Noise Transfer Function Research Articles

Readout circuit noise analysis and low-noise design for piezoelectric micro-machined ultrasonic transducers with large parasitic capacitance.

Readout circuits are fundamental components in many application systems that utilize piezoelectric micro-machined ultrasonic transducers (pMUTs). This study models the noise and signal transfer functions of trans-impedance amplifiers (TIAs), charge-sensitive circuits, and voltage-mode readout circuits in detail. A series of simulations and experiments were conducted to elucidate the advantages and disadvantages of these circuit types. Both theoretical and experimental results indicate that the intrinsic capacitance of large pMUTs can significantly degrade the quality of the readout signal. Furthermore, while the TIA-based readout circuit demonstrates clear gain advantages, it is also susceptible to considerable noise interference. This work proposes an improved readout circuit design that effectively mitigates noise interference while preserving the gain advantages of the TIA architecture. The implemented prototype circuit successfully reduces the noise from 73 mVp-p to 13 mVp-p.

A First-Order Noise-Shaping SAR ADC with PVT-Insensitive Closed-Loop Dynamic Amplifier and Two CDACs

This paper presents a first-order noise-shaping (NS) successive approximation register (SAR) analog-to-digital converter (ADC) with a process, (supply) voltage, and temperature (PVT)-insensitive closed-loop integrator and data-weighted averaging (DWA). The use of a cascode floating inverter amplifier (FIA)-type dynamic amplifier with high gain enables an aggressive noise transfer function while minimizing the power consumption associated with the use of an active filter. In the proposed ADC, the residue is generated by a capacitive digital-to-analog converter (CDAC) employing DWA, which is made possible by employing a second CDAC, which operates after the SAR operation is completed. The proposed ADC is designed with a 28 nm CMOS process with 1 V power supply. The simulation results show that the ADC achieves the SNDR of 71.2 dB and power consumption of 228 μW when operated with a sampling rate of 80 MS/s and oversampling ratio (OSR) of 10. The Schreier figure-of-merit (FoM) is 173.6 dB, and Walden FoM is 9.6 fJ/conversion-step.

Experimental validation on structure-borne underwater radiated noise transfer function analysis for marine structure

In this paper, an experimental validation of a numerical procedure for estimating the structure-borne Underwater Radiated Noise (URN) Transfer Function (TF) of a marine structure based on the SEA theory has been performed. For the purpose, the structure-borne URN TF of a central point-excited one-side fluid-loaded four-edge stiffened plate in a reverberant water tank has been measured and compared with the SEA result. Additionally, the practical applicability of the procedure for a real ship structure has been demonstrated by comparing the URN analysis result based on the transfer function method and the measurement result for a Korean research vessel, ‘Cheong-Hae’. From the results, it is confirmed that the presented procedure can be used to estimate the structure-borne URN level emitted from the vibrating fluid-loaded side shells of a ship structure.

A 3.07 mW 30 MHz-BW 73.2 dB-SNDR Time- Interleaved Noise-Shaping SAR ADC With Self-Coupling Second-Order Error-Feedforward

A noise-shaping successive approximation register (NS-SAR) ADC combines the merits of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Sigma $</tex-math> </inline-formula> and SAR ADC, transforming it into an emerging ADC architecture to reach high resolution with good power efficiency. The single-channel NS-SAR with high resolution, however, suffers from bandwidth (BW) limitations. The time-interleaved (TI) NS-SAR mitigates the speed bottleneck but faces challenges in obtaining high resolution and BW simultaneously due to the lack of a sharp noise transfer function (NTF). This article presents a calibration-free two-channel TI-NS-SAR with an aggressive second-order NTF for high resolution. Based on a one-time error feedback (FB) at midway, we propose a second-order error-feedforward (FF) to enhance the noise-shaping (NS) effect further meanwhile avoiding the excessive NTF peaking and dynamic range (DR) loss. A dynamic residue amplifier shared between two channels lowers the offset, which reduces the redundant bit to only one bit, thus improving the efficiency of SAR conversion. Fabricated in a 28 nm CMOS with 1 V supply, the prototype achieves 73.2 dB-signal-to-noise-and-distortion-ratio (SNDR) over 30 MHz-BW when operating at 330 MHz. It consumes 3.07 mW and exhibits a Schreier FoM (FoMs) of 173.1 dB.

