Analysis of delay impact on active engine noise control performance

Abstract

The vehicle active engine noise control (ENC) system enhances driving comfort by generating anti-noise waves to cancel engine noise. Delay is a critical bottleneck affecting practical performance of ENC systems. In this paper, the impact of reference signal delay and secondary path delay on the performance of ENC system based on Filtered-x Least Mean Square (FxLMS) algorithm is thoroughly investigated. A delay module was incorporated into the traditional ENC model. The system’s performance was simulated using an analytical solution, which was subsequently validated through vehicle experiments. This study demonstrates that increases in both reference signal delay and secondary path delay degrade ENC system performance under dynamic acceleration conditions, while having a negligible impact under static steady-state conditions. This research elucidates the mechanism by which delay influences ENC system performance, underscores the critical importance of minimizing delay in system design, and provides a theoretical foundation for developing delay compensation algorithms to enhance system robustness in dynamic scenarios.

Keywords

engine active noise control delay reference signal secondary path FxLMS algorithm

1. Introduction

In recent years, with rapid development of the automotive industry, the user requirements for driving comfort continuously grow as well as new noise challenges brought by cost reduction and fuel efficiency, an amount of automotive manufacturers pay more attention on active noise control (ANC) ^1–6 technology to effectively suppress interior vehicle noise. Especially in the luxury and high-end vehicle market, ENC is gradually becoming a key factor in enhancing vehicle quietness and driving quality.^1–6

In research on active noise reduction technology in vehicles, acoustics and algorithm constitute the dual cores of technical optimization. Acoustic research focuses on noise source property, transducer or speaker layout, and sound wave propagation property^2,7–10; while algorithm research is dedicated to efficiently and stably generating anti-noise fields, as well as improving the response speed of real-time control systems.^11–20 In practical scenarios, time delay is one of the key bottlenecks restricting the performance of active noise control systems, which originates from various factors such as sensor signal acquisition, controller operation, and actuator response. The delay can disrupt the synchronization between the control signal and the primary noise, thereby impairing the noise reduction performance of the algorithm. In 2013, Zhang et al. investigated the effects of delay on the noise reduction performance of feedforward active noise reduction headphones. The research indicated that noise incident from specific angles can result in secondary path delay exceeding primary path delay in feedforward systems which violates the principle of causality and thus induces degradation in active noise reduction performance.²¹ In 2019, Cheer et al. studied a multi-reference-based feedforward active noise reduction headphone strategy, which jointly controls the reference signals on both sides of the ear cups and effectively enhances system robustness.^11–20 In 2022, Lopes’s research demonstrated that delay is a key bottleneck limiting the performance of broadband active noise control systems. By employing Σ-ΔD/A and A/D conversion quantization along with noise shaping techniques, delay can be significantly reduced without increasing computational complexity.²² In 2023, Zhang et al. proposed a multi-channel delayed notch FxLMS structure for vehicle interiors, in which a new time-delay method was introduced to simplify the filtering process of the reference signal to greatly improve the calculation efficiency.²³ In 2025, Zhuang proposed a multiphase filtering method based on minimum phase decomposition to address the time delay issues in ANC hardware implementation, significantly reducing computational complexity and improving system performance without adding additional delay.²⁴ Furthermore, some studies focusing on robust ANC algorithms have been proposed. Inspired by the maximum correntropy criterion (MCC), Chien et al.²⁵ proposed a modified filtered-x affine-projection-like MCC (MFxAPLMCC) algorithm to enhance robustness. Qian et al.²⁶ proposed a novel robust adaptive filtering algorithm to tackle the challenge of estimation biases when ANC system is faced with nonlinear scenarios involving censored measurement data.

Existing literature on time delay issues has mostly focused on the algorithmic level, while systematic research on the impact of time delay on the active noise reduction performance of automotive engines remains relatively scarce. Therefore, this study investigates the effects of reference signal delay and secondary path delay on the performance of an ENC system based on the Filtered-x Least Mean Square (FxLMS) algorithm, clarifying the influence of time delay on ENC system performance under different operating conditions. This work provides a theoretical foundation for the development of delay compensation algorithms to enhance system robustness.

