Sigma-delta Research Articles

Efficient Sigma-Delta Sensor Array Beamforming.

Nowadays, sensors with built-in sigma-delta modulators (ΣΔMs) are widely used in consumer, industrial, automotive, and medical applications, as they have become a cost-effective and convenient way to deliver data to digital processors. This is the case for micro-electro-mechanical system (MEMS), digital microphones that convert analog audio to a pulse-density modulated (PDM) bitstream. However, as the ΣΔMs output a PDM signal, sensors require either built-in or external high-order decimation filters to demodulate the PDM signal to a baseband multi-bit pulse-code modulated (PCM) signal. Because of this extra circuit requirement, the implementation of sensor array algorithms, such as beamforming in embedded systems (where the processing resources are critical) or in very large-scale integration (VLSI) circuits (where the power and area are crucial) becomes especially expensive as a large number of parallel decimation filters are required. This article proposes a novel architecture for beamforming algorithm implementation that fuses delay and decimation operations based on maximally flat (MAXFLAT) filters to make array processing more affordable. As proof of concept, we present an implementation example of a delay-and-sum (DAS) beamformer at given spatial and frequency requirements using this novel approach. Under these specifications, the proposed architecture requires 52% lower storage resources and 19% lower computational resources than the most efficient state-of-the-art architecture.

PDM-OFDM 1-bit DSM 1024QAM/4096QAM signals at W-band transmission over 4.6-km wireless distance.

In this Letter, we propose the application of delta-sigma modulation (DSM) higher-order quadrature amplitude modulation (QAM) technology in long-distance transmission of W-band wireless communication, and demonstrate, for the first time to the best of our knowledge, the wireless transmission of millimeter wave signals in the W-band based on 1-bit DSM quantization using polarization-division-multiplexed orthogonal frequency division multiplexing (PDM-OFDM) 1024QAM/4096QAM for 4.6 km. We successfully achieved a bit error rate (BER) of 40-Gbit/s PDM-OFDM 1024QAM and 48-Gbit/s PDM-OFDM 4096QAM after 4.6-km wireless transmission, both lower than the soft decision forward error correction (SD-FEC) of 4.2 × 10-2. To the best of our knowledge, this is the first time that up to 4096QAM signals have been quantized and transmitted based on 1-bit DSM in a 4.6-km-long distance W-band millimeter wave system.

A 13-Level SC DAC Achieving High Linearity With a Simple DEM for Wideband CT DSMs

Wideband continuous-time (CT) Delta-Sigma modulators (DSMs) generally demand multi-level digital-to-analog converters (DACs), which require a linearization technique to overcome the problem of component mismatches. Dynamic element matching (DEM) is a popular DAC linearization approach but can be challenging to implement in a wideband DSM, particularly when there are many DAC elements. In this manuscript, we introduce a 13-level switched-capacitor (SC) DAC achieving high linearity with a simple DEM that rotates three unit elements only and does not incur excess loop delay. In a traditional CT DSM, a DAC of the SC type increases the amplifier settling requirements and damages the alias rejection. Earlier works have shown that these problems can be solved if the CT DSM adopts a passive RC frontend. A 10-MHz bandwidth CT DSM is designed in the 65-nm CMOS technology to validate the proposed DAC. Simulations show that the DAC enables a spurious-free dynamic range greater than 87.7 dB and a signal-to-noise pulse distortion ratio greater than 80.5 dB under a 1% capacitor mismatch, a 2% reference voltage error, and process variations.

Scalable Resource Optimized LUT-Based All-Digital Transmitter

In this paper, we present a low-resource look-up table (LUT) based solution for all-digital transmitters (ADTs) that addresses both the wide bandwidth and high carrier frequency flexibility. Traditional ADTs use real-time delta-sigma modulation (DSM) to convert a multiple-bit signal into a single-bit one, enabling the use of fast and inexpensive one-bit digital-to-analog converters (DACs) in the transmission chain. However, real-time DSM requires significant computational power to provide wide bandwidths and high carrier frequency agility. Our LUT-based solution achieves carrier frequency agility from 0.1 GHz to 7.62 GHz and delivers wide bandwidths of up to 150 MHz. We also introduce a new technique called “Half LUT Implementation” that allows us to halve the size of the LUT without sacrificing performance. The focus on simplifying and reducing resources in the transmitter is intended to reduce energy consumption and enable ADTs to be used in massive multiple-input/multiple-output (Massive-MIMO) applications.

