Mathematics of Multipath Distortion

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# Mathematics of Multipath Distortion - PowerPoint PPT Presentation

Mathematics of Multipath Distortion. Dr. A. J. Van Dierendonck AJ Systems. Multipath Effects. Composite Signal a = Relative multipath signal amplitude d = Multipath delay in seconds C f ( t ) = Pre-correlation filtered PN Code Filtered Autocorrelation Function. Composite Discriminators.

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### Mathematics of Multipath Distortion

Dr. A. J. Van Dierendonck

AJ Systems

IMA

Multipath Effects
• Composite Signal
• a = Relative multipath signal amplitude
• d = Multipath delay in seconds
• Cf(t) = Pre-correlation filtered PN Code
• Filtered Autocorrelation Function

IMA

Composite Discriminators
• Coherent DLL
• Non-Coherent DLL (Dot Product)

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Computing Multipath Error
• Set the E(dtk) to zero; Solve (iteratively) for tk as a function of phase fm and multipath delay d
• fm = 0°and 180° yields maximum error amplitude results (error envelope)

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MULTIPATH ERROR ENVELOPES WITH 20 MHz BANDWIDTH
• Non-Coherent Discriminator; a = 0.5

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MULTIPATH ERROR ENVELOPES WITH NARROWER BANDWIDTHS
• Non-Coherent Discriminator; a = 0.5

IMA