Solution to I/Q Imbalance in OFDM Systems

OFDM modulation, widely used in communication systems like IEEE 802.11, suffers from I/Q Imbalance (IQI), impacting performance. This document proposes a robust solution called I-Q Decoupled OFDM (DC-OFDM), where independent data sets generate real (I) and imaginary (Q) signals, mitigating IQI effects. Details include fundamentals of OFDM, DFT/IDFT expressions, and the impact of IQI on OFDM signals.

• OFDM Systems
• I/Q Imbalance
• DC-OFDM
• Communication Systems
• IEEE 802.11

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1. March 2016 doc.: IEEE 802.11-16/0319r2 I-Q Decoupled OFDM: A Solution to I/Q Imbalance Date: 2016-03-14 Authors: Name Affiliations Address Phone Email Shouxing Simon Qu BlackBerry, Ltd. 1001 Farrar Rd., Ottawa, ON, Canada 1-613-595-4205 squ@blackberry. com Submission Slide 1 Shouxing Simon Qu, BlackBerry, Ltd..

2. March 2016 doc.: IEEE 802.11-16/0319r2 Abstract OFDM has been adopted by various communications systems including IEEE 802.11. I-Q Imbalance (IQI) has adverse impact on OFDM performance, as pointed out in [1]-[2]. A new OFDM modulation scheme, called I-Q Decoupled OFDM (DC-OFDM), is proposed in this submission. In DC-OFDM, the real (I) and the imaginary (Q) time-domain signals are generated using independent input data sets. DC-OFDM is robust to I-Q Imbalance. Submission Slide 2 Shouxing Simon Qu, BlackBerry, Ltd.. ..

3. March 2016 doc.: IEEE 802.11-16/0319r2 OFDM Basics In regular OFDM, N subcarriers are independently modulated by N complex numbers. A set of N complex symbols, {??}, is transformed to a set of time- domain complex numbers, {??}, through IDFT, 1 ? ?=0 ? 1????? ?2??? IDFT: , (1) ??= ? ? 1????? ?2??? DFT: . (2) ??= ?=0 ? k & n: 0, 1, , N-1. ??: specifies the signal magnitude and phase of the k-th subcarrier at frequency ??= ? ?? Hz. Submission Slide 3 Shouxing Simon Qu, BlackBerry, Ltd.. ..

4. March 2016 doc.: IEEE 802.11-16/0319r2 General Expressions for DFT/IDFT with Frequency Offset 1 ? ?=0 ? 1????? ?2? ?+? ? IDFT: , (3) ?? ???? ?? = ? ? 1????? ?2?(?+?)? DFT: . (4) ?? ???{??} = ?=0 ? ? = 0 or 0.5: o ? = 0:without frequency offset,i.e. 1 (2) o ? = 0.5: with a frequency offset equal to half of subcarrier space. Submission Slide 4 Shouxing Simon Qu, BlackBerry, Ltd..

5. March 2016 doc.: IEEE 802.11-16/0319r2 PSD PSD k k 0 1 2 3 4 5 6 7 0 0 1 2 3 4 5 6 7 0 Subcarriers (b) N=8, = 0.5 Subcarriers (a) N=8, = 0 Fig. 1 o Sequences are cyclically periodic in discrete signal processing. Submission Slide 5 Shouxing Simon Qu, BlackBerry, Ltd..

6. March 2016 doc.: IEEE 802.11-16/0319r2 Impact of I-Q Imbalance on OFDM (1) Transmitted time-domain symbol: ??= ??+ ???. Due to IQI, received time-domain symbol: ??= ??+ ? ??, ??= (? + ?)??and ??= (? ?)??. . Thus, ??= ???+ ??? = conjugate of ??, is interference (in time-domain). ?? In frequency Domain, ?? ??? ?? = ???+ ??? ? 2? , :is interference to detecting ??. where, ?? ? 2? = ??? ?? Submission Slide 6 Shouxing Simon Qu, BlackBerry, Ltd..