An intermediate frequency reconfigurable bandpass noise‐shaping SAR ADC for IoT and mobile application

AbstractThis letter proposes a reconfigurable bandpass noise‐shaping successive approximation register analog‐to‐digital converter (ADC) with a cascade of integrators with feedforward (CIFF) structure. Unlike conventional CIFF structures that use a passive feedforward path, the new design incorporates an amplifier within the filter, providing effective bandpass noise transfer function regardless of passband location, and facilitating the use of a unity gain 2‐input comparator for low noise and high stability. The loop filter includes amplification by a low power Gm‐R amplifier and two‐step charge sharing. The proposed ADC supports three different intermediate frequencies (IFs), and 12‐bit resolution is achieved for all IFs in a 28‐nm complementary metal‐oxide‐semiconductor (CMOS) process.

Quad path, CG-CS resistive feedback LNA architecture for 25–35 GHz band

In this paper, a Quad Path Noise Cancellation (QPNC) Low Noise Amplifier (LNA)presented for 5G sub-band 25-35GHz using GPDK 45 nm Complementary Metal Oxide Semiconductor (CMOS) technology; which is composed of Common Source (CS) & Common Gate (CG) stages with resistive feedback and current reuse at the output. QPNC is used to cancel the noise of common gate transistors, which leads to reduce the noise fig. (NF). Resistive feedback is used to tradeoff between the input matching, gain, and NF i.e. overall refining the Figure of Merit (FoM) of the circuit. Mathematical analysis of impedance matching, gain, noise transfer function, and NF have been done using the small signal model of QPNC-LNA. Simulation has been done on Cadence Virtuoso software using GPDK 45 nm CMOS technology. Pre layout simulation result shows the minimum value of gain is 13.38 dB at 30.9GHz while the maximum value is 14.12 dB at 25.87GHz and flat over the entire frequency range. S11 i.e. input reflection coefficient is ranging from −16.16 dB at 25.21GHz to −11.52 dB at 35GHz for 50 Ω input impedance matching. NF value ranges from 2.69 dB at 25.69GHz to 3.77 dB at 35GHz. The IIP3 value for the proposed QPNC-LNA is 5.3 dB. For the four corners SS, SF, FS, and FF, process corner simulation has been performed. Post-layout simulation results depict the maximum value of gain is 12.71 dB at 25.75GHz. NF value is varying from 2.88 dB to 4.02 dB while the input reflection coefficient is ranging from −10.12 dB to −14.13 dB for 10GHz bandwidth. The circuit consumes 17.53 mW power at 1.2 V under a DC current of 14.61 mA, FoM1 is 8.36 dB and FoM2 of the proposed LNA is 49.35 dB. The layout of the proposed LNA is having an area of 0.03026mm2.

Data filtering based multi‐innovation gradient identification for bilinear systems with colored noise

SummarySystem identification is the powerful tool to establish the mathematical models of practical systems. This article considers the parameter identification for bilinear systems with colored noise. First, the bilinear system is transformed into an input‐output form by eliminating the state variables in the model. Then, based on the data filtering technique, the measured input‐output data is filtered using an estimated noise transfer function, and a filtering based generalized extended stochastic gradient (F‐GESG) algorithm is proposed to enhance the parameter estimation accuracy. Furthermore, the multi‐innovation identification theory is employed to improve the convergence speed of the proposed F‐GESG algorithm, and a filtering based multi‐innovation generalized extended stochastic gradient (F‐MI‐GESG) algorithm is developed to identify the parameters of bilinear systems. The GESG algorithm is given for comparison. Finally, a numerical simulation example is provided to illustrate the effectiveness and excellent performance of the proposed algorithms.

