Directional Gain of IEEE 802.11 MIMO Devices Employing Cyclic Delay Diversity April 5, 2013 Technical Research Branch Laboratory Division Office of Engineering and Technology Federal Communications Commission OET Report Prepared by: FCC/OET 13TR1003 Stephen R. Martin ACKNOWLEDGMENTS The author is grateful to the following Federal Communications Commission employees for reviewing a draft of this document and providing many suggestions that improved the final version: Martin Doczkat, Mark Settle, and Robert Pavlak. i This page is intentionally blank ii TABLE OF CONTENTS INTRODUCTION ......................................................................................................................................................... 1 BACKGROUND ........................................................................................................................................................... 1 Directional Gain in the FCC Rules ........................................................................................................................... 1 Meaning of Directional Gain .................................................................................................................................... 2 Array Gain ................................................................................................................................................................ 2 CYCLIC DELAY DIVERSITY (CDD) IN IEEE 802.11 ............................................................................................. 3 MODELING .................................................................................................................................................................. 4 Array Configurations for FCC Analysis of 802.11 Cyclic Delay Diversity ............................................................. 5 Methodology ............................................................................................................................................................. 5 RESULTS ...................................................................................................................................................................... 5 Narrowband Beam Patterns ...................................................................................................................................... 6 Broadband Beam Patterns ......................................................................................................................................... 6 Array Gain Versus Frequency .................................................................................................................................. 7 Array Gain Versus Bandwidth .................................................................................................................................. 9 CONCLUSIONS ......................................................................................................................................................... 15 APPENDIX A - MATLAB CODE ........................................................................................................................... A-1 ILLUSTRATIONS Figure 1. Array Configurations for FCC Analysis of 802.11 Cyclic Delay Diversity ................................................ 16 Figure 2. Narrowband Azimuth Beam Patterns (2400-2500 MHz) of Four-Antenna Rectangle-2 ............................ 17 Figure 3. Narrowband Azimuth Beam Patterns (5700-5800 MHz) of Four-Antenna Rectangle-2 ............................ 18 Figure 4. Narrowband Azimuth Beam Patterns (5700-5800 MHz) for Eleven Array Configurations ....................... 19 Figure 5. Broadband 16.6-MHz Azimuth Beam Patterns (5700-5800 MHz) of Four-Antenna Rectangle-2 ............. 23 Figure 6. Array Gain Versus Center Frequency (5700-5800 MHz) For an Array With Two Antennas ..................... 24 Figure 7. Array Gain Versus Center Frequency (5700-5800 MHz) For Arrays With Four Antennas ........................ 25 Figure 8. Array Gain Versus Center Frequency (5700-5800 MHz) For Arrays with Five Antennas ......................... 26 Figure 9. Array Gain Versus Center Frequency (5700-5800 MHz) For Arrays With Eight Antennas ....................... 27 Figure 10. Array Gain Versus Center Frequency in Two Frequency Bands For 5-Antenna Square-1 ....................... 28 Figure 11. Maximum Array Gain Across 5700-5800 MHz Center Frequency Span Versus Bandwidth ................... 29 Figure 12. Median Array Gain Across 5700-5800 MHz Center Frequency Span Versus Bandwidth ........................ 29 Figure 13. Maximum Array Gain Versus Bandwidth in Two Frequency Bands For 5-Antenna Square-1 ................ 30 Figure 14. Median Array Gain Versus Bandwidth in Two Frequency Bands For 5-Antenna Square-1 ..................... 30 Figure 15. Maximum and Median Array Gains in 1 MHz Bandwidth ....................................................................... 31 Figure 16. Maximum and Median Broadband Array Gains for 20-MHz Channels.................................................... 31 Figure 17. IEEE 802.11 Channels that Straddle FCC Band Boundaries .................................................................... 32 Figure 18. Maximum Array Gain Versus Bandwidth With Straddle-Channel Bandwidths Identified ....................... 32 TABLES Table 1. Short Cyclic Delays Adopted by IEEE 802.11 for Non-High-Throughput Fields ......................................... 3 Table 2. Long Cyclic Delays Adopted by IEEE 802.11 for High-Throughput Fields .................................................. 3 iii This page is intentionally blank iv EXECUTIVE SUMMARY This report documents the theoretical modeling behind the formulas employed by the Federal Communications Commission (FCC) Laboratory for determining directional gain of radio transmissions from IEEE 802.11-compliant wireless local area network (LAN) devices when transmitting on multiple antennas in modes employing cyclic delay diversity (CDD). The new formulas are included in the guidance for computing directional gain in Knowledge Database (KDB) Publication 662911, “Emissions Testing of Transmitters with Multiple Outputs in the Same Band (e.g., MIMO, Smart Antenna, etc)”.1 Many of the FCC’s technical rules for “intentional radiators”, i.e., devices that intentionally transmit signals on radio frequencies, specify limits on maximum total transmit power and on maximum power spectral density that are dependent on the directional gain associated with those transmissions. This is true of the rules under which most IEEE 802.11-compliant wireless LAN devices operate (sections 15.247 and 15.407 of the FCC Rules)2 as well as a number of other rules. For devices that have a single transmitter output driving an antenna, the directional gain is simply that of the antenna. However, devices employing multiple input multiple output (MIMO) technology can achieve additional directional gain, called array gain, beyond the gains of the individual antennas by transmitting signals that are mutually correlated. In some cases this additional gain is intentionally created to improve performance, as is the case when transmit beamforming is employed. In other cases, as with cyclic delay diversity (CDD), the array gain is not intentional. Previous FCC guidance for determining directional gain of MIMO transmissions required that the maximum array gain that is theoretically possible for correlated transmissions be assumed whenever the transmissions exhibited any mutual correlation. That maximum possible array gain is given by 10 log(NANT) dB, where NANT is the number of transmit antennas. In some cases this approach was known to overestimate array gain, resulting in greater reductions in transmit power than would be required if a more accurate way of computing array gain were available. This report describes the development by the FCC Laboratory of a more accurate way to estimate array gain for the specific case of cyclic delay diversity (CDD) transmissions by devices operating under the IEEE 802.11 standard. The new techniques are based on theoretical calculations of beam patterns and the resulting array gains for twelve sample antenna array configurations with simulated transmissions using the CDD delays specified in the IEEE 802.11 standard. Based on the modeled array gain results as a function of transmit signal bandwidth, the new approach requires the continued use of the 10 log(NANT) formula when computing narrowband array gain for determining the required reductions in power spectral density of transmissions. However, a new formula computes broadband array gain as either 0 dB or 3 dB depending on transmit signal bandwidth and number of transmit antennas. The broadband array gain value is used to compute array gain for determining required reductions in transmit power. 1 Available at www.fcc.gov/labhelp by clicking “Major Guidance Publications” or by clicking “Advanced KDB Search” and entering the publication number. The array gain computations described in this technical report were implemented in version v01r01 of KDB Publication 662911, dated September 26, 2012. 2 The FCC rules are found in Title 47 of the Code of Federal Regulations (abbreviated as 47 CFR), available at http://www.ecfr.gov. Sections 15.247 and 15.407 are contained within Part 15, which governs unlicensed radio frequency devices. v This page is intentionally blank vi Directional Gain of IEEE 802.11 MIMO Devices Employing Cyclic Delay Diversity INTRODUCTION This report documents the theoretical