2. Theoretical analysis

2.1. ENC system based on the head unit controller

The ENC systems apply ANC technology to cancel engine noise. It deploys vehicle woofer to emit sound waves that possess the same amplitude but opposite phase relative to the target noise (primary engine noise). By virtue of acoustic wave interference and cancellation, the system effectively attenuates in-vehicle noise levels. As illustrated in Figure 1, within the architecture of the head unit controller, the ENC system operates via four core functional modules, which are elaborated as follows.

(1) The reference signal is generated based on the engine speed signal highly correlated with the target noise transmitted by the vehicle’s ECU (Electronic Control Unit), MCU (Microcontroller Unit), and QNX (Quantum UNIX Operating System). This signal serves as the core input to the ENC system.

(2) An adaptive filter, acting as the system’s key component, operates on a dedicated DSP (Digital Signal Processor) integrated within the head unit controller, generating a secondary cancellation signal. Its filter coefficients are dynamically updated in real time based on reference signal and residual noise feedback from error sensors (microphones), which enables continuous optimization of noise reduction performance and adaptation to varying vehicle operating conditions.

(3) The secondary sound source, typically the vehicle’s built-in audio system loudspeakers, converts the electronic control signals from automotive head unit controller into acoustic anti-noise waves powered by power amplifiers.

(4) The error sensors, usually microphones strategically placed within the vehicle cabin to real-time monitor the residual noise after noise reduction processing. Their output signals are fed back to the adaptive filter as input for coefficient updating, thereby forming a closed-loop control loop for the ENC system.

Figure 1.

Block diagram of ENC system based on automotive domain controller.

Leveraging the in-vehicle domain controller as its hardware foundation, the ENC system fully utilizes the head unit controller’s inherent advantages—including high integration, robust data fusion capabilities, and powerful computing performance. However, it also confronts unique delay challenges inherently introduced by whole vehicle architecture, which are specifically manifested in two key types of delays:

The first type is reference signal delay. The reference signal (e.g., engine speed) is transmitted from the ECU to the head unit controller via the Controller Area Network (CAN) bus. Subsequently, it undergoes internal processing and forwarding within the head unit controller—including MCU data parsing, QNX communication scheduling, and other procedures before being transmitted to DSP processor. This entire process is influenced by factors such as CAN bus load, data processing delay, and internal processing/forwarding delays of the head unit controller, resulting in non-negligible reference signal delay.

The second type is secondary path delay. Within the integrated head unit controller system, the control signals generated by the ENC algorithm undergo a complete transmission and feedback chain—encompassing signal mixing, DAC (Digital-to-Analog) conversion, power amplifier driving, loudspeaker sound radiation, in-vehicle acoustic wave propagation, microphone pickup, ADC (Analog-to-Digital Conversion) conversion, and audio bus feedback before ultimately being fed back to head unit controller’s processing module. This entire chain, which integrates both electronic conversion and acoustic propagation processes, includes loudspeaker-to-microphone acoustic path delay, ADC/DAC conversion delay, audio bus transmission delay, and algorithm buffering delay. All these components collectively contribute to a non-negligible secondary path delay.

This study focuses on revealing the influence mechanism of the reference signal delay and the secondary path delay on the performance of the in-vehicle ENC system, which are key factors for optimizing ANC effects in a real head unit control integrated environment.

2.2. FxLMS algorithm

The FxLMS algorithm employed in the ENC system is illustrated in Figure 2, where P(z) is the primary path and S(z) is the secondary path. The control filter at time n is defined as w(n) with length $N_{w}$ , $w (n) = {[w_{0} (n), w_{1} (n), \cdot \cdot \cdot, w_{N_{w} - 1} (n)]}^{T}$ .The reference signal x(n) is used to generate the control signal y(n) that drives the secondary loudspeaker through the adaptive filter.

y (n) = x^{T} (n) w (n)

(1)

Here

x (n) = {[x (n), x (n - 1), \cdot \cdot \cdot, x (n - N_{w} + 1)]}^{T}

is the reference signal vector, the control signal y(n) is filtered through the secondary path S(z) to obtain the control signal y'(n) at the error microphone position:

y^{'} (n) = {\bar{y}}^{T} (n) S

(2)

\bar{y} (n) = {[y (n), y (n - 1), \cdot \cdot \cdot, y (n - N_{s} + 1)]}^{T}

{S = [S_{0}, S_{1}, \cdot \cdot \cdot, S_{N_{s} - 1}]}^{T}

is a secondary path weight vector of length

N_{s}

Figure 2.

