Hybrid analog/digital multiple-input multiple-output architectures were recently proposed as an alternative for fully digital-precoding in millimeter wave wireless communication systems. This is motivated by the possible reduction in the number of RF chains and analog-to-digital converters. In these architectures, the analog processing network is usually based on variable phase shifters. In this paper, we propose hybrid architectures based on switching networks to reduce the complexity and the power consumption of the structures based on phase shifters. We define a power consumption model and use it to evaluate the energy efficiency of both structures. To estimate the complete MIMO channel, we propose an open-loop compressive channel estimation technique that is independent of the hardware used in the analog processing stage. We analyze the performance of the new estimation algorithm for hybrid architectures based on phase shifters and switches. Using the estimate, we develop two algorithms for the design of the hybrid combiner based on switches and analyze the achieved spectral efficiency. Finally, we study the tradeoffs between power consumption, hardware complexity, and spectral efficiency for hybrid architectures based on phase shifting networks and switching networks. Numerical results show that architectures based on switches obtain equal or better channel estimation performance to that obtained using phase shifters, while reducing hardware complexity and power consumption. For equal power consumption, all the hybrid architectures provide similar spectral efficiencies.

Hybrid MIMO Architectures for Millimeter Wave Communications: Phase Shifters or Switches?

Hybrid analog/digital MIMO architectures were recently proposed as an alternative for fully-digitalprecoding in millimeter wave (mmWave) wireless communication systems. This is motivated by the possible reduction in the number of RF chains and analog-to-digital converters. In these architectures, the analog processing network is usually based on variable phase shifters. In this paper, we propose hybrid architectures based on switching networks to reduce the complexity and the power consumption of the structures based on phase shifters. We define a power consumption model and use it to evaluate the energy efficiency of both structures. To estimate the complete MIMO channel, we propose an open loop compressive channel estimation technique which is independent of the hardware used in the analog processing stage. We analyze the performance of the new estimation algorithm for hybrid architectures based on phase shifters and switches. Using the estimated, we develop two algorithms for the design of the hybrid combiner based on switches and analyze the achieved spectral efficiency. Finally, we study the trade-offs between power consumption, hardware complexity, and spectral efficiency for hybrid architectures based on phase shifting networks and switching networks. Numerical results show that architectures based on switches obtain equal or better channel estimation performance to that obtained using phase shifters, while reducing hardware complexity and power consumption. For equal power consumption, all the hybrid architectures provide similar spectral efficiencies.

SARs are one of the most energy-efficient ADC architectures for medium resolution and low-to-medium speed. To improve the limited bandwidth of SAR ADCs, the time-interleaved (TI) structure is often used [1,2]. However, TI ADCs have several issues caused by mismatches between channels, such as offset, gain, and timing-skew errors. Unlike the other errors, timing-skew causes errors that increase with input signal frequency. Considering that the TI structure is typically employed to increase bandwidth, timing-skew can be a dominant error source of TI ADCs. Recent works [1,3] have demonstrated a background timing-skew calibration using a dedicated additional channel as a timing reference. In this work, we present a TI SAR ADC that enables background timing-skew calibration without a separate timing reference channel and enhances the conversion speed of each channel.

22.4 A 1GS/s 10b 18.9mW time-interleaved SAR ADC with background timing-skew calibration

A 12 bit 160 MS/s two-step pipelined SAR ADC was fabricated in a 40 nm CMOS low-leakage digital process. A background bit-weight calibration exploiting the comparator resolving time information and the employment of a sub-binary DAC in the first SAR stage are two key techniques in this work to attain high conversion throughput and power savings at the same time using a simple, low-gain ( $\sim$ 30 dB) residue amplifier. The overall architecture and the digital calibration also enable the downsizing of the first SAR stage to that of the kT/C limit, yielding a wideband input network delivering an over 80 dB spurious-free dynamic range (SFDR) while digitizing a 300 MHz input at 160 MS/s. The core ADC consumes 4.96 mW and occupies an area of 0.042 mm $^{2}$ ; the calibration circuits dissipate 0.1 mW (estimated). An 86.9 dB SFDR and a 66.7 dB signal-to-noise plus distortion ratio (SNDR) were measured with a 2 V $_{\rm pp}$ , 5 MHz sine-wave input at full speed. The ADC achieves a Walden figure-of-merit (FoM) of 20.7 fJ/conversion-step with a Nyquist input.

