SYSC 4607 – Lecture 14 Outline. Review of Previous Lecture Diversity Systems Methods for Obtaining Diversity Branches Diversity Combining Techniques Performance of Diversity in Fading Channels. Review of Previous Lecture. Average P s in fast fading:
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- Averaged over fast fading distribution
- Good metric when Tc~Ts
- Used for combined fast and slow fading: average over fast fading, outage relative to slow fading
- Differential modulation has a poor phase reference due to phase decorrelation
- Little impact on high speed systems
- Self-interference due to delay spread
- Without compensation, severely limits data rates
- Same Information is Sent over Independent Fading Paths
- Signals are Combined to Mitigate the Effects of Fading
- Methods to Obtain Diversity Branches
- Diversity Combining Methods
- Receiver versus Transmitter
- Predetection versus Postdetection
- Microscopic versus Macroscopic
- Multiple antenna elements spaced apart by decorrelation distance. Theoretical decorrelation λ/2. Most common form of diversity. No additional power or bandwidth.
- Multiple narrowband channels separated by channel coherence bandwidth. Less often used. Wasteful of scarce spectrum.
- Two antennas (one horizontally, the other verticallypolarized) are used. Orthogonal polarization in wireless channels exhibit uncorrelated fading. Only two-branch diversity possible. Not common.
-Directional antennas facing widely different directions. Scattered signal from different directions having approximately independent fading.
- Transmission of the same information in time slots separated by channel coherence time. Inefficient for high-speed transmissions. Useless for stationary users.
- Same as Time-diversity, except that branches are provided by channel through multipath. Takes advantage of channel provided usually undesirable multipath echoes. Principle of Rake Receivers.
- Strongest signal is selected. Cophasing not required.
- Signal above a given threshold is used. Switching to a different branch if it drops below the threshold.
- Signals are cophased and summed after optimal weighting proportional to individual SNR’s. Goal is to maximize SNR at the combiner output.
- Branch signals are cophased and added (Maximal Ratio with equal weights).
- Gain in SNR from coherent addition of signals and non-coherent addition (averaging) of noise over multiple antennas
- Gain in both fading and non-fading channels
- Gain in SNR due to elimination of weak signals (deep fades). Changes slope of probability of error.
- Gains in fading channels
(Assuming independent branches)
For iid Rayleigh fading (ri Rayleigh, γi exponential):