Comments on Ergodic and Outage Capacity

1. Comments on Ergodic and Outage Capacity Yang-Seok Choi, yschoi@vivato.net Siavash M. Alamouti, siavash@vivato.net Yang-Seok Choi et al., ViVATO

2. Questions? • From IEEE802.11-03/940r1, TGn-channel-models • Can we achieve 10 b/s/Hz at 10 dB SNR? • If not, how much spectral efficiency can we get at 10 dB SNR? • Model B provides better capacity than C? Table III: 4x4 MIMO channel mean capacity for the NLOS conditions at 10 dB SNR. Yang-Seok Choi et al., ViVATO

3. Comments • The table may mislead 802.11n participants regarding practical interpretation of capacity. • The numbers are neither a lower nor an upper bound for 802.11n performance criteria (FER as a function of SNR for a given bandwidth efficiency) • Relative “theoretical” performance for the different channels (compared to iid) does not correspond to the relative practical difference for known techniques. • “Outage Capacity” is a more useful metric than Ergodic “Average Capacity”. • We suggest the table be updated and/or perhaps replaced. Yang-Seok Choi et al., ViVATO

4. Assumptions • Block Fading Channel • Channel is invariant over a frame • Channel is independent from frame to frame • CSI is available to Rx only • Perfect CSI at RX • No feedback channel • Gaussian codebook Yang-Seok Choi et al., ViVATO

5. System Models where Yang-Seok Choi et al., ViVATO

6. “Instantaneous” Capacity • Capacity under given realization of channel matrix with perfect knowledge of channel at Rx • If transmitted frames have spectral efficiency less than above capacity, with arbitrarily large codeword, FER will be arbitrarily small • If transmitted frames have spectral efficiency greater than above capacity, with arbitrarily large codeword, FER will approach 100%. Yang-Seok Choi et al., ViVATO

7. Ergodic Capacity • Ergodic Capacity : Ensemble average of “instantaneous” capacity over all possible channel matrices • If , does this mean that in average we achieve 10 b/s/Hz spectral efficiency? • No in the sense of practical implementation! • But if CSI is available at Tx, by using adaptive modulation it can be true when the adaptive modulation can handle spectral efficiency from 0 to infinity. But if CSI is known to Tx, you can achieve better capacity. • Is it possible to achieve Ergodic Capacity? Yang-Seok Choi et al., ViVATO

8. Ergodic Capacity (cont’d) • How to achieve Ergodic capacity when CSI is not available to Tx? • At least, Your codeword should be spanned over all possible channel matrices. Otherwise there is no way to achieve Ergodic Capacity. • The codeword may have to be spread over all possible locations. • Or the frame duration should be much longer than coherence time. • And your coding structure should be able to achieve Ergodic capacity. • Ergodic capacity does not provide a useful metric Yang-Seok Choi et al., ViVATO

9. Outage Capacity • In fading channel, the capacity is a random variable. • Due to delay limitation, outage capacity is more meaningful than ergodic capacity • Outage capacity at outage probability • When • The above does not mean that in average we achieve 10 bps/Hz spectral efficiency • But it means that FER is 0.5 even with ideal code if your frame has 10 b/s/Hz spectral efficiency Yang-Seok Choi et al., ViVATO

10. Outage Capacity (cont’d) • CDF in Log scale : Low outage probability is of interest (some consider zero-outage probability) • Recall definition of “Capacity” – Maximum rate without error • Linear scale may not reveal behaviors at low outage probabilities • Outage Probability • With ideal code, outage probability is equal to FER of which spectral efficiency is C0 • With non-ideal code, outage probability is lower bound of FER • Slope of Log outage probability vs. Log SNR plot : Diversity Order • Slope of non-ideal code FER Diversity order Yang-Seok Choi et al., ViVATO

11. Outage Capacity (cont’d) • 100Mbps MAC SAP • 150 Mbps PHY SAP : required spectral efficiency for OFDM systems = (PHY Overhead such as Preamble is excluded) • Capacity in 11n • SNR=Received Signal Power per Rx antenna/Noise Power (at each subcarrier) where is a channel matrix at subcarrier k assuming and Max delay<GI Yang-Seok Choi et al., ViVATO

12. Outage Capacity (cont’d) • Outage Prob. 4-by-4 MIMO OFDM(NLOS, No shadow fading) • 0.5 l spacing • 1 l spacing Yang-Seok Choi et al., ViVATO

13. Outage Capacity (cont’d) • Loss due to • Non-Ideal code (Space and Frequency diversity) • Non-Ideal Channel Estimation • Implementation Loss • NF Yang-Seok Choi et al., ViVATO

14. Comparison Table (4x4) • Required SNR at 10% FER for 12.5 b/s/Hz with ideal coding Yang-Seok Choi et al., ViVATO

15. Comparison at PHY • Compare Proposals with ideal coding case • Slope • Required SNR at 10% FER Yang-Seok Choi et al., ViVATO

16. Thank you for your attention!! Questions? Yang-Seok Choi et al., ViVATO

17. Back-up • 100Mbps MAC SAP • 150 Mbps PHY SAP : required spectral efficiency = (PHY Overhead such as Preamble is excluded) • Capacity in 11n • SNR=Total Received Signal Power per Rx antenna/Noise Power (at each subcarrier) where is a channel matrix at subcarrier k assuming and Max delay<GI Capacity in OFDM Yang-Seok Choi et al., ViVATO