Frequency-Agile Real-Time All-Digital Transmitter With 1 GHz of Bandwidth

This paper presents an all-digital transmitter implemented in a field programmable gate array (FPGA) that surpasses the state of art in terms of carrier frequency agility as well as in bandwidth using a single multi-gigabit transmitter. These figures of merit were achieved through the optimization of the delta-sigma modulator architecture as well as by the utilization of higher-order filters in such modulator. Results show an error vector magnitude (EVM) of around 4% for carrier frequencies in the 2 to 9 GHz range and under 8% in the 1 to 2 GHz and 9 to 12 GHz range using a 1 GHz bandwidth, 16-QAM signal, which would comply with EVM standards under the 5G protocol.

Computationally efficient low-power sigma delta modulation-based image processing algorithm

Digital Image Processing has dominated Digital Signal Processing at the cost of more memory, resources, and high computational power. In image processing, filtering transformations and other operations need complex multiplications, and the multiplier is one of the most resources consuming elements. Recently, mitigating the multiplier complexity in the digital signal processing (DSP) algorithms sigma-delta modulation based general purpose and adaptive DSP algorithms are developed in MATLAB and compared with its counterpart multi-bit algorithms for functionality and area-performance-power in FPGA. The contemporary multiplier algorithms are also optimized to overcome the multiplier complexity challenge as computation becomes simple and fast. This paper extends the reported work by investigating the sigma-delta modulation approaches for developing a computationally efficient low-power image processing algorithm. The proposed model is designed, developed, and simulated in MATLAB. The simulation results are analyzed using SNR, MSE, and Peak SNR. The simulation results show that the proposed system can better mitigate the noise effect, making it robust for noisy environment.

Flexible mm-Wave Sigma-Delta-Over-Fiber MIMO Link

Millimeter-wave and multiple-input-multiple-output (MIMO) technologies combine broad bandwidth with spatial diversity to offer a greater data rate. This paper investigates a flexible millimeter-wave sigma-delta-over-fiber based transmitter solution with digital beamforming MISO and MIMO functionality. Those functions are controlled by a central unit connecting a remote radio head with a standardized QSFP28 fiber link. The central unit generates binary encoded intermediate frequency signals using bandpass sigma-delta modulation. The QSFP28 based fiber link transmits the intermediate frequency bitstreams to the remote radio head. The remote radio head consists of a QSFP28 module, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$90^{\circ }$</tex-math></inline-formula> hybrids, and upconverters. The remote radio head feeds four parallel, independent, coherent, and central-unit controlled 28 GHz signals to a linear array transmitting antenna. The transmitter performance is experimentally verified, demonstrating up to 800 Msym/s at an EVM/NMSE of 6.7%/-23.5 dB when tested with a 64 quadrature amplitude modulation (64-QAM) modulation scheme. Digital over-the-air beamforming MISO functionality is demonstrated up to 700 Msym/s across 1 m wireless distance. MIMO communication capabilities is demonstrated by over-the-air transmission of two independent 500 Msym/s to two spatially separated receivers. The results show that the proposed link can be used for realization of scalable, low-cost and flexible transmitter solution for emerging distributed antenna systems.

Delay Error Shaping in ΔΣ Modulators Using Time-Interleaved High Resolution Quantizers

As wideband Delta-Sigma-Modulators (DSMs) are restricted in oversampling ratio (OSR), and low OSR reduces the benefit of higher order loop filters, the increase of the internal resolution is an obvious way to achieve high signal-to-quantization-noise ratio (SQNR). State-of-the-art implementations restrict the internal resolution to mostly 4-6 bits, as efficient QTZs with higher resolution add excessive delay into the DSM. Multi-step or time-interleaved-quantizer (TI-QTZs) are an effective way to enhance resolution at high sampling rate, but the resulting latency in excess of one clock cycle usually prohibits their usage in DSMs. This paper proposes a new architecture to employ high resolution multi-step QTZs, such as TI SAR or pipeline ADCs. In the proposed architecture, an excess loop delay (ELD) of several clock cycles in the LSBs is purposefully allowed. While the MSBs are conventionally ELD-compensated, the LSBs are not. The resulting error is corrected in the digital domain. It is shown that matching requirements are relaxed by first-order shaping. The idea is also applicable to a Leslie-Singh and noise-coupling architecture, which are compared to the proposed architecture in an extensive system-level analysis and simulation. Depending on the target application, an advantageous design recommendation can be given based on the presented results depending on OSR, internal bitwidth and expected analog-digital matching.

