Range-Doppler Map dB Compression for Low-Bandwidth Telemetry
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Solution Overview
Problem
Existing systems face challenges in efficiently converting and compressing binary floating-point numbers, particularly range Doppler map (RDM) values, into decibel (dB) format for real-time telemetry applications, requiring effective compression to meet low latency and bandwidth constraints.
Innovation Solution
A telemetry device converts binary floating-point RDM values into compressed dB format by calculating a first number based on the exponent and a constant proportional to the logarithm of 2, using mantissa bits as an index into a lookup table, and rounding the sum of these values to determine the compressed RDM value, achieving a compression ratio and facilitating transmission over telemetry links.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If floating point RDM values are transmitted in uncompressed format, then measurement precision is maintained, but bandwidth consumption increases and latency increases
Solution Approach 1:
The floating-point number is segmented into exponent and mantissa components, which are processed separately through the compression algorithm. The exponent is scaled and rounded independently, while the mantissa is looked up in a pre-computed table, allowing efficient compression while preserving the essential precision of each component.
Solution Approach 2:
Lookup tables are pre-computed and stored, containing the relationship between mantissa values and their corresponding dB representations. This preliminary preparation allows the compression algorithm to quickly retrieve pre-calculated values rather than performing complex logarithmic calculations in real-time, significantly reducing computation time while maintaining precision.
2Quantity of substance
If floating point RDM values are compressed to dB format, then bandwidth consumption is reduced, but device complexity increases
Solution Approach 1:
The complex mathematical operation of computing logarithms is replaced with a simpler lookup table approach. Instead of performing floating-point logarithmic calculations, the system uses pre-computed tables that map mantissa values to dB values, substituting complex computation with simple memory access and arithmetic operations.
Solution Approach 2:
The representation parameters of RDM values are changed from standard floating-point format to dB scale format. This parameter transformation involves scaling the exponent by a constant factor and applying logarithmic transformation to the mantissa, resulting in a compressed representation that uses fewer bits while preserving the essential information.
3Loss of time
If real-time conversion from floating point to dB is performed, then latency is reduced, but measurement precision may be lost
Solution Approach 1:
The algorithm performs partial precision conversion by rounding the scaled exponent to the nearest integer and using a limited-precision lookup table for the mantissa. This partial action approach achieves real-time conversion speed by accepting some precision loss, which is acceptable for the application's latency requirements while maintaining sufficient accuracy for telemetry purposes.
Data Source
AI summary
Embodiments of a telemetry device and methods to convert a binary floating point number to a compressed number is described herein. The binary floating point number may comprise a mantissa and an exponent. The telemetry device may determine a first number based on a product of the exponent and a constant, wherein the constant may be proportional to a logarithm of the number two. The telemetry device may determine a second number using one or more bits of the mantissa as an index into a predetermined lookup table. Values of the lookup table may be proportional to logarithms of candidate mantissa values. The telemetry device may determine the compressed number based on rounding of a sum. The sum may include the first and second numbers. The rounding may be based on a predetermined step size.