Block diagram of conventional FxLMS algorithm.

The residual signal picked up by the error microphone can be represented as:

e (n) = d (n) + y^{'} (n)

(3)

d(n) is the primary noise signal at the error microphone.

The updating formula for the control filter is:

w (n + 1) = w (n) - μ x_{r} (n) e (n)

(4)

Where μ is the step size,

x_{r} (n) = {[x_{r} (n), x_{r} (n - 1), \cdot \cdot \cdot, x_{r} (n - N_{w} + 1)]}^{T}

is the filtered reference signal vector.

x_{r} (n)

is given by the following equation:

x_{r} (n) = x_{s}^{T} (n) S^{'}

(5)

Here

x_{s} (n) = {[x (n), x (n - 1), \cdot \cdot \cdot, x (n - N_{s} + 1)]}^{T}

{S^{'} = [{S_{0}}^{'}, {S_{1}}^{'}, \cdot \cdot \cdot, {S_{N_{s} - 1}}^{'}]}^{T}

is the estimated value of the actual weight vector s of the secondary path, which is generally obtained through offline or online modeling methods.²⁷

2.3. Embedding of the reference signal delay module

Based on the FxLMS algorithm, the ENC system incorporates a DDS (Direct Digital Synthesis) module to generate a reference signal x(n) based on the engine speed signal, which reflects real-time characteristics of engine noise. Nevertheless, a certain lag effect inevitably arises, which can be attributed to inherent delays in signal processing (e.g., signal acquisition, filtering, ECU delay, and CAN signal transmission delay). To simulate the reference signal transmission lag phenomenon in actual vehicle operating environments, a delay module is embedded into the reference signal path of FxLMS algorithm illustrated in Figure 2.

As shown in Figure 3, the time delay module is located between the reference sensor and the adaptive filter, and its function can be described as:

r (n) = x (n - int (\frac{d e l a y_r e f}{T}))

(6)

x(n) is the original reference signal converted by the DDS module, delay_ref is the time of reference delay, T is the sampling interval, int (

\cdot

) means taking the integer value. r(n) represents the delayed reference signal, which serves as the input to the adaptive filter. This delay directly modifies the phase characteristics of the reference signal, thereby influencing the update of filter coefficients and the generation mechanism of control signals. Quantitative analysis of reference delay impact on the ENC module is conducive to optimizing the engine speed signal acquisition, CAN signal transmission, and internal forwarding processes of the head unit controller, ultimately enhancing the system’s robustness.

Figure 3.

Block diagram of FxLMS algorithm with additional reference signal delay.

2.4. Embedding of the secondary path delay module

In the ENC system based on the FxLMS algorithm, the secondary path $S_{d} (z)$ and its estimation model ${S_{d}}^{'} (z)$ are integrated into the delay module to simulate the total transmission delay of the secondary path in actual vehicular environments, as illustrated in Figure 4. This delay comprises two components: one is the delay associated with electro-acoustic conversion and signal transmission, and the other is the delay induced by acoustic propagation and structural coupling. By introducing secondary path time delay (delay_sec) to quantify the transmission lag effect, this module directly influences the interference cancellation efficiency between the control signal y′(n) and the primary noise d(n). Quantitative analysis of this impact mechanism is crucial for guiding the layout optimization of loudspeakers and microphones, reducing the inherent delay of the audio hardware, and thereby enhancing the system’s stability under dynamic operating conditions.

Figure 4.

Block diagram of FxLMS algorithm with additional secondary path delay.