A Reconfigurable 12-to-18-Bit Dynamic Zoom ADC With Pole-Optimized Technique

This paper presents a resolution-reconfigurable discrete-time dynamic zoom analog-to-digital converter (ADC) with a 20-kHz bandwidth. It employs a coarse 6-bit successive approximation register (SAR) ADC that dynamically updates the references for the post-stage single-bit second-order delta-sigma modulator to obtain a higher resolution with lower power. The sampling rate of the proposed ADC can be configured to be 1.6, 3.2, 6.4 and 10-MS/s such that four resolution modes, including 12, 14, 16 and 18-bit, can be provided accordingly. Note that pole locations of the noise transfer function (NTF) vary with different OSR’s, and noise-shaping effect, together with the power efficiency, can be degraded. To solve this issue, the pole-optimization technique is proposed in this paper. In this way can the pole locations be reconfigured according to the specific OSR. Additionally, the bandwidths of the operational amplifiers are also modulated in different oversampling ratio (OSR) scenarios to further improve the energy efficiency. Fabricated in a 0.18- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula> m CMOS process, the prototype occupies 1.01 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> . On condition of an OSR of 250, the proposed ADC achieves a signal-to-noise-and-distortion-ratio (SNDR) of 102.8 dB, while dissipating 1.3 mW.

A 77.3-dB SNDR 62.5-kHz Bandwidth Continuous-Time Noise-Shaping SAR ADC With Duty-Cycled Gm-C Integrator

This article presents a first-order continuous-time (CT) noise-shaping successive-approximation-register (NS-SAR) analog-to-digital converter (ADC). Different from other NS-SAR ADCs in literature, which are discrete-time (DT), this ADC utilizes a CT Gm-C integrator to realize an inherent anti-aliasing function. To cope with the timing conflict between the DT SAR ADC and the CT integrator, the sampling switch of the SAR ADC is removed, and the integrator is duty cycled to leave 5% of the sampling clock period for the SAR conversion. Redundancy is added to track the varying ADC input due to the absence of the sampling switch. A theoretical analysis shows that the 5% duty-cycling has negligible effects on the signal transfer function (STF) and the noise transfer function. The output swing and linearity requirements for the integrator are also relaxed thanks to the inherent feedforward path in the NS-SAR ADC architecture. Fabricated in 65-nm CMOS, the prototype achieves 77.3-dB peak signal-to-noise and distortion ratio (SNDR) in a 62.5-kHz bandwidth while consuming <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$13.5~\mu \text{W}$ </tex-math></inline-formula> , leading to a Schreier figure of merit (FoM) of 174.0 dB. Moreover, it provides 15-dB attenuation in the alias band.

Study on interior noise control of minibus based on structural acoustic radiation

Aiming at the problem of excessive low-frequency noise inside a minibus, the interior noise control scheme was studied to improve the NVH (Noise, Vibration, and Harshness) performance of the vehicle based on the characteristics of the structural acoustic radiation. With acoustic contribution as the evaluation index, the ability of the structure to radiate noise to the vehicle was studied from the perspective of modal participation and panel contribution. In this study, the legacy finite element model of the vehicle was firstly established, and the model was validated through the modal test of the BIW (Body in White), and the noise transfer function analysis was carried out to identify the critical frequency points. Furthermore, the improved super element method (SEM) was used to establish the super element simulation model of the vehicle, the simulation analysis of the modal contribution and panel contribution was carried out for the critical frequency points, and the panels that provide the main contribution were determined. In addition, a single-factor experimental study was carried out on the position of the critical panel by using the dynamic vibration absorbers with different performance parameters, so as to verify the accuracy of the simulation results of the panel acoustic contribution for the critical frequency. Finally, the structural optimization schemes of the critical panels were designed and verified by experiments. It was indicated that optimizing the acoustic radiation characteristics of the structure by improving the body panel structure to reduce interior noise was feasible.

