. Intrinsically, the received signal model as depicted in Equation 1 in part 1
of this blog series is scaled up for MIMO systems with Nt
transmitting antennas and Nr
receiving antennas, including both TX and RX imperfections. The received kth Nr
x1 subcarrier carrier xm
) for the mth
OFDM symbol is given by Schenk . The system is assumed to be perfectly synchronized.
being the gain and phase imbalance for all RX independent branches. Similarly G1and G2 are defined in Shenk to mimic the IQ gain and phase imbalance on the TX branches .
Intuitively, in case of perfect transmitter matching on the IQ analog arms, G1 = I and G2 = O . This would usually be the case for current radios such as Radio420X, which demonstrates gain and phase imbalance compensation for better than 50dBc SSB rejection at the transmitter antenna port. Hence the kth subcarrier, xm (k), will be left under the influence of receiver IQ gain and phase imbalance. It has also being quantitatively demonstrated that the effect of receiver IQ imbalance is greater than the transmitter IQ imbalance in case of channel fading. This can be seen from assessing the effect of the term K2H* (-k) G1* associated with the subcarrier mirror image, sm (-k).
Several compensation methods have been proposed. Some are standard dependent [3-4] while others rely on blind parameter estimation [5-6]. In Shenk, the adaptive IQ gain and phase estimation approach uses a preamble based on Walsh-Hadamard sequences . Rabiei et al present a joint estimation and compensation scheme for MIMO-OFDM systems assuming quasi-static channel . They have developed a compensation scheme for SISO systems which they generalized to the MIMO case. The proposed scheme requires more training symbols with an increasing number of transmit-receive antennas, and the complexity of the method is high due to the required maximum likelihood (ML) estimation.
Unfortunately, pilot based techniques will be limited to certain communications system with a predefined training sequence. In addition, these are also not immune to radio and channel imperfections. The technique presented Windisch and Fettweis (2004) does not rely on any signal structure which makes it suitable for MIMO OFDM SDRs . The literature on IQ gain and phase imbalance compensation is abundant to the extent that several subjects were treated from different angles, which include even join IQ imbalance and phase noise compensation in fading channels.
For SDR beginners, we recommend an interesting and simple scheme found in a short article by S. W. Ellingson . The implementation of this method easily lends itself to Nutaq’s PicoSDR development unit.
- Windisch, Marcus, and Gerhard Fettweis. 2006 “Performance degradation due to I/Q imbalance in multi-carrier direct conversion receivers: A theoretical analysis.” Proc. IEEE International Conference on Communications (ICC’06) 1(257-262). doi: 10.1109/ICC.2006.254737
- Schenk, Tim. 2008. RF Imperfections in High-rate Wireless Systems: Impact and Digital Compensation. Dordrecht: Springer.
- Schuchert, A., R. Hasholzner, and P. Antoine. 2001. “A novel IQ imbalance compensation scheme for the reception of OFDM signals.” IEEE Transactions on Consumer Electronics 47:3(313–318). doi: 10.1109/30.964115.
- Tubbax, J., B. Come, L. Van der Perre, L. Deneire, S. Donnay, and M. Engels. 2003 “Compensation of IQ imbalance in OFDM systems.” Proc. IEEE International Conference on Communications (ICC’03) 5(3403–3407). doi: 10.1109/ICC.2003.1204086
- Rykaczewski, Piotr, Volker Blaschke, and Friedrich K. Jondral. 2003. “I/Q Imbalance Compensation for Software Defined Radio OFDM Based Direct Conversion Receivers.” Proc. 8th International OFDM Workshop (279-283). Hamburg.
- Windisch, Marcus, and Gerhard Fettweis. 2004.”Standard-independent I/Q imbalance compensation in OFDM direct-conversion receivers.” Proc. 9th International OFDM Workshop (57-61). Dresden.
- Rabiei, P., Won Namgoong, and N. Al-Dhahir. 2010. “Reduced-Complexity Joint Baseband Compensation of Phase Noise and I/Q Imbalance for MIMO-OFDM Systems,” IEEE Transactions on Wireless Communications 9:11(3450-3460). doi: 10.1109/TWC.2010.100110.091507
- Ellingson, S. W. 2003. “Correcting I-Q Imbalance in Direct Conversion Receivers.” Virginia Polytechnic Institute and State University. http://www.ece.vt.edu/swe/argus/iqbal.pdf