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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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sysc 4607 lecture 14 outline
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
Review of Previous Lecture
  • Average Ps in fast fading:

- Averaged over fast fading distribution

- Good metric when Tc~Ts

  • Combined outage and average Ps

- Used for combined fast and slow fading: average over fast fading, outage relative to slow fading

  • Irreducible error floor due to Doppler

- Differential modulation has a poor phase reference due to phase decorrelation

- Little impact on high speed systems

  • Irreducible error floor due to ISI

- Self-interference due to delay spread

- Without compensation, severely limits data rates

diversity systems basic principles and classifications
Diversity Systems: Basic Principles and Classifications
  • Basic Concept

- Same Information is Sent over Independent Fading Paths

- Signals are Combined to Mitigate the Effects of Fading

  • Design Issues

- Methods to Obtain Diversity Branches

- Diversity Combining Methods

  • Different Classifications

- Receiver versus Transmitter

- Predetection versus Postdetection

- Microscopic versus Macroscopic

methods to obtain diversity branches
Methods to Obtain Diversity Branches
  • Space

- Multiple antenna elements spaced apart by decorrelation distance. Theoretical decorrelation λ/2. Most common form of diversity. No additional power or bandwidth.

  • Frequency

- Multiple narrowband channels separated by channel coherence bandwidth. Less often used. Wasteful of scarce spectrum.

  • Polarization

- Two antennas (one horizontally, the other verticallypolarized) are used. Orthogonal polarization in wireless channels exhibit uncorrelated fading. Only two-branch diversity possible. Not common.

methods to obtain diversity branches1
Methods to Obtain Diversity Branches
  • Angle of Arrival

-Directional antennas facing widely different directions. Scattered signal from different directions having approximately independent fading.

  • Time

- Transmission of the same information in time slots separated by channel coherence time. Inefficient for high-speed transmissions. Useless for stationary users.

  • Multipath

- 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.

diversity combining techniques
Diversity Combining Techniques
  • Selection Combining (SC)

- Strongest signal is selected. Cophasing not required.

  • Threshold (Switching) Combining

- Signal above a given threshold is used. Switching to a different branch if it drops below the threshold.

  • Maximal Ratio Combining (MRC)

- Signals are cophased and summed after optimal weighting proportional to individual SNR’s. Goal is to maximize SNR at the combiner output.

  • Equal Gain Combining (EGC)

- Branch signals are cophased and added (Maximal Ratio with equal weights).

linear diversity combining
Linear Diversity Combining
  • Individual branches are weighed by αi and summed
  • Selection and Threshold Combining: all αi = 0, except one. Cophasing not required
  • Maximal Ratio Combining: αi function of γi. Co-phasing required
  • Equal Gain: αi = 1. Co-phasing required
linear diversity combining1
Linear Diversity Combining
  • is a random variable with PDF and CDF which depends on the type of fading and the choice of combining
  • Most often PDF is obtained by differentiating CDF
  • is the random probability of error for AWGN non-fading channel
  • Most often closed form solution for CDF, Pout and unavailable. Results based on computer simulation.
array and diversity gains
Array and Diversity Gains
  • Array Gain

- 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

  • Diversity Gain

- Gain in SNR due to elimination of weak signals (deep fades). Changes slope of probability of error.

- Gains in fading channels

selection combining
Selection Combining
  • Combiner outputs the signal with the highest SNR
  • The chance that all the branches are in deep fade simultaneously is very low.
  • Since at each instant only one signal is used co-phasing is not required.
selection combining1
Selection Combining

(Assuming independent branches)

For iid Rayleigh fading (ri Rayleigh, γi exponential):

selection combining2
Selection Combining
  • The average SNR gain (array gain) increases with M, but not linearly.
threshold switching combining
Threshold (Switching) Combining
  • Branches are scanned sequentially. First one above a given threshold is selected. The signal is used as long as its SNR is above threshold.
  • Since at each instant only one signal is used, co-phasing is not required.
threshold switching combining1
Threshold (Switching) Combining
  • For two-branch diversity with iid branch statistics:
  • For iid Rayleigh fading with
maximal ratio combining
Maximal Ratio Combining
  • In the general model set
  • Then,
  • Assuming the same noise psd at all branches:
  • Maximizing by Cauchy-Schwartz inequality:
maximal ratio combining1
Maximal Ratio Combining
  • Assuming iid Rayleigh fading in each branch with equal average branch SNR, , resulting has chi-squared distribution with 2M degrees of freedom:
equal gain combining
Equal Gain Combining
  • In maximal ratio combining, set
  • Then,
  • In general, no closed-form solution for . For iid two-branch Rayleigh channel with same CDF in terms of Q function:
main points
Main Points
  • Diversity overcomes the effects of flat fading by combining multiple independent fading paths
  • Diversity typically entails some penalty in terms of rate, bandwidth, complexity, or size.
  • Different combining techniques offer different levels of complexity and performance.