7. March 2016 doc.: IEEE 802.11-16/0319r2 Impact of I-Q Imbalance on OFDM (2) ? ??= ??? ? 2? k-th tone. : Image leaking from (? ? 2?)-thtone to Image Leakage Ratio (ILR): ??? 20???10 ? ? (dB). Example 1: Assuming ??= 1.1??+ ?0.9??, then . ??= 1.0 + 0.1 ??+ ? 1.0 0.1 ??= 1.0 ??+ 0.1?? That is, ? = 1.0, ? = 0.1. ??? = 20 dB. Submission Slide 7 Shouxing Simon Qu, BlackBerry, Ltd..

8. March 2016 doc.: IEEE 802.11-16/0319r2 Impact of I-Q Imbalance on OFDM (3) ? ??= ??? ? 2? k-th tone. : Image leaking from (? ? 2?)-thtone to Example 2: Value of (? ? 2?) with N=8: 0 1 2 3 4 5 6 7 k 7 0 6 7 5 6 4 5 3 4 2 3 1 2 0 1 ? = 0.5 ? = 0 See Fig. 1: Tones of same color interfere each other Submission Slide 8 Shouxing Simon Qu, BlackBerry, Ltd..

9. March 2016 doc.: IEEE 802.11-16/0319r2 Impact of I-Q Imbalance on MU OFDM [1] RF I/Q Amplitude Imbalance: 1dB, Phase Imbalance: 5deg 10 Without Impairment With Impairment 5 Image Interference 0 -5 -10 PSD -15 -20 -25 -30 -35 -40 -10 -8 -6 -4 -2 0 2 4 6 8 10 MHz Fig. 2 [1] Rui Yang et al.: I/Q Imbalance Impact to TGax OFDMA Uplink Reception , IEEE 802.11-15/1314r1, Nov. 9, 2015. Submission Slide 9 Shouxing Simon Qu, BlackBerry, Ltd..

10. March 2016 doc.: IEEE 802.11-16/0319r2 OFDM Signal Robust To I-Q Imbalance Due to IQI, the interference to ??? is ??? ? 2? . Solution to IQI: intentionally set . (5) ?? ? 2?= ?? Then the interference becomes The received signal becomes ??? ? 2? =???. ??= (? +?)??. without interference. Eq.(5): The sequence of {??} is of Conjugate Symmetry in frequency domain. Submission Slide 10 Shouxing Simon Qu, BlackBerry, Ltd..

11. March 2016 doc.: IEEE 802.11-16/0319r2 Conjugate Symmetry in Frequency Domain Example: for N=8, For = 0.5: o ?7=?0 ,?6=?1 , ?4=?3 . ,?5=?2 o [ 1 3?,3 + 3?, 3 ?, 1 ?, 1 + ?, 3 + ?, 3 3?, 1 + 3?]. For = 0: o ?4= ?4 , ?6= ?2 , ?7= ?1 . , ?5= ?3 , ?0= ?0 o ?0 and ??/2 should be real. o [ 1,3 + 3?, 3 ?, 1 ?, 3, 1 + ?, 3 + ?,3 3?]. Submission Slide 11 Shouxing Simon Qu, BlackBerry, Ltd..

12. March 2016 doc.: IEEE 802.11-16/0319r2 Frequency Conjugate Symmetry for = 0.5 Fig. 3 Submission Slide 12 Shouxing Simon Qu, BlackBerry, Ltd..

13. March 2016 doc.: IEEE 802.11-16/0319r2 Frequency Conjugate Symmetry for = 0 Fig. 4 Submission Slide 13 Shouxing Simon Qu, BlackBerry, Ltd..

14. March 2016 Power Spectrum with Conjugate Symmetry doc.: IEEE 802.11-16/0319r2 Fig. 5 Submission Slide 14 Shouxing Simon Qu, BlackBerry, Ltd..