A 12 bit 160 MS/s Two-Step SAR ADC With Background Bit-Weight Calibration Using a Time-Domain Proximity Detector

This paper presents a mostly digital multiplying delay-locked loop (MDLL) architecture that leverages a new time-to-digital converter (TDC) and a correlated double-sampling technique to achieve subpicosecond jitter performance. The key benefit of the proposed structure is that it provides a highly digital technique to reduce deterministic jitter in the MDLL output with low sensitivity to mismatch and offset in the associated tuning circuits. The TDC structure, which is based on a gated ring oscillator (GRO), is expected to benefit other PLL/DLL applications as well due to the fact that it scrambles and first-order noise shapes its associated quantization noise. Measured results are presented of a custom MDLL prototype that multiplies a 50 MHz reference frequency to 1.6 GHz with 928 fs rms jitter performance. The prototype consists of two 0.13 μm integrated circuits, which have a combined active area of 0.06 mm 2 and a combined core power of 5.1 mW, in addition to an FPGA board, a discrete DAC, and a simple RC filter.

A Highly Digital MDLL-Based Clock Multiplier That Leverages a Self-Scrambling Time-to-Digital Converter to Achieve Subpicosecond Jitter Performance

A compact decision-error-tolerant 2b/cycle SAR ADC architecture is presented. Two DACs with different designated functions, SIG-DAC and REF-DAC, are implemented to make the structure compact and to eliminate the sampling skew issue. Use of a nonbinary decision scheme with decision redundancies not only increases the ADC speed with a relaxed DAC settling requirement but also makes the performance robust to reference fluctuations and comparator offset variations. The proposed dynamic register and direct DAC control scheme enhance the conversion speed by minimizing logic delay in the SAR decision loop. The proposed comparator-error detection with digital error correction scheme enhances high-speed ADC performance. A prototype 7b ADC fabricated in a 45 nm CMOS process operates at a sampling rate of 1 GS/s under a 1.25 V supply while achieving a peak SNDR of 41.6 dB and maintaining an ENOB higher than 6 up to 1.3 GHz signal frequency. The FoM under a 1.25 V supply is an 80 fJ/conversion-step with a power consumption of 7.2 mW.

A Decision-Error-Tolerant 45 nm CMOS 7b 1 GS/s Nonbinary 2b/Cycle SAR ADC

This paper presents an asynchronous SAR-assisted time-interleaved SAR (SATI-SAR) ADC as a suitable architecture in a low-supply-voltage condition. Settling-While-Conversion enabled by the Assist-ADC relaxes the DAC settling time requirement and makes it possible to insert a minimized capacitor shuffling logic with no speed penalty. A proposed gain-boosting dynamic pre-amplifier enhances the noise performance of the comparator and a self time-reference generation function is embedded in the pre-amplifier for a speed-enhanced asynchronous decision. A proposed dual-mode clock generator generates a low-jitter fixed-width sampling pulse for high-frequency operation while it generates a low-power-but-low-quality clock for low-frequency operation. With the dual-mode clock generator enabled, a prototype 65 nm CMOS 0.6 V 12 b 10 MS/s ADC achieves an ENOB of 10.4 at a Nyquist-rate input, and the peaks of DNL and INL are measured to be 0.24 LSB and 0.45 LSB, respectively. The FoM is 6.2 fJ/conversion-step with a power consumption of $83~\mu \text {W}$ . The ADC operates under the lowest supply voltage of 0.6 V among comparable designs with ENOBs over 10 and conversion rates over 1 MS/s.