A New Noise Shaping Approach for Sigma-Delta Modulators Using Two-Stage Feed-Forward Delays and Hybrid MASH-EFM

Sigma-delta modulators use a noise-shaping technique to curtail the noise power in the band of interest during digital-to-analog conversion. Error feedback modulator employs an efficient noise transfer function for time varying inputs than any other sigma-delta modulators. However, the efficiency of the conventional noise transfer function degrades and the quantizer saturation issue provokes when the input signal reaches to full scale. This work proposes a new noise transfer function which is a combination of transfer functions of two-stage Feed-forward delays and a novel Hybrid multi-stage noise shaping-error feedback sigma-delta modulator. The noise transfer function of two-stage Feed-forward delays mitigates the concern of quantizer saturation. The noise transfer function offered by the Hybrid multi-stage noise shaping-error feedback architecture provides sustainable solutions to limit cycles and idle tones. The simulation concludes that the proposed noise-shaping approach obtains comparatively high signal-to-quantization noise ratio than the conventional error feedback modulators. Other performance parameters like spurious-free dynamic range, effective number of bits and signal-to-noise plus distortion ratio are also significantly improved.

A Detailed Model of Cyclostationary Noise in Switched-Resistor Circuits

The Switched-Resistor (S-R) technique is becoming more and more interesting to implement low-voltage low-power active- RC filters with high tuning range and front-end amplifiers for biomedical circuits and systems. This approach exploits MOS switches driven by a duty-cycle-controlled clock signal to achieve tunability of the equivalent resistance and, hence, of the RC time constant. Since S-R circuits can be considered as linear periodically time variant (LPTV) systems with sampled outputs, we exploit the theory of the adjoint (inter-reciprocal) network in order to develop a detailed model of the cyclostationary noise involved in this kind of circuits. The proposed model allows to gain insight into the different noise sources and transfer functions involved, highlighting the circuit parameters on which the cyclostationary noise depends. Validation of the proposed model has been carried out by comparing analytical results against periodic noise simulations referring to a commercial 130nm CMOS process. The validation activity has confirmed the good accuracy of the proposed noise model and provided some useful design guidelines to optimize the noise performance of S-R circuits.

High sensitivity of indirect noise predictions in non-isentropic nozzles

In aircraft engine combustors, incomplete mixing and air cooling give rise to flow inhomogeneities. When accelerated through the nozzle guide vane downstream of the combustor, these inhomogeneities give rise to acoustic waves. This is commonly known as indirect combustion noise. When these sound waves are reflected off the outlet and travel upstream of the combustor, they can lead to thermoacoustic oscillations. To predict indirect noise, models proposed in the literature assume the frequency of impinging disturbances to be small (compact nozzle assumptions). However, in reality, the assumption might not hold; hence, a mismatch in the predicted and experimental results can be observed. First, we present a semi-analytical solution to a non-isentropic nozzle indirect noise model using asymptotic expansion. Second, we show that the indirect noise predictions are sensitive to a small change in the Helmholtz number for a nearly compact nozzle, especially in the subsonic flow regime. We also show the predictions become lesser sensitive as the non-isentropicity increases. This study highlights the importance of non-compact assumptions for the accurate prediction of indirect noise transfer functions and thermoacoustic instability in aeronautical gas turbines.

Numerical and experimental-aided framework based on TPA for acoustic contributions of individual transfer paths on a vehicle door in the slamming event

The luxury sound quality of a vehicle door in the slamming event will increase consumers’ willingness to purchase the vehicle, thus its detailed investigation is a crucial consequence for the advancement of the automobile industry. This paper proposes a numerical and experimental approach on a transfer path analysis (TPA) to determine the sound quality for the individual transfer paths of the vehicle door in the slamming event. In our previous investigations, the transient impact loads of the vehicle door in the slamming event had been determined based upon lab experiment and bench test. These transient impact loads will be selected as input values for a numerical and experimental approach on the TPA. The noise transfer functions (NTFs) from the discretized path points to the driver’s ear are obtained by a numerical simulation technique. The sound pressure value at the driver’s ear is calculated and synthesized from the above transient impact loads and the NTFs and is verified by the sound pressure acquisition experiment. Then sound quality with objective evaluation is quantitively investigated utilizing five characteristic criterions: main impact time, low frequency duration, A-weighted sound pressure level, loudness, sharpness. Simultaneously, the subject evaluation is implemented to estimate the sound quality employing the laboratory-scale jury test. The back-propagation neural network (BPNN) improved via the genetic algorithm (GA) is suggested to appraise the mathematical relationship between the subjective and objective evaluation of the sound quality for the vehicle door slamming event. Finally, the built GA-BPNN model is applied to predict the subjective evaluation for the sound quality of the TPA. The transfer paths with a large contribution to the sound quality will be deemed to be suppressed objects in the subsequent analysis. This appraisal approach can be employed as a productive evaluation tool of the vehicle door slamming event for subsequent vibration and noise optimization.