Efficacious Zero Sequence Voltage Elimination in Space Vector Modulation by Sigma Delta Modulation

The growing popularity of electric motor driven systems emphasize the need for proper motor maintenance and necessitates zero sequence voltage (ZSV) elimination in electrical machines and drives. A spread spectrum modulation scheme for eliminating zero sequence voltage, utilizing space vector pulse density modulation (SVPDM) approach is proposed in this article. In the presented five-level inverter scheme, when vectors that do not contribute zero sequence voltage are considered, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$30^{0}$</tex-math></inline-formula> tilted three-level space vector diagram with inner and outer layer is formed. Reference vector residing in outer layer is mapped to inner layer and is vector quantized in a space vector quantizer to generate inner layer switching vectors. Outer layer switching vectors are then realized by the process of reverse mapping. The article investigates two-level SVPDM scheme and ZSV eliminated two-level SVPDM scheme, to prove that effectiveness of ZSV elimination can be determined from the shape of demodulated waveform. Better the ZSV elimination, better will be the resemblance of demodulated waveform to sinusoidal signal. The scheme is experimentally validated with 2.2 kW five-level dual inverter fed induction motor drive and is compared with space vector pulse width modulation (SVPWM) scheme. Results of comparison confirms the effectiveness of proposed scheme.

4096-QAM OFDM THz-Over-Fiber MIMO Transmission Using Delta-Sigma Modulation

A terahertz (THz)-over-fiber multiple-input multiple-output (MIMO) transmission of 4096-ary quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) supported by 46-GBaud quadrature phase shift keying (QPSK) signal at 320 GHz is experimentally demonstrated in this letter. By employing the polarization division multiplexing (PDM) technique and 1-bit delta-sigma modulation (DSM) quantization, we successfully implement 4.6-GHz 4096-QAM OFDM signal transmission over 20 km of standard single-mode fiber (SSMF) and a 3-m MIMO wireless link, and satisfy the soft-decision forward error correction (SD-FEC) threshold of 1.0 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> with 15% overhead, which corresponds to a net rate of 84.4 Gbps for THz-over-fiber transmission. To the best of our knowledge, fusing OFDM and PDM, this is the highest rate achievable for DSM applications in THz communication. This experimental demonstration can provide a promising solution for high-order QAM signals in a fiber-wireless seamless network in future 6G networks.

Demonstration high-order QAM transmission based on one-bit delta-sigma modulation in radio-over-fiber system

In the letter, we propose to use delta-sigma modulator (DSM) technology to transmit OFDM high-order QAM signals in a single-carrier radio-over-fiber (RoF) system, and conduct experimental verification. The experiment demonstrates the transmission of OFDM-256/1024/4096 QAM signals using one-bit DSM in the W band in a 20 km SSMF and 1 m wireless RoF system, and successfully realized that the BER of OFDM-256 and 1024 QAM after system transmission is lower than the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10−3, and the BER after 4096 QAM transmission is lower than the soft decision forward error correction (SD-FEC) threshold of 4.0 × 10−2. The combination of DSM and the photonics-aided RoF solution can effectively solve the problem that the nonlinear damage caused by the bottleneck of the optoelectronic device in the RoF system limits the transmission of high-order QAM signals, and it is expected to be applied in the future 6G optical wireless network.

104-m wireless transmission of 4096-QAM for mobile backhaul based on delta-sigma modulation in 145 GHz

104-m wireless transmission of 4096-QAM for mobile backhaul based on delta-sigma modulation in 145 GHz

