Radio-frequency (RF) circuits are utilized to up- and down-covert baseband signals between a transmission radio frequency and a baseband frequency. In realistic hardware circuits, this conversion processes introduce I/Q imbalances in terms of gain errors and phase errors, resulting in unwanted-image and desired-signal blending in decoded signals. Un-calibrated or free-designed RF circuits may perform up to 1dB gain error and 10 phase error that destroy correct signal decoding. Most of existing design approaches solves this problem by analog approaches that require circuit overdesign, large device area for reduce mismatch, and design experience. Even the most carefully design cannot prevent the imbalance from the non-ideal circuit implementation, manufacturing, board-level design, etc, resulting in remaining unsolved mismatch and degraded system performance.
Accordingly, this chapter describes an all-digital front-end calibration scheme, I/Q-mismatch calibration. This digitally-assisted signal calibration releases design efforts in the RF front-end analog circuit designs, especially in the systems with the OFDM modulation. This calibration is achieved by the digital-signal process techniques so that any remaining or imbalanced distortion during signal down conversion process can be computationally eliminated, improving the overall system performance and easing the system matching efforts. The role of this digitally RF calibration is introduced as shown in Fig. 3-1.
Digitally-Based Analog Circuit Calibration/Controlling
Digital Design
ADIQMC RF Calibration
DSTC Data Converter Controlling
HDC Clock Source Design
DCGPC Chip Implementation
ESCG External Component Elimination
Main Contributions (OFDM Baseband Processor)
System Level Architecture
Level
Circuit Level
Baseband Processor
(a)
RF Front-End Calibration
Dynamic
Sample-Timing Control
Modem Core
OFDM Baseband Processor
MAC/
Processor RF
DACADC
ADCADC
Clock Generator Embedded
Crystal
(b)
Fig. 3-1. The role of the digitally RF front-end calibration in the power and data proximity scheme
Orthogonal Frequency Division Multiplexing (OFDM) [28][29] is an effective and spectrally efficient signaling technique for wireless communications over frequency selective fading channels. Unfortunately, OFDM is sensitive to non-ideal front-end effect and non-perfect synchronization such as residual carrier frequency
offset (CFO), clock timing drift (CTD), symbol timing misalignment (STM), etc., leading to serious system performance degradation. It also demands severe front-end specifications, and results in an expensive front-end circuit in terms of design complexity and development period. There exist mature approaches in parameter estimation and compensation [30]. However, those algorithms become unstable or invalid when the non-ideal RF effect, I/Q mismatch (IQM), is involved. This problem is due to gain and phase mismatch between in-phase (I) and quadrature-phase (Q) paths in RF circuits. IQM is especially obvious as the transceiver in OFDM system uses the direct-conversion architecture because of design complexity and hardware cost [31][36].
To be more specifically, IQM occurs when the RF mixers in I and Q channels have different power gain, and the generated waveforms do not possess exact 90 degree phase difference. Usually, IQM effect is ignored by designers in system simulation level since the mismatch phenomenon does not appear until RF circuit is manufactured. In other words, IQM arises when the circuit size cannot be made exactly as the expected size in manufacturing process, and the behavior does not meet simulation conditions due to process, voltage, and temperature (PVT) variations.
As a result, the IQM correction capability plays an important role especially in high speed wireless communication since the error tolerance becomes much smaller as modulation order gets higher. Such systems, for example, can be found in [28][37]
with 64QAM and 256QAM. Likewise, the broadband RF circuit will inevitably suffer from more challenge in designing accurate I/Q balanced signal paths, and consequently emphasize the importance of IQM correction capability.
Among existing IQM correction techniques, some are proposed to combat IQM under Rayleigh fading channel with gain and phase errors within 0.414dB and 10 degree respectively [32]. This gain error tolerance 0.414dB is not large enough as suggested 1dB in [35], and the non-adaptive estimation accuracy is not adequate due to limited samples for calculation. On the other hand, the CFO effect will largely degrade IQM estimation, thus the algorithm has to be modified in accordance with joint IQM and CFO phenomenon [33]. Although both CFO and IQM are jointly considered, the tolerated CFO range under IQM effect is only 5% OFDM subcarrier frequency spacing, which is far from the general requirement 38.4% or ±25ppm at carrier frequency 2.4GHz [28]. In addition, some designs apply FIR filters for signal correction [34]. This uses the matrix computation and minimum cost function search, resulting in higher cost and computation complexity as the number of filter coefficient increases.
The IQM problems can be modeled as narrowband [40] or wideband [34][42]
scenarios depending on the concerned signal bandwidth. In the narrowband modeling, gain and phase errors are considered as a constant. With this assumption [40] presents a theoretical analysis on the mismatch problem. Also, adaptive compensation schemes are exploited in the literatures with post-FFT approach [39] and pre/post-FFT approach [43]. Considering joint IQM and DC offset problems, a data-aided calibration approach can be found in [41]. Under the narrowband assumption, the channel frequency response is considered as quasi-continuous in consecutive subcarriers, [32] estimates the gain and phase errors based on the smooth-channel property.
In wideband IQM problems, gain and phase errors vary with spectrum frequency, i.e. a non-constant (frequency selective) gain and phase errors in the concerned signal band. Therefore, [42] exploits IQM effects from different filter responses with a two-tone calibration technique. [34] takes IQM estimation in time domain in a NLS adaptive manner. The IQM calibration in a chip implementation can be found in [38].
Considering system performance, error tolerance, computation cost, and robustness to channel complexity, we propose an all digital hybrid-domain filterless adaptive compensation (HD-FAC) technique. It calculates the error function in frequency domain and adaptively updates the single coefficient for signal compensation in time domain without using any delayed-line filters. Moreover, HD-FAC is able to estimate and compensate IQM under Rayleigh fading channel and CFO effect with gain error 1dB and phase error 10 degree as suggested in [35]. Also, the Rayleigh fading channel has the statistics of RMS 50ns, and CFO tolerance is 38.4% subcarrier frequency spacing or ±25ppm at 2.4GHz carrier frequency, which satisfies the specification [28].