1. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 1 Comparison of 128QAM mappings/labelings for 802.11n Ravi Mahadevappa, ravi@realtek-us.com Stephan ten Brink, stenbrink@realtek-us.com Realtek Semiconductors, Irvine, CA

2. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 2 Overview 128QAM for increasing data rate of 802.11n –MIMO 2xN: can achieve 2x54Mbps = 108Mbps in 20MHz –108Mbps peak too small to get 100Mbps MAC throughput –MIMO 2xN, 128QAM, R=7/8 code, 20MHz: 147Mbps achievable Consider four 128QAM constellations/labelings –Determine the one which is most suitable Performance comparison using mutual information in bit-interleaved coded modulation (BICM) [1], [2] BER chart in AWGN and Rayleigh channel PER chart in an 802.11a-like setting (2x2, 2x3 MIMO)

3. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 3 Introduction Bit Interleaved Coded Modulation (BICM) –Gray-labeling of the constellation points is best to achieve a low bit error rate (BER), if no iterative decoding is applied [2] For QPSK, 16QAM, 64QAM, 256QAM –True Gray-labeling possible, using a square constellation –Gray-labeling per I-/Q-channel –I-/Q-channel independent, can be demapped separately For 128QAM –no true Gray-labeling possible –e.g. 128QAM: 7 bits; one bit has to be “distributed” over I/Q

4. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 4 802.11a Transmitter Bit interleaved coded modulation –Channel encoder (error correcting coding) and QAM symbol mapper are connected through a bit interleaver –The 802.11a WLAN system [3] exhibits this structure

5. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 5 802.11a Receiver

6. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 6 64QAM Example: Gray-labeling 64QAM with Gray- labeling: bit labels of neighboring signal points differ by one binary digit Most systems with QAM modulation use Gray-labeling, e.g. 802.11a WLAN [3] Allows low-complexity bit detection (I/Q can be dealt with separately)

7. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 7 128QAM Constellations: Shifted I Based on two shifted 64QAM constellations Proposed for different systems, e.g. [4] Motivation: I&Q can be demapped separately Bit labels of neighboring signal points differ by two binary digits See later: Good for iterative BICM (demapper/decoder iterations), but not good for BICM

8. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 8 128QAM: Shifted II, 64QAM/Gray Based on two 64QAM constellations, shifted Gray-labeling per 64QAM constellation Bit labels of neighboring signal points differ by more than one binary digit at several places

9. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 9 128QAM: Cross I, DVB-C DVB-C(able) [5] uses cross constellation and this bit labeling The two MSB’s are differentially encoded, to be rotationally invariant against 90degree flips “Almost” Gray-labeling within one quadrant, but bit labels differ by many bits along the zero I- and Q-axis Not designed for BICM

10. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 10 128QAM: Cross II, Gray-like Center: 64QAM with Gray-labeling as 802.11a; the 7th bit (most significant bit, MSB) is set to zero Borders: mirrored 64QAM; horizontally, vertically flipped from center, MSB set to one Labels of neighboring signal points differ by 3 digits at few places All other bit labels of neighboring signal points differ by only one binary digit

11. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 11 128QAM: Cross II, Gray-like Generation by mirroring, flipping center 64QAM Gray constellation to outside and setting MSB from 0 to 1

12. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 12 128QAM: Comparison, EXIT Chart Extrinsic information transfer (EXIT) chart [6] to predict performance AWGN, E b /N 0 =9dB, at code rate 3/4 For BICM, start of curve essential (this is the mutual information, that demapper “sees”) Cross II: highest start –best for BICM Cross I has “moderate” slope; Shifted II similar –Mediocre for BICM Shifted I: lowest start –bad for BICM –but would be best for iterative demapping and decoding Only start of curve relevant for good BICM performance (the higher, the better)

13. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 13 128QAM: BER Chart, AWGN AWGN, rate 3/4 memory 6 convolutional code 64QAM (Gray) as reference Best: Cross II Worst: Shifted I Difference about 2dB

14. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 14 128QAM: BER Chart, Rayleigh Rayleigh channel (ergodic), rate 3/4 memory 6 convolutional code 64QAM as reference Best: Cross II Worst: Shifted I Difference about 2dB

15. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 15 PER, 802.11a-like High-Rate System MIMO-OFDM simulation, with 11a parameters for symbol duration, guard time, 64FFT etc. M=2 TX antennas (spatial multiplexing), 128QAM rate 3/4 mem. 6 conv. code; PHY rate of 126Mbps MIMO sub-channels: independent fading, with exp. decay profile, T rms = 60ns MIMO ZF detection with soft post processing Ca. 1dB-advantage of Cross II over Shifted II

16. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 16 Conclusion To increase spectral efficiency, the use of 128QAM is a possible option 128QAM helps to smoothen the rate table Constellation mapping and labeling important Recommendation: If 128QAM is to be considered for 11n, cross- constellation with Gray-like labeling (Cross II) should be used

17. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 17 References [1]E. Zehavi, “8-PSK trellis codes for a Rayleigh channel”, IEEE Trans. Commun., vol. 40, pp. 873-884, May 1992 [2]G. Caire, G. Taricco, E. Biglieri, “Bit-interleaved coded modulation”, IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 927-946, May 1998 [3]IEEE Std 802.11a-1999, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, High-speed Physical Layer in the 5 GHz Band [4]IEEE P802.15-15-03-0311-00-003a, “Reasons to use non-squared QAM constellations with independent I&Q in PAN systems”, July 2003 [5]“Digital Video Broadcasting (DVB): Framing structure, channel coding and modulation for cable systems”, EN 300 429, V. 1.2.1 (1998-04), European Standard (Telecommunications series) [6]S. ten Brink, “Convergence of iterative decoding,”, Electron. Lett., vol. 35, no. 10, pp. 806-808, May 1999

18. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 18 Backup Slides

19. doc.: IEEE 802.11-03/825r0 Submission November 2003 Ravi Mahadevappa, Stephan ten Brink, Realtek Slide 19 128QAM: Comparison, EXIT Chart For Cross I, one needs to increase E b /N 0 by 1dB to achieve the same starting point as Cross II For Shifted I, one needs to increase E b /N 0 by 2.2dB to achieve the same starting point as the Cross II constellation Shifted II: Increase by 1.4dB required Next step: Verify E b /N 0 - offset predictions by BER simulations using memory 6 convolutional code of rate 3/4