2.5. The comprehensive impact of time delay on the system

Considering that engine noise is the superposition of several unrelated harmonic noises, the frequency of each harmonic can be modeled and analyzed independently. To determine the effect of delay on noise reduction at a specific frequency, the primary noise d(n) is assumed as a sinusoidal signal:

d (n) = A_{d} \cos (w_{d} n T + ϕ_{d}),

(7)

A_{d}

w_{d}

, and

ϕ_{d}

represent the amplitude, frequency, and phase of d(n) respectively, the reference signal

x (n)

can also be expressed as the following sinusoidal sequence:

x (n) = A_{0} \cos (w_{0} n T + ϕ_{0}),

(8)

A_{0}

w_{0}

, and

ϕ_{0}

represent the amplitude, frequency, and phase of

x (n)

. Let

Δ_{r e f}

represent the sampling points of reference signal delay, the system function

H_{x} (z)

of the time delay can be expressed as:

H_{x} (z) = z^{- Δ_{r e f}},

(9)

Assuming the secondary path is perfectly modeled, $S (z) = S^{'} (z)$ , the transfer function $H (z)$ between $d (n)$ and $e (n)$ is:

H (z) = D_{H A} / [D_{H A} + β S (z) D_{H B}],

(10)

Here:

D_{H A} = z^{2} - 2 z c o s (w_{0} T) + 1,

(11)

D_{H B} = [z c o s (w_{0} T - ϕ_{d}) - \cos ϕ_{d}],

(12)

β = μ {A_{0}}^{2} .

(13)

Let $S_{d} (w)$ be the power spectral density of the primary noise $d (n)$ , then the power spectral density of the error signal $S_{e} (w)$ is:

S_{e} (w) = {| H (e^{j w}) |}^{2} S_{d} (w),

(14)

H (e^{j w})

is the frequency characteristic function of

H (z)

. For the

d (n)

expressed in Equation (7), the power spectral density of primary noise

S_{d} (w)

is:

S_{d} (w) = \frac{1}{2} π {A_{d}}^{2} [δ (w - w_{d}) + δ (w + w_{d})],

(15)

The steady-state mean square value $J (\infty)$ of $e (n)$ is correlated with $S_{e} (w)$ by the following relation:

J (\infty) = \int_{- \frac{1}{2}}^{\frac{1}{2}} S_{e} (w) d w,

(16)

Assuming the amplitude of $e (n)$ before control is $A_{d}$ , the noise reduction NR can be obtained from Equations (7)–(13):

N R = - 10 \log_{10} [J (\infty) / {(\frac{\sqrt{2}}{2} A_{d})}^{2}] = - 10 \log_{10} [4 {N_{A}}^{2} / (D_{N A} + D_{N B})] d B,

(17)

Let $ζ$ denote the frequency variation of the reference signal within a single sampling interval, and define $w_{d} = w_{0} + 2 π ζ Δ_{r e f}$ , each variable in Equation (17) can be expressed as follows:

N_{A} = \cos ((w_{0} + 2 π ζ Δ_{r e f}) T) - \cos (w_{0} T),

(18)

\begin{array}{l} D_{N A} = [β \cos ((w_{0} + 2 π ζ Δ_{r e f}) T + ϕ_{d}) \cos (w_{0} T - ϕ_{d}) \\ {- β \cos^{2} (ϕ_{d}) + 2 N_{A} \cos ((w_{0} + 2 π ζ Δ_{r e f}) T)]}^{2} \end{array},

(19)

\begin{array}{l} D_{N B} = [β \sin ((w_{0} + 2 π ζ Δ_{r e f}) T + ϕ_{d}) \cos (w_{0} T - ϕ_{d}) \\ {- β \sin (ϕ_{d}) \cos (ϕ_{d}) + 2 N_{A} \sin ((w_{0} + 2 π ζ Δ_{r e f}) T)]}^{2} \end{array},

(20)

This result indicates that the overall noise reduction performance of the system is closely correlated with the delay of the reference signal.

For secondary path delay, define the sampling points as $Δ_{\sec}$ , the corresponding system function $H_{s} (z)$ is given by:

H_{s} (z) = z^{- Δ_{\sec}},

(21)

The relational expression satisfying Equation (17) can also be derived through the theoretical deduction sequence from Equation (10) to Equation (16).

