To evaluate the proposed wideband IQM calibration capability, the multi-band OFDM ultra-wideband (MB-OFDM) [2] is selected as the simulation platform, in which signals are modulated as QPSK in a 528MHz bandwidth with maximum data rate 480Mbps. Each OFDM symbol is formed by 128 subcarriers, and 112 out of them ( k={−56~56|k∈R,k≠0} ) are information subcarriers, including 12 pilot tones (k={−55,−45,...,45,55}), which are then used for IQM estimation. In the outer receiver, a Viterbi decoder is provided for error correction.
The 1dB gain error and 10 degree phase error are applied to the system as the simulated IQM range. The Hcm,k and Hdf,k reflect if the IQM is frequency independent or frequency selective. In a frequency-independent IQM, we have the responses
The table lists the operators and necessary value storages for the proposed HD-FAC and its comparison
H
cm,k=Hdf,k=1 for all index k. When a frequency-selective IQM is considered, we set the filter response to be [34]]}
The amplitude and phase responses of filters HI and HQ are shown in Fig. 3-16.
The pilot tones in each OFDM symbols are used for IQM estimation, and the estimation results are refined adaptively when an OFDM symbol comes. Since there are only limited subcarrier indices representing the pilot tones, only the pilot indices perform exact IQM estimations when a noiseless channel is assumed. If the IQM is constant over the whole concerned frequency range, the estimation results from pilot indices are duplicated to every subcarrier indices. When IQM is frequency selective, however, an interpolation becomes necessary to provide SGs and IGs in every spectrum index. Fig. 3-17 shows the SG and IG responses in a frequency-selective manner, in which the SG and IG values are estimated exactly in the pilot indices, say -35 and -25. The rest SG and MG between two pilot tones are calculated by 1st-order (linear) or 2nd-order interpolation. The resulting IRR is illustrated in Fig. 3-18, which shows that the pilot indices have infinite IRR values representing a perfect estimation.
It is also found that the 2nd-order interpolation promises a reasonable IRR level (min.
45dB) for signal compensation [42]. In a noiseless channel the signal constellation before and after compensation are shown in Fig. 3-19. The calibrated signal constellation in Fig. 3-19(b) has an average IRR 47.9dB, which presents a matching result by calculating from (3-38) directly. Fig. 3-20 shows the signal constellation before and after calibration in a SNR 20dB condition.
Finally, we show the overall system performance in terms of packet error rate (PER) in frequency-independent and frequency-selective conditions. In a frequency-independent IQM scenario, it is found that the PER curves with adaptive calibrations almost merge with the zero-IQM AWGN curve when 1dB gain error and 10o phase error are simulated. In a frequency-selective IQM scenario, it is found the uncompensated signals perform diverged PER even when the gain and phase errors are zeros. By the proposed adaptive calibration, the PER curves approach the AWGN zero-IQM curve with SNR loss less than 0.4dB, which also performs better by SNR 2.5dB than the one with non-adaptive behavior.
-64 -48 -32 -16 0 16 32 48 64
subcarrier index k abs(H I)
Gain response of filter HI
-64 -48 -32 -16 0 16 32 48 64
subcarrier index k phase(H I)
Phase response of filter HI
(a)
subcarrier index k abs(H Q)
Gain response of filter HQ
-64 -48 -32 -16 0 16 32 48 64
subcarrier index k abs(H Q)
Phase response of filter HQ
(b)
Fig. 3-16. The frequency-selective IQM modeling with transfer function of (a) filter HI (b) filter HQ
-64 -48 -32 -16 0 16 32 48 64 0
0.5 1
subcarrier index k abs(α k)
The gain response of SG and IG
ideal 1st-order 2nd-order
-64 -48 -32 -16 0 16 32 48 64
0 0.5 1
subcarrier index k abs(β k)
ideal 1st-order 2nd-order
Fig. 3-17. The ideal SG and IG responses with the estimations in 1st-order and 2nd-order interpolations.
-64 -48 -32 -16 0 16 32 48 64
30 40 50 60 70 80 90
Subcarrier Index (k)
IRR (dB)
IRR under variant order interpolation 1st-order interpolation 2nd-order interpolation
Fig. 3-18. The image rejection ratio (IRR) after compensation in a frequency selective IQM condition.
-35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 0.9
0.95 1 1.05 1.1
ideal 1st-order 2nd-order
(a)
(b)
Fig. 3-19. The signal constellation under the frequency-selective IQM in 1dB gain error and 10o phase error (a) without and (b) with calibration.
(a)
(b)
Fig. 3-20. The signal constellation under the frequency-selective IQM in 1dB gain error and 10o phase error (a) without and (b) with calibration in a SNR 20dB AWGN channel.
4 5 6 7 8 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 Frequency Independent IQM
SNR
PER
AWGN 0/0 Adaptive 1/10 Adaptive 0/0 Non-Adaptive 1/10 Non-Adaptive 1/10 Non Comp
Fig. 3-21. The packet error rate in a frequency-independent IQM condition.
4 5 6 7 8 9 10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 Frequency-Selective IQM
SNR
PER
AW GN 0/0 Adaptive 1/10 Adaptive 0/0 Non-Adaptive 1/10 Non-Adaptive 0/0 Non Comp 1/10 Non Comp
Fig. 3-22. The packet error rate in a frequency-selective IQM condition.
3-6 Summary
Adaptive IQM calibration approaches are presented in this chapter. The calibration is achieved in either frequency-independent or frequency-dependent scenario. The adaptive behavior is only achieved when an error function is defined.
This work provides both the error functions for the frequency-independent and frequency-dependent schemes. All of the calibration processes are done in an all-digital manner so that the signals are compensated by signal process techniques.
The frequency-independent calibration is realized by the proposed hybrid-domain filterless adaptive compensation scheme (HD-FAC). With an adaptive step size μ = 0.5, the overall performance loss under different channel conditions is simulated to be less than 0.3dB in AWGN channel and 0.5dB in Rayleigh fading channel, respectively, in the 1dB gain-error and 10o phase-error scenario.
The frequency-dependent calibration is achieved by the pilot-based IQM calibration. This approach achieves an average image rejection ratio 47.9dB in a frequency-selective mismatch condition with gain error 1dB and phase error 10o. The overall system performance at packet error rate=8% has SNR loss less then 0.4dB, and requires a reduced 2.5dB SNR to reach this performance level compared to a non-adaptive calibration approach.