Backpropagation Based Background Compensation of TI-DAC Errors in High-Speed Transmitters

Digital Background Compensation of Analog Impairments in Jointly Frequency-Time Interleaved DACs

“…Among the most important TI-DAC impairments we can mention [10]: a) Bandwidth limitations, and mismatches in the frequency responses of sub-DACs. Typically, sub-DACs should present an ideal flat LPF response with a BW equal to or higher than the one needed to synthesize the transmitted signal.…”

“…be the gain of the l-th sub-DAC of the TI-DAC. It has been found that the TI-DAC with N sub-DACs can be modeled as a periodically time-variant channel with period N (e.g., see [10]). Neglecting the offset errors of sub-DACs, the continuous-time signal at the output of the TI-DAC results [10]…”

“…where m ∈ {0, ..., M − 1}, q ∈ {0, 1}, mod(.) N denotes the modulo N operation while T s = 1/f s is the sampling period of the JFTI-DAC (see [10] for more details). Notice that expressing the output of every TI-DAC as a function of the input samples s (m,q) [k] at sampling rate fs 2M , requires a set of N different impulse responses (i.e., f (m,q) p (t) with p = 0, 1, .., N −1).…”

“…Background compensation of FI [8], [9] and TI [10] DACs with M and N SBs and sub-channels respectively, were proposed. In this work, we extend the technique of [10], based on a digital adaptive pre-filtering with a periodic time-varying impulse response to compensate for the impairments in the proposed JFTI-DAC architecture. To this aim, we use a digital adaptive pre-filter with a P-periodic time-varying impulse response denoted as PTV Equalizer (PTVE), that is…”

“…voltage and temperature variations and fabrication deviations, without interrupting the communication. Previous works [8]- [10] address similar problems in FI and TI architectures, but individually. To the best of our knowledge, this is the first work dealing with all the impairments simultaneously.…”