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5.9 Summary

  • Single-path propagation channels delay and attenuate the received signal.

  • Multipath propagation channels create intersymbol interference. The discrete-time complex baseband equivalent channel includes the transmit and receive pulse shaping. It can be modeled with FIR filter coefficients e309-1.jpg.

  • Equalization is a means of removing the effects of multipath propagation. Linear equalization designs a filter that is approximately the inverse of the channel filter. Equalization can also be performed in the frequency domain using OFDM and SC-FDE frameworks.

  • Frame synchronization involves identifying the beginning of a transmission frame. In OFDM, frame synchronization is called symbol synchronization. Known training sequences or the periodic repetition of a training sequence can be used to estimate the beginning of the frame.

  • Carrier frequency offset is created by (small) differences in the carrier frequencies used at the transmitter and the receiver. This creates a phase rotated on the received signal. Carrier frequency offset synchronization involves estimating the offset and derotating the received signal to remove it. Special signal designs are used to enable frequency offset estimation prior to channel estimation.

  • Training sequences are sequences known to both the transmitter and the receiver. They are inserted to allow the receiver to estimate unknown parameters like the channel, the frame start, or the carrier frequency offset. Training sequences with good correlation properties are useful in many algorithms.

  • Propagation channel models are used to evaluate the performance of signal processing algorithms. Large-scale fading captures the average characteristics of the channel over hundreds of wavelengths, whereas small-scale fading captures the channel behavior on the order of wavelengths. Channel models exist for the large-scale and the small-scale fading components.

  • Path loss describes the average loss in signal power as a function of distance. It is normally measured in decibels. The log-distance path-loss model describes the loss as a function of the path-loss exponent and possibly an additional random variable to capture shadowing. The LOS/NLOS path-loss model has a distance-dependent probability function that chooses from an LOS or NLOS log-distance path-loss model.

  • The small-scale fading characteristics of a channel can be described through frequency selectivity and time selectivity.

  • Frequency selectivity is determined by looking at the power delay profile, computing the RMS delay spread, and seeing if it is significant relative to the symbol period. Alternatively, it can be assessed by looking at the coherence bandwidth and comparing the bandwidth of the signal.

  • Time selectivity is quantified by looking at the spaced-time correlation function and comparing the frame length. Alternatively, it can be determined from the RMS Doppler spread or the maximum Doppler shift and comparing the signal bandwidth.

  • There are several different flat-fading and frequency-selective channel models. Most models are stochastic, treating the channel as a random variable that changes from frame to frame. Rayleigh fading is the most common flat-fading channel model. Frequency-selective channels can be generated directly based on a description of their taps or based on a physical description of the channel.

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