Channel measurements 111 早 一 点 Figure 5.4 The measurement setting for measuring the phase noise The term()in (5.4)represents the instantaneous normalized frequency deviation from the carrier frequencyf which is computed as 1,d =2m不。d (5.5) mn thar the of the phaeThe of c2m0=2w-2m2amr24an）-2oa+oa识 1 -2 (5.6) and denoting an dmer rein tothe tora number of am of p ase no el so same fixed atremuaror ThathRx eachquipp with individual clock operate in the way as in real eviation,1.e.y m1 is computed an iustrated in Figure 5.5.In this figure,both r ed onar o th and th of0 for the lan variance of the phase noise isidentical with that obrained froma whit 5.5.3 Mitigation of the impact on the high-resolution parameter estimation A method proposed in Taparugssanagorn et al.(2007d)for mitigating the impact of phase noise on the parameter ultiple secut napshots of r ement data as the observ on of the function is to average over multiple channel observations,such that the impact of the phase noise can be compromised cvcles of data.similan 8 and 5.9 respectively.It can be observed nois thm is derved t sed n the sinasod icity,th dified the assumption t r than the is referred to as the inverse of delay spread of the channe TheTDM channel bandwidth.Here I sounChannel measurements 111 Figure 5.4 The measurement setting for measuring the phase noise The term y(t) in (5.4) represents the instantaneous normalized frequency deviation from the carrier frequency fc, which is computed as y(t) = 1 2πfc · dφ(t) dt (5.5) with φ(t) denotes the instantaneous phase variation. Assuming that the sampling rate of the phase 1 T . The samples of the Allan variance at τ = mT can be estimated as ˆσ 2 y (mT ) = 1 2(N − 2m)(2πfcmT ) 2 N X−2m i=1 (φ(ti+2m) − 2φ(ti+m) + φ(ti))2 , (5.6) with m = 1, . . . , N−1 2 and N denoting an odd number referring to the total number of samples of the phase. An example of measuring the phase noise is illustrated as follows. Fig. 5.6 depicts the measurement setting used to measure the phase noise of a single-input single-output channel sounder. An RF cable connects the Tx and the Rx with a 50 dB fixed attenuator. The Tx and the Rx each equipped with individual clock operate in the same way as in real field measurements. The Allan deviation, i.e. σˆy(mT ), is computed and illustrated in Figure 5.5. In this figure, both the sample Allan variance and their asymptotic characteristics computed from the measured phase noise sequence are depicted. Furthermore the curves computed based on proposed models are also illustrated. It can be observed that an ARMA model with model parameters computed based on the sample Allan variance can be used to describe the behavior of the Allan variance. Furthermore, the short term phase noise component predominates within the range of τ ∈ [0, 200µs]; for τ > 200µs, the Allan variance of the phase noise is identical with that obtained from a white phase noise, as suggested in Characterization of frequency and phase noise (1986); for τ > 1s, the phase noise can be described using random walk models. 5.5.3 Mitigation of the impact on the high-resolution parameter estimation A method proposed in Taparugssanagorn et al. (2007d) for mitigating the impact of phase noise on the parameter estimation performance is to consider multiple consecutive snapshots of measurement data as the observation of the same channel. This method is called “sliding window”. For the considered TDM-based sounding system, this sliding window solution is extended to the spatial domain, i.e. by considering more antennas. In general, the sliding window function is to average over multiple channel observations, such that the impact of the phase noise can be compromised to certain degree. Fig. 5.7 (a) and (b) depict respectively the comparison of the estimation results obtained by using the SAGE algorithm with and without using the sliding window solution over 20 cycles of data. Similarly results obtained with 8 × 8 and 4 × 4 MIMO channel matrices are also illustrated in Figure 5.8 and 5.9 respectively. It can be observed that by using the sliding window function, it is possible to reduce the probability of generation of artifact estimates. Another method introduced in Taparugssanagorn et al. (2007b) is to modify the specular-path SAGE algorithm Fleury et al. (1999) to include a whitening function based on the known covariance matrix of the phase noise. The modified SAGE algorithm is derived based on the signal model introduced in Section 3.3. For simplicity, the bidirection-delay-Doppler frequency generic specular path model is modified to a narrowband channel model based on the assumption that the signal bandwidth is much smaller than the channel bandwidth. Here, the channel bandwidth is referred to as the inverse of delay spread of the channel. The TDM sounding scheme is considered