An autocorrelation-less single-bit Weiner filter on FPGA

Filtering, transformations, and convolution in digital signal processing (DSP) are relatively resource-intensive algorithms, typically involving massive computations and complex processing architectures. Effective methods to manage this complexity include reducing the data word length using techniques such as sigma-delta modulation (SDM) and algorithmic optimization, either targeting coding style or via changes to the algorithm itself. In this paper, an SDM-based autocorrelation-less Weiner filter is proposed and compared with traditional multi-bit and SDM-based single-bit Weiner filters. The proposed design is first functionally verified using MATLAB simulations, and statistical parameters such as Signal to Noise Ratio (SNR), Mean Square Error (MSE), and Probability of Error (PE) are derived. The results show that the proposed design offers comparable performance to conventional filters. The proposed autocorrelation-less filter and equivalent conventional filters are then synthesized in FPGA for area-performance analysis. The SDM-based autocorrelation-less Weiner filter demonstrates a 30% improvement in performance over an equivalent traditional filter, which in result provides the shift in operating frequency from approximately 240 MHz to around 340 MHz, with about 63% less resources consumption. This improved performance and reduced resources increase the potential range of applications for this Weiner filter.

A 143 dB Delta-Sigma Modulator for Biomedical Applications

This paper presents a single loop forth-order delta-sigma modulator topology of cascade of integrator with multiple feedback This paper presents a single loop forth-order delta-sigma modulator topology of cascade of integrator with multiple feedback (CIFB) . The number of levels in the quantizer increases for higher performance. The modulator noice transfer function (NTF) and signal transfer function (STF) exploited for higher performance. The out-of-band gain (OBG) of 1.5 selected considering the stability of higher order modulator. The high oversampling ratio (OSR) considered for small bandwidth applications. The maximum quantization noise is suppressed by NTF zeros optimization. A full-scale signal of the modulator is 0.55-V considering the higher order loop filter stability. Due to CIFB topology, there is no peaking in the STF while STF response is flat. The zeros of the NTF are optimized for maximum quantization noise and poles are placed inside the unit circle. The complete modulator loop filter has four integrators in the loop filter with multiple feedback digital-to-analog converter (DAC) for maximum stability. The complete modulator simulation shows it an achieve signal-to-noise (SNR) of 1.43 dB with oversampling ratio (OSR) of 128.

Radio-over-fiber systems with delta-sigma-modulation for MMW-based indoor communication

In this paper, we propose and demonstrate a delta-sigma modulator (DSM) based radio-over-fiber (RoF) system for MMW indoor communication. In the experiment, 2-bit DSMs are used to quantize the high-order QAM orthogonal frequency division multiplexing (OFDM) signal into the 16QAM signal. At the receiver, the original high-order signal can be recovered by the low pass filter (LPF) and down-sampling operation. Based on the experimental results, up to 16,384 QAM signals can be transmitted over the DSM-based RoF system without noticeable performance degradation. When the received optical power is high enough, the corresponding error vector magnitude (EVM) and bit error rate (BER) are 0.53% and 7 × 10−3, respectively.

Multiple-Degree-of-Freedom Modeling and Simulation for Seismic-Grade Sigma–Delta MEMS Capacitive Accelerometers

The high-order mechanical resonances of the sensing element in a high-vacuum environment can significantly degrade the noise and distortion performance of seismic-grade sigma–delta MEMS capacitive accelerometers. However, the current modeling approach is unable to evaluate the effects of high-order mechanical resonances. This study proposes a novel multiple-degree-of-freedom (MDOF) model to evaluate the noise and distortion induced by high-order mechanical resonances. Firstly, the MDOF dynamic equations of the sensing element are derived using the principle of modal superposition and Lagrange’s equations. Secondly, a fifth-order electromechanical sigma–delta system of the MEMS accelerometer is established in Simulink based on the dynamic equations of the sensing element. Then, the mechanism through which the high-order mechanical resonances degrade the noise and distortion performances is discovered by analyzing the simulated result. Finally, a noise and distortion suppression method is proposed based on the appropriate improvement in high-order natural frequency. The results show that the low-frequency noise drastically decreases from about −120.5 dB to −175.3 dB after the high-order natural frequency increases from about 130 kHz to 455 kHz. The harmonic distortion also reduces significantly.

Hematoloechus sp. attachment shifts endothelium in vivo from pro- to anti-inflammatory profile in Rana pipiens: evidence from systemic and capillary physiology.

