EE 359 Lecture 12 Outline l Combining Techniques

EE 359 – Lecture 12 Outline l Combining Techniques l Maximal Ratio Combining l MGF Approach to MRC Performance l EGC l Transmit Diversity l Not covered in lecture or on exam l Midterm Review

Review of Last Lecture l Performance in ISI and Doppler l Introduction to Diversity l Send same bits over independent fading paths l Time, space, frequency, or polarization diversity l Combine paths to mitigate fading effects t l l Performance metrics: Array and Diversity gain Structure of a Diversity Combiner

Combining Techniques l Selection Combining l l Maximal Ratio Combining l l All paths cophased and summed with optimal weighting to maximize combiner output SNR Equal Gain Combining l l Fading path with highest gain used All paths cophased and summed with equal weighting Array/Diversity gain l Array gain is from noise averaging (AWGN and fading)

Selection Combining Analysis and Performance l Selection Combining (SC) Combiner SNR is the maximum of the branch SNRs. l CDF easy to obtain, pdf found by differentiating. l Diminishing returns with number of antennas. l Can get up to about 20 d. B of gain. Outage Probability l

MRC and its Performance l With MRC, g = gi for branch SNRs gi l l Standard average BER calculation l l l Optimal technique to maximize output SNR Yields 20 -40 d. B performance gains Distribution of g hard to obtain Hard to obtain in closed form Integral often diverges MGF Approach

EGC and Transmit Diversity l EGQ simpler than MRC l Paths co-phased, combined with equal gain l Harder to analyze l Performance about 1 d. B worse than MRC l Transmit diversity l With channel knowledge, similar to receiver diversity, same array/diversity gain l Without channel knowledge, can obtain

Main Points l MRC optimally combines fading paths to maximize combiner SNR MRC vs SC trade off complexity for performance. l MRC yields 20 -40 d. B gain, SC around 20 d. B. l l Analysis of MRC simplified using MGF approach l EGC easier to implement than MRC: hard to analyze: Performance about 1 d. B worse than MRC l Transmit diversity can obtain diversity gain

Midterm Review l Overview of Wireless Systems l Signal Propagation and Channel Models l Modulation and Performance Metrics l Impact of Channel on Performance l Fundamental Capacity Limits l Diversity Techniques l Main Points