A Review of Noise Reduction Techniques in Noise-shaping SAR ADCs

Noise-shaping successive-approximation-register (NS-SAR) ADCs have become one of the most promising candidates for high-resolution data converters over the past decade. This is due to the fact that they combine the advantages of delta-sigma modulation and SAR ADCs. In this hybrid architecture, the quantizer and residue feedback DAC can be replaced by SAR, a replacement which achieves high SNR while also benefiting from superior power efficiency and low cost. For NS-SAR ADCs, various implementations of loop filters for residue processing exist that can realize the noise transfer function (NTF) for NS effects. In addition, many noise reduction techniques have been proposed that suppress additional noises not shaped by NTF. This paper describes the basics of NS-SAR ADCs while also reviewing noise reduction techniques, which include the implementation of a loop filter for residue handling, kT/C noise rejection, and capacitive DAC mismatch error shaping. It also outlines advanced architectures that can overcome the limitations of NS-SAR ADCs.

A 2.5-MHz BW, 75-dB SNDR Noise-Shaping SAR ADC With a 1st-Order Hybrid EF-CIFF Structure Assisted by Unity-Gain Buffer

This article presents a 1st-order noise-shaping (NS) successive approximation register (SAR) analog-to-digital converter (ADC) with a hybrid error-feedback (EF) and cascaded-integrator-feed-forward (CIFF) structure assisted by a unity-gain buffer (UGB). Without using a multi-input comparator which is widely adopted in conventional 1st-order passive NS structures, the proposed hybrid EF-CIFF structure realizes a more ideal 1st-order noise transfer function (NTF) with a reasonable capacitance ratio, so as to obtain better NS effect. Fabricated in a 28-nm CMOS technology, the prototype NS-SAR ADC consumes 150 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula> under a 0.9-V supply voltage when operating at 40-MS/s sampling rate. A 75-dB signal-to-noise-and-distortion ratio (SNDR) is measured for a 2.47-MHz sinusoid input under an oversampling ratio (OSR) of 8. It achieves a peak Schreier figure-of-merit (FoM) of 177.2 dB and the core circuit occupies 0.012-mm2 area.

A fully dynamic third-order EF-CIFF noise-shaping SAR ADC with NTF zeros optimization and passive integration

In this paper, a third-order noise-shaping successive approximation register (NS-SAR) analog-to-digital converter (ADC) is proposed which is simple and fully dynamic. A passive integrator is utilized in the feed-forward (FF) path of a second-order NS-SAR ADC with 2nd-order error-feedback (EF) filter to reduce the effect of inband quantization and comparator noise. The integrator implements a passive gain of 4x to make up its loss arising from the charge sharing between the integrator and digital-to-analog converter capacitors at the integration phase. Another advantage of the proposed structure is employing a simple low noise and low power one-input pair comparator unlike many published NS-SAR ADCs which use a comparator with multi-input pairs leading to enhanced comparator input-referred noise and power consumption. In this work, the zeros of the noise transfer function are optimized to enhance inband noise suppression. The proposed ADC is designed at circuit level using 0.18 μm TSMC CMOS technology with Cadence Virtuoso tool. The oversampling ratio, sampling frequency, and bandwidth are 8, 2.5 MS/s, and 156.25 kHz, respectively. According to the detailed post-layout simulation results, the achieved signal-to-noise and distortion ratio of the simulated ADC is 83.1 dB with 70.3 µW power consumption from a 1.1 V supply.

A PVT-Robust AFE-Embedded Error-Feedback Noise-Shaping SAR ADC With Chopper-Based Passive High-Pass IIR Filtering for Direct Neural Recording.