This prospective, descriptive study focused on lung flukes (Hematoloechus sp., H) and their impact on systemic and individual capillary variables measured in pithed Rana pipiens, a long-standing model for studies of capillary physiology. Three groups were identified based on Hematoloechus attachment: no Hematoloechus (No H), Hematoloechus not attached (H Not Att), and Hematoloechus attached (H Att). Among 38 descriptive, cardiovascular, and immunological variables, 18 changed significantly with H. Symptoms of H included weight loss, elevated immune cells, heart rate variability, faster coagulation, lower hematocrit, and fluid accumulation. Important capillary function discoveries included median baselines for hydraulic conductivity (Lp) of 7.0 (No H), 12.4 (H Not Att), and 4.2 (H Att) × 10-7 cm·s-1·cmH2O-1 (P < 0.0001) plus seasonal adaptation of sigma delta pi [σ(πc-πi), P = 0.03]. Pro- and anti-inflammatory phases were revealed for Lp and plasma nitrite/nitrate concentration ([NOx]) in both H Not Att and H Att, whereas capillary wall tensile strength increased in the H Att. H attachment was advantageous for the host due to lower edema and for the parasite via a sustained food source illustrating an excellent example of natural symbiosis. However, H attachment also resulted in host weight loss: in time, a conundrum for the highly dependent parasite. The study increases overall knowledge of Rana pipiens by revealing intriguing effects of H and previously unknown, naturally occurring seasonal changes in many variables. The data improve Rana pipiens as a general scientific and capillary physiology model. Diseases of inflammation and stroke are among the clinical applications.

Support 16384QAM mobile fronthaul based on 3 amplitude quantization Delta-Sigma Modulation

We experimentally demonstrated 16384-ary quadrature amplitude modulation (16384QAM) mobile fronthaul based on 3-amplitude quantization high-pass Delta-sigma Modulation (DSM) in the O band intensity-modulated direct detection (IM/DD) system. By using 3-amplitude quantized high-pass DSM, we successfully quantize the analog waveform of intermediate frequency (IF) Orthogonal Frequency Division Multiplexing (OFDM) signal into 3-Level Pulse Amplitude Modulation (PAM3) signal, and 1 GHz bandwidth 16384-QAM and 1024QAM are successful transmission in 20Gb/s IM/DD link. 0.63% Error Vector Magnitude (EVM) of 16384QAM and 0.7% EVM of 2048QAM are achieved after 25km SSMF and 50km SSMF transmission, respectively. The signal-to-noise ratio (SNR) of the retrieved OFDM signal is 43 dB, which shows that the proposed scheme can support 16384QAM mobile fronthaul network.

Optimization of Slew Mitigation Capacitor in Passive Charge Compensation-Based Delta–Sigma Modulator

In this paper we propose a scheme of optimizing the size of charge compensation (CC) capacitor in a delta-sigma modulator (DSM) using a passive charge compensation (PCC) based switched capacitor integrator (SCI). The slewing behavior of a PCC based SCI is analyzed in both integration phase (IP) and sampling phase (SP) to optimize the size of CC capacitor. The effectiveness of the proposed scheme is demonstrated by implementing a 2-1 cascaded DSM using PCC based SCI with optimized value of CC capacitor in 0.18-μm CMOS technology. The DSM operates at a frequency of 5-MHz and achieves a peak SNDR of 103.1-dB in the audio bandwidth of 20-kHz. The power consumption of DSM is 220-μW at a supply voltage of 0.85-V and it consumes 1.3 mm of area. Post-layout simulations show an improvement of 10.8-dB in the SNDR of DSM by using the optimized value of CC capacitor in PCC based SCI.

A sigma-delta interface built-in self-test and calibration for microelectromechanical system accelerometer's utilizing interpolation method

This work presents the capacitive micromechanical accelerometer with a completely differential high-order switched capacitor sigma-delta modulator interface. Such modulation interface circuit generates one-bit output data using a third sigma-delta modulator low-noise front-end, doing away with the requirement for a second enhanced converter of resolution to encode the feedback route analog signal. A capacitive micromechanical sensor unit with just a greater quality factor has been specifically employed to give greater resolution. The closed-loop and electrical correction control are used to dampen the high-Q values to get the system's stability with high-order. This microelectromechanical system (MEMS) capacitive accelerometer was calibrated using a lookup table and Akima interpolation to find manufacturing flaws by recalculating voltage levels for the test electrodes. To determine the proper electrode voltages for fault compensation, COMSOL software simulates a number of defects upon that spring as well as the fingers of the sensor system. When it comes time for the feedback phase of a proof mass displacement correction, these values are subsequently placed in the lookup table.