A 0.6 V 12 b 10 MS/s Low-Noise Asynchronous SAR-Assisted Time-Interleaved SAR (SATI-SAR) ADC

With the growing interest in time-interleaved (TI) structures, the conversion rates of ADCs have greatly improved, which has inevitably increased power consumption. Despite the advantages of TI structures, power consumption is increased due to the stricter matching requirements between channels; in some cases, >50% of total power is for calibration purposes [1]. Thus, to realize high-speed and high-resolution ADCs with TI structures, it is important to alleviate the calibration burden by choosing a suitable number of power-efficient high-speed single channels. Previously reported CDAC-based 2b/cycle structures [2-5] made contributions in realizing high-speed single-channel ADCs [2-4] with high resolution [5] by using additional capacitive DACs and modified switching logic. The power overhead and the complexity of the additional logic and DACs for 2b/cycle implementations have been of trivial concern for low resolution ADCs. However, as resolution increases, the complexity of such circuits becomes considerable, with power taking up a big share of the total. In this paper, a multi-step hardware-retirement (MSHR) technique, which disables low-accuracy hardware blocks of scaled sizes with the requirement relaxations from redundancies in an advancement to the reconfiguration scheme in [5], is reported to alleviate the overhead of additional logic and DACs for ADCs, requiring high resolutions. A low-power 2.6b/cycle-based SAR ADC architecture is presented as a proof of concept.

26.7 A 2.6b/cycle-architecture-based 10b 1 JGS/s 15.4mW 4×-time-interleaved SAR ADC with a multistep hardware-retirement technique

By taking advantage of the merits of the low power consumption and hardware simplicity of SAR ADCs, 2b/cycle conversion structures in SAR ADCs have been actively studied in recent years for enhanced conversion rates and excellent FoM [1-3]. However, many error sources in the 2b/cycle SAR ADCs, such as mismatches between DACs and comparators, and the signal-dependent errors from comparators, namely kickback noise and offset, make it difficult to achieve high resolution. To date, pure 2b/cycle structures operating above hundreds of MS/s have shown a somewhat limited resolution with an ENOB lower than 7 at Nyquist rates [1,2]. As a derivation of the structure, a sub-ADC could be implemented using the 2b/cycle SAR ADC structure for high resolution as in [4], at the cost of increased circuit complexity and static current flow. In this work, we present a resolution-enhancing design technique for 2b/cycle SAR ADCs with negligible hardware overhead, while relieving the requirements for the aforementioned errors: Reconfiguration from a 2b/cycle structure to a normal 1b/cycle SAR ADC with error-correction capability achieves an 8.6 ENOB from a 9b ADC.

An 8.6 ENOB 900MS/s time-interleaved 2b/cycle SAR ADC with a 1b/cycle reconfiguration for resolution enhancement

A 45nm CMOS 7b nonbinary 2b/cycle SAR ADC that operates up to 1GS/s with a 1.25V supply is presented. Use of a nonbinary decision scheme for decision error correction in a 2b/cycle structure not only increases the ADC speed with a relaxed DAC settling requirement but also makes the performance robust to reference fluctuation and signal-dependent comparator offset variation. Proposed dynamic registers and a register-to-DAC direct control scheme enhance the conversion speed by minimizing logic delay in the decision loop. At a sampling rate of 1 GS/s, the chip achieves a peak SNDR of 41.6dB and maintains ENOB higher than 6b up to 1.3GHz signal frequency. The FoM is 80fJ/ conversion-step at 1GS/s with a power consumption of 7.2mW.

Hyeok-Ki Hong

Papers

A Decision-Error-Tolerant 45 nm CMOS 7b 1 GS/s Nonbinary 2b/Cycle SAR ADC

A 0.6 V 12 b 10 MS/s Low-Noise Asynchronous SAR-Assisted Time-Interleaved SAR (SATI-SAR) ADC

26.7 A 2.6b/cycle-architecture-based 10b 1 JGS/s 15.4mW 4×-time-interleaved SAR ADC with a multistep hardware-retirement technique

An 8.6 ENOB 900MS/s time-interleaved 2b/cycle SAR ADC with a 1b/cycle reconfiguration for resolution enhancement

A 7b 1GS/s 7.2mW nonbinary 2b/cycle SAR ADC with register-to-DAC direct control