This paper presents a PVT-robust error-feedback (EF) noise-shaping SAR (NS-SAR) ADC for direct neural-signal recording. For closed-loop bidirectional neural interfaces enabling the next generation neurological devices, a wide-dynamic-range neural recording circuit is required to accommodate stimulation artifacts. A recording structure using an NS-SAR ADC can be a good candidate because the high resolution and wide dynamic range can be obtained with a low oversampling ratio and power consumption. However, NS-SAR ADCs require an additional gain stage to obtain a well-shaped noise transfer function (NTF), and a dynamic amplifier is often used as the gain stage to minimize power overhead at the cost of vulnerability to PVT variations. To overcome this limitation, the proposed work reutilizes the capacitive-feedback amplifier, which is the analog front-end of the neural recording circuit, as a PVT-robust gain stage to achieve a reliable NS performance. In addition, a new chopper-based implementation of a passive high-pass IIR filter is proposed, achieving an improved NTF compared to prior EF NS-SAR ADCs. Fabricated in a 180-nm CMOS process, the proposed NS-SAR ADC consumes 4.3-μW power and achieves a signal-to-noise-and-distortion ratio (SNDR) of 71.7 dB and 82.7 dB for a bandwidth of 5 kHz and 300 Hz, resulting in a Schreier figure of merit (FOM) of 162.4 dB and 162.1 dB, respectively. Direct neural recording using the proposed NS-SAR ADC is demonstrated successfully in vivo, and also its tolerance against stimulation artifacts is validated in vitro.

A SPICE-Compatible Model to Simulate RFI-Induced Buzz Noise Problem in a Camera

This article proposeda SPICE-compatible model to fast simulate the buzz noise problem in a camera device. Based on the reciprocity theorem, the proposed SPICE-compatible model consists of cascaded scattering (S) parameters extracted from the field coupling. It can provide an accurate estimation of the buzz noise transfer function (TF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">total</sub> ) between the radio-frequency antenna and the audio system within an average error of 1 dB. Besides, the proposed model allows for coupling decomposition by separating the audio system into different regions, fast buzz noise mitigation by adding filtering circuits, and fast antenna evaluation/selection by characterizing the TF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">total</sub> with different antenna structures. The advantage of the proposed model is that, instead of multiple 3-D simulations during the predesign-stage troubleshooting, it is a fast SPICE-compatible method with SPICE simulation time of 4.5 min and one-time 3-D full-wave simulation on the camera system studied. It provides quick estimation on the potential buzz noise problems, coupling decomposition,buzz noise mitigation methods, and selection of antenna structures.

Optimal design of both multi‐input multi‐output loop filter and multi‐input single‐output reconstruction filter of sigma delta modulator

This paper considers a sigma delta modulator (SDM) with the outputs of the quantizers directly fedback to the inputs of the loop filter without being subtracted from the input sequence. The design of the multi-input multi-output (MIMO) loop filter is formulated as an optimization problem. In particular, the sum of the inner products between the elements in the signal transfer function (STF) and the corresponding elements in the noise transfer function (NTF) of the SDM is minimized. The constraints of the optimization problem are defined based on the specifications on the maximum absolute difference between the magnitude response of the designed STF and that of the desirable STF as well as that between the magnitude response of the designed NTF and that of the desirable NTF of the SDM. Similarly, the design of the multi-input single-output (MISO) reconstruction filter is also formulated as an optimization problem. In particular, the sum of the total absolute difference between the designed magnitude response of the reconstruction filter and the desirable magnitude response of the STF of the SDM is minimized. The constraint of the problem is defined based on the specification on maximum absolute difference between the designed magnitude response of the reconstruction filter and the desirable magnitude response of the STF of the SDM. In this paper, the genetic algorithm is employed to find a near global solution of the formulated optimization problems. In order to reduce the required computational power, the matrix inversion lemma is applied. The computer numerical simulation results show that the SDM designed by our proposed method outperforms the SDMs designed by the Matlab function in terms of the signal to noise ratio (SNR) performance.