In an aspect, when a device (e.g., the transmitter 502, the receiver 504) includes multiple antennas, it may be able to determine or otherwise estimate its own GDs. For example, assume that the device includes first and second antennas. The device then can use the first antenna to transmit a signal and use the second antenna to receive the same signal. The device then can measure the transmit time tt and the receive time tr. Then the total GD through both transmit and receive chains becomes (tr?tt?ts) where ts accounts for the separation between the first and second antennas. If the separation is negligible, then the total GD can be reduced to (tr?tt).
Note the total delay (tr?tt) accounts for sum of the transmission and reception GDs of the device. When translated to the transmitter 502: (tr?tt)=(t1′?t1)+(t4?t4′)??(5) and when translated to the receiver 504: (tr?tt)=(t2?t2′)+(t3′?t3).??(6)
For convenience, the sum of the transmission and reception GDs at the transmitter 502 (represented in equation (5)) will be referred to as the “transmitter total group delay”, and the sum of the transmission and reception GDs at the receiver 504 (represented in equation (6)) will be referred to as the “receiver total group delay”. In short, the transmitter 502 can determine the transmitter total GD=(t1′?t1)+(t4?t4′), and the receiver 504 can determine the receiver total GD=(t2?t2′)+(t3′?t3). It is then seen that the Σ(delays) may be expressed as: Σ(delays)=transmitter total GD+receiver total GD ??(7).