1. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 1 Comments on Ergodic and Outage Capacity Yang-Seok Choi, yschoi@vivato.net Siavash M. Alamouti, siavash@vivato.net

2. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 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? Model (NLOS)Mean capacity in b/s/Hz % of iid mean capacity A (optional)9.183 B8.981 C8.678 D10.092 E9.385 F10.495 iid10.9100 Table III: 4x4 MIMO channel mean capacity for the NLOS conditions at 10 dB SNR.

3. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 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.

4. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 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

5. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 5 System Models where

6. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 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%.

7. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 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?

8. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 8 Ergodic Capacity (contd) 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 is not a useful metric

9. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 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

10. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 10 Outage Capacity (contd) 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 C 0 –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

11. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 11 Outage Capacity (contd) 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

12. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 12 Outage Capacity (contd) Outage Prob. 4-by-4 MIMO OFDM(NLOS, No shadow fading) – 0.5 spacing – 1 spacing

13. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 13 Outage Capacity (contd) Loss due to –Non-Ideal code (Space and Frequency diversity) –Non-Ideal Channel Estimation –Implementation Loss –NF

14. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 14 Comparison Table (4x4) Required SNR at 10% FER for 12.5 b/s/Hz with ideal coding Model (NLOS) 0.5 spacing1 spacing B15.6 dB13.6 dB C15.4 dB13.4 dB D13.2 dB12.2 dB E14 dB13.1 dB iid (flat)13.4 dB iid (200 nsec rms)12.1 dB

15. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 15 Comparison at PHY Compare Proposals with ideal coding case –Slope –Required SNR at 10% FER

16. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 16 Thank you for your attention!! Questions?

17. doc.: IEEE 802.11-04/0015r2 Submission January 2004 Yang-Seok Choi et al., ViVATOSlide 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