Mathematics of Multipath Distortion

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Mathematics of Multipath Distortion

• Dr. A. J. Van Dierendonck
• AJ Systems

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Multipath Effects

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

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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