15. March 2016 doc.: IEEE 802.11-16/0319r2 I-Q Decoupled OFDM Signal (1) The OFDM signals with (frequency) conjugate symmetry are robust to IQI. Problem: with N subcarriers, it only carries information of N/2 complex numbers. Compared to regular OFDM, data rate is reduced by half. Submission Slide 15 Shouxing Simon Qu, BlackBerry, Ltd..

16. March 2016 doc.: IEEE 802.11-16/0319r2 I-Q Decoupled OFDM Signal (2) Property of Fourier Transform: A signal being conjugate symmetrical in frequency domain is a real signal in time domain. Solution: Generate two independent real OFDM signals, combined into a complex signal, carrying information of N complex numbers with N subcarriers. Submission Slide 16 Shouxing Simon Qu, BlackBerry, Ltd..

17. March 2016 doc.: IEEE 802.11-16/0319r2 I-Q Decoupled OFDM Signal (2) Fig. 6 B1 and B2 can be any box in Fig.3 and Fig. 4. Submission Slide 17 Shouxing Simon Qu, BlackBerry, Ltd..

18. March 2016 doc.: IEEE 802.11-16/0319r2 Generation of DC-OFDM Signal with Precoding Fig. 7 (( = 0.5) When B0 is bypassed, it becomes a regular OFDM generator. Submission Slide 18 Shouxing Simon Qu, BlackBerry, Ltd..

19. March 2016 doc.: IEEE 802.11-16/0319r2 DC-OFDM for MU Applications DC-OFDM can be used for single user or multi-user (MU) applications. For MU applications: For each pair of symmetric tones, The two tones of each symmetric pair are allocated to a same user; Two tones of each symmetric pair are modulated by a data symbol and its conjugate respectively. Submission Slide 19 Shouxing Simon Qu, BlackBerry, Ltd..

20. March 2016 doc.: IEEE 802.11-16/0319r2 Example: Four Users, N=8, = 0.5 Fig. 8 Submission Slide 20 Shouxing Simon Qu, BlackBerry, Ltd..

21. March 2016 doc.: IEEE 802.11-16/0319r2 Simulation Results: I-Q Imbalance Impact Fig. 9 Submission Slide 21 Shouxing Simon Qu, BlackBerry, Ltd..

22. March 2016 doc.: IEEE 802.11-16/0319r2 Conclusions IQI has adverse impact on regular OFDM systems. Real OFDM (time-domain) signal is robust to IQI. Real time-domain = Conjugate-symmetric in frequency domain. DC-OFDM signal: o A complex OFDM signal formed by two independently generated real time-domain OFDM signals. o Robust to IQI. o Same data rate as regular OFDM. o Providing frequency diversity gain. o SU & MU. Submission Slide 22 Shouxing Simon Qu, BlackBerry, Ltd.. .

23. March 2016 doc.: IEEE 802.11-16/0319r2 References [1] Rui Yang et al., I/Q Imbalance Impact to TGax OFDMA Uplink Reception , IEEE 802.11-15/1314r1, Nov. 9, 2015. [2] Marcus Windisch, and Gerhard Fettweis, On the impact of I/Q imbalance in multi-carrier systems for different channel scenarios , IEEE International Symposium on Circuits and Systems 2007 (ISCAS2007), New Orleans, LA, USA, May 27-30, 2007. Submission Slide 23 Shouxing (Simon) Qu, Blackberry, Ltd.

24. March 2016 doc.: IEEE 802.11-16/0319r2 Straw Poll 1) Do you agree that I-Q decoupled OFDM is more robust to I-Q imbalance than the regular OFDM ? 2) Would you consider adding I-Q decoupled OFDM, or a modified version of this proposal, in a future version of 802.11ax draft ? Submission Slide 24 Shouxing (Simon) Qu, Blackberry, Ltd.