Limits On Wireless Communication In Fading Environment Using Multiple Antennas

1. Limits On Wireless Communication In Fading Environment Using Multiple Antennas Presented By Fabian Rozario ECE Department Paper By G.J. Foschini and M.J. Gans

2. Outline • Introduction. • Mathematical model. • Capacity formulas. • Lower bound on capacity. • Capacity improvement. • Comparison of various systems. • Min-Max strategy. • Summary.

3. Introduction • We make the following assumptions • Receiver knows channel characteristics but not transmitter. • Ie: fast feedback link required otherwise. • We allow changes to propagation environment to be slow in time scale compared to burst rate. • Model used is Rayleigh fading. • Use information theory to find out increase in bit/cycle compared to no of antennas used.

4. Introduction: Rayleigh fading • Model useful when no LOS path exists. • Zero mean Gaussian process. • Can be used to model ionospheric and tropospheric scatters. • If relative motion exists between TX and RX: fading is correlated and varying in time. • We can decorrelate path losses by using antennas separated by λ/2 on a rectangular lattice. • This belongs to small scale fading.

5. Introduction: Information Theory • Use Shannon capacity formula. • We get capacity in terms of bits/second. • In our application we can get the increase in bps/Hz for given no of TX and RX. • Roughly for n antennas increase is n bits per 3db increase in SNR.

6. Mathematical model • Focus on single point to point channel. where • How does receiver diversity affect capacity • Noise remains same but output signal is linear combination of diff antennas. • This is maximal ratio combiner.

7. Capacities: Matrix channel is Rayleigh • Random channel model(|H|) is treated as Rayleigh channel model with zero mean, unit variance, complex. • H matrix is assumed to be measured at receiver using training preamble. • No Diversity case: nt=nr=1 |H| replaced by Chi squared variate with 2 degree of freedom.

8. Capacities: Contd • Receiver Diversity case: nt=1, nr=n • Transmit Diversity case: nt=n, nr=1 • Combined Transmit and Receiver Diversity: nt=nr • Cycling using one transmitted at a time:

9. Lower Bound On Capacity • Employs unitarily equivalent rectangular matrices, here H is unitarily equivalent to m*n matrix. • Where are chi squared variables with j degree freedom. • Final result: contribution of the form L+Q where and Q is positive, negative term are cancelled out by positive Q hence C>L with probability 1.

10. Capacity Derivation: • One spatially cycled transmitting antenna/symbol: • Channel capacity defined in terms of mutual information between input and output. Where ε- entropy

11. Capacity improvement: CCDF 4 antenna case 2 antenna case

12. Capacity per dimension:

13. Comparison of systems

14. Min-Max communication system • When multiple antennas are used the other antennas will add noise. • Detectors have optimal combining. • Detect 1st signal component using optimal combining and treat 2nd component as noise. • After 1st is detected subtract that from received signal vector and extract 2nd signal by optimal combining. • 2nd component affected by thermal noise as 1st already removed. • Same procedure for second detector.

15. Min Max performance

16. Summary • We were able to analyze receiver and transmitter diversity. • Conclude that increase in bit rate is n bits/cycle for n antennas for each 3db increase in SNR. • Compare various combinations of systems with different no of Rx and Tx. • See the use of min-max strategy. • This application is useful for indoor wireless LAN.

17. Thank You