TGn Sync Calibration for Beamforming

1. TGn Sync Calibrationfor Beamforming • John S. Sadowsky • Intel Corporation5000 W. Chandler Blvd.Chandler, AZ USA 85226 • e-Mail: john.sadowsky@intel.com John S. Sadowsky, Intel

2. Overview The TGn Sync proposal includes optional BF (beamforming) transmission modes. This requires a calibration to equalize response differences between the Tx and Rx RF and analog chains of a given STA. This contribution does not provide an exhaustive treatment of calibration. Rather, we provide mathematical details for one important case; the case of an AP transmitting BF on the downlink to a low cost client. Our design criterion, for this example case, is to minimize complexity in the client. A future revision of the TGn Sync proposal will include the details of this calibration procedure, as well as other protocols to support bi-directional BF. John S. Sadowsky, Intel

3. Terminology • Correction • The correction is a complex coefficient applied to the transmit streams on a per antenna – per subcarrier basis. • The purpose of the correction is to equalize response difference between transmit and receive processing paths (up to an unknown constant across antennas). • Calibration • The process of calculating correction coefficients. John S. Sadowsky, Intel

4. Tx Corrections The correction matrix is a diagonal matrix of per antenna correction coefficients that is applied after beam-forming trans-formations and before IFFT processing. There is a different correction matrix for each subcarrier. We have suppressed subcarrier dependence in the notation. John S. Sadowsky, Intel

5. Frequency Domain Model Tx chain response matrix for device i: Rx chain response matrix for device i: Physical antenna-to-antenna channel for transmission from device i to device j: John S. Sadowsky, Intel

6. Mismatch ratio forantenna k of STA i Tx Calibration The purpose of calibration is to select the correction coefficients so that for each device we have Since these are diagonal matrices, we can also express this element-wise as The constant is constant across antennas (but may vary across subcarriers). It is not necessary to know as beam-forming is phase invariant. Definition: The composite channel is Under calibration John S. Sadowsky, Intel

7. Reciprocity of Composite Channel Reciprocity of physical channel: Reciprocity of composite channel, up to an unknown constant: by reciprocity of physical channel John S. Sadowsky, Intel

8. Calibration Uncorrected composite channel: Since A and B are diagonal matrices, we can work element-wise: Thus STA 1 mismatch ratio STA 2 mismatch ratio reciprocity X John S. Sadowsky, Intel

9. Calibration (2) Calibration of STA 2 uses both and . Select fixed k1. For k2 = 0, …, N-1 because k1 is fixed John S. Sadowsky, Intel

10. Two Types of STACorrection Capabilities • Basic BF-Rx only STA • Does not transmit BF • Does not apply any corrections • BF-Tx&Rx STA • STA can transmit and receive BF • Must have Tx correction capability John S. Sadowsky, Intel

11. Basic DL Only BF Solution • BF transmission • BF only in DL (AP → client) • Client is a BF-Rx only STA • Client Calibration Exchange • AP sends sounding PPDU to client on DL • May or may not transmitted with correction • Client responds with sounding packet (no correction) containing DL channel estimates from previous AP PPDU in data payload • AP has both UL and (uncorrected) DL channel estimates • AP calculates both AP and client correction coefficients • If not already calibrated, AP my also calculate its own correction coefficients as well John S. Sadowsky, Intel

12. Basic Rx Only Solution • Packet Exchange • Sounding packets from client (carrying RAC or RTS, and/or ACK) provide uncorrected composite UL channel • AP corrects UL channel estimate by applying client Tx correction coefficients • AP calculates SVD for corrected UL channel transpose • AP transmits SVD using AP correction coefficients • Key features of basic Rx solution • Minimal complexity at the client • Client requirements are only that the client transmit sounding packets and participate in the calibration protocol exchange including transmitting channel estimates in protocol packet data payload. • AP complexity • AP must apply Tx corrections to DL BF transmissions, and AP must store client correction coefficients for UL channel estimate correction John S. Sadowsky, Intel

13. Summary and Conclusion • Basic Rx-only BF • Tx correction capability is not mandatory • This eliminates complex multiplies form low cost clients • Mandatory requirements for basic STA • Ability to transmit sounding packets • Calibration exchange • Respond to inquiry by sending channel estimates • Additional Calibration Protocols • Support for bi-directional BF • Modification of Rx-only protocol is straight-forward John S. Sadowsky, Intel