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TGn Sync Calibration for Beamforming. John S. Sadowsky Intel Corporation 5000 W. Chandler Blvd. Chandler, AZ USA 85226 e-Mail: Overview.

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tgn sync calibration for beamforming
TGn Sync Calibrationfor Beamforming
  • John S. Sadowsky
  • Intel Corporation5000 W. Chandler Blvd.Chandler, AZ USA 85226
  • e-Mail:

John S. Sadowsky, Intel


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

  • 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

tx corrections
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

frequency domain model
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

tx calibration

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

reciprocity of composite channel
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


Uncorrected composite channel:

Since A and B are diagonal matrices, we can work element-wise:



mismatch ratio


mismatch ratio



John S. Sadowsky, Intel

calibration 2
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

two types of sta correction capabilities
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

basic dl only bf solution
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

basic rx only solution
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

summary and conclusion
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