
Solution Approach 2:
The patent creates virtual copies of corner symbol data by mapping multiple different symbol types to the same fourth-power values. This allows the estimation algorithm to treat non-corner symbols as if they were corner symbols, effectively multiplying the available estimation data without requiring actual corner symbols to be transmitted more frequently.
2Measurement precision
If normalization of the fourth power of received symbols is implemented, then noise in carrier frequency estimation is reduced, but division operations increase processing complexity and delay
Solution Approach 1:
The patent replaces the mechanical division operation with an equivalent rotation operation implemented via the CORDIC algorithm. Instead of dividing by the magnitude (which requires complex division circuitry), the system rotates the fourth-power symbol to a standardized position, achieving the same normalization effect through addition and bit-shifting operations that are computationally simpler and faster to execute.
Solution Approach 2:
The patent changes the normalization approach from magnitude-based division to phase-based rotation. By representing the normalization as a phase rotation rather than a magnitude division, the system achieves the same statistical normalization effect while avoiding the computational complexity of real-time division operations in favor of simpler iterative rotation calculations.
3Measurement precision
If CFE introduces a 180 degree phase shift on received symbols, then carrier phase estimation can be performed, but the phase shift complicates the estimation process
Solution Approach 1:
The patent extracts and handles the 180-degree phase shift as a separate, identifiable condition. By checking the sign of the real part of the fourth-power symbol, the system identifies when a phase shift has occurred and applies compensation only in those specific cases, rather than continuously processing all symbols through complex phase correction circuits.
Solution Approach 2:
The patent introduces an intermediary classification step that categorizes symbols based on the sign of their fourth-power real part. This intermediary classification allows the system to apply simple conditional phase compensation (adding or subtracting π) rather than implementing continuous complex phase estimation, reducing the overall computational burden while maintaining accuracy.
4Productivity
If real-time carrier frequency and phase estimation is required, then processing delays must be minimized, but accurate estimation typically requires complex calculations that increase processing time
Solution Approach 1:
The patent substitutes complex division-based normalization with CORDIC-based rotation operations. The CORDIC algorithm uses only addition, subtraction, and bit-shifting operations in its iterative process, avoiding multiplication and division entirely. This substitution dramatically reduces the computational time required for each symbol processing step while maintaining the statistical properties needed for accurate estimation.
Solution Approach 2:
The patent segments the estimation process into distinct phases: fourth-power transformation, optional phase shift compensation based on sign classification, and CORDIC rotation. This segmentation allows each step to be optimized independently and enables parallel processing of multiple symbols through the pipeline, improving real-time throughput while preserving estimation accuracy.
Data Source
AI summary
In part, the disclosure relates to a method of carrier frequency estimation. The method includes selecting a first group of symbols from a constellation of a carrier signal, wherein the first group includes one or more subgroups of symbols from the constellation; estimating a carrier frequency or carrier frequency offset of the carrier signal by approximating the carrier frequency offset as Δf, whereinΔf=14argmax<semantics definitionURL="">❘<annotation encoding="Mathematica">"\[LeftBracketingBar]"</annotation></semantics>DFT(cos(θ)+j sin(θ))<semantics definitionURL="">❘<annotation encoding="Mathematica">"\[RightBracketingBar]"</annotation></semantics>;and determining cos(θ) and sin(θ) using a coordinate rotation digital computer (CORDIC) algorithm, wherein the CORDIC algorithm calculates rotation of a two-dimensional vector by θ using add and/or shift operations.