3. Numerical simulation

To further verify the impact of delay on ENC performance, engine noise signals under uniform acceleration condition are generated for numerical simulation. During vehicle operation, the engine speed is generally maintained within the range of 600–3000 rpm (revolutions per minute, referring to the number of rotations performed by the engine per minute), with the corresponding fundamental frequency concentrated between 20 Hz and 100 Hz. Assuming that the engine speed varies uniformly over time, Figure 5 separately depicts speed rise curve corresponding to the simulated sine noise signal for speed variations of 60 rpm ( $ζ$ = 0.001), 600 rpm ( $ζ$ = 0.010) and 900 rpm ( $ζ$ = 0.015) occurring within a 1-second interval.

Figure 5.

Speed rise curve corresponding to the sine noise signal for simulation under different $ζ$ .

Here, the amplitude of the reference signal is set to 1.0, the initial phase is uniformly set to 0, the sampling frequency is 2000 Hz, and the reference signal frequency is set to twice the 50 Hz frequency value, i.e. 100 Hz, equivalent to a normalized reference frequency of $π / 10$ . As is shown in Figure 6(a), the noise reduction decreases as delay_ref increases. Furthermore, a larger frequency variation per unit sampling interval results in a lower theoretical maximum noise reduction performance of the system. Given that the delay of reference signal and secondary path have analogous impact on ENC system, as is shown in Figure 6(b), the trend of noise reduction curve related to $Δ_{r e f}$ is consistent with that of $Δ_{\sec}$

Figure 6.

The relationship curve between noise reduction and signal delay sampling points of the FxLMS algorithm under different $ζ$ :(a) $Δ_{r e f}$ , (b) $Δ_{\sec}$ .

4. Experiments

4.1. Signal acquisition

A simulation model of the ENC system was established on the MATLAB platform, and the impact of delay on noise reduction performance was evaluated through real-vehicle tests. The test vehicle was a production model of Chery Automobile Co., Ltd. (equipped with a 4-cylinder engine) and was tested on a standardized smooth road to mitigate tire noise interference. The data acquisition system adopted the Siemens SCM205 vibration and noise test system as core data acquisition device, which was mounted on the vehicle as illustrated in Figure 7(a). Additionally, a G.R.A.S. Type 46AE 1/2-inch capacitive microphone (sensitivity: 39.5 mV/Pa) was configured as the error microphone, installed on the left roof handle of the driver’s compartment as shown in Figure 7(b); the reference signal was derived from the original hall-type crankshaft position sensor of the vehicle (58 pulses per rotation).

Figure 7.

Data acquisition system: (a) Main data acquisition equipment; (b) Schematic diagram of microphone arrangement.

The experimental conditions are summarized in Table 1, which include primary noise data collected under three operating conditions: idle steady-state at 4000 rpm, wide-open throttle (WOT) in 1st gear and partially-open throttle (POT) in 1st gear. Additionally, the table includes secondary path modeling data, where the left front door woofer of the original vehicle was employed as the secondary sound source. The key experimental parameters are specified as follows: a sampling rate of 65536 Hz; a white noise signal with a bandwidth of 3200 Hz used for modeling; data stored in 32-bit floating-point WAV format (dynamic range: 144 dB); the secondary sound source was driven by an S.M.S.L DA-1 power amplifier (total harmonic distortion (THD) < 0.003%).

Table 1.

Configurations of each recording.

Recording team	Channel configuration	Working condition	Duration
1	Channel 1: Microphone, Channel 2: Rotational speed signal	Steady idling speed: 4000 rpm	90 s
2	Channel 1: Microphone, Channel 2: Rotational speed signal	Full throttle acceleration in first gear	15 s
3	Channel 1: Microphone, Channel 2: Rotational speed signal	Partial throttle acceleration in first gear	15s
4	Channel 1: Microphone, Channel 2: Rotational speed signal	Static secondary path modeling	20 s

4.2. Parameter settings

In the experiments, the sampling rate was set to 2000 Hz via down sampling; the orders of the secondary path filter and the control filter were fixed at 128 taps, and the step-size parameter μ was dynamically adjusted to suitable value corresponding to the current delay. It should be noted that an inappropriate step size would cause the entire ENC system to diverge, making subsequent experiments unfeasible. Therefore, the step size under each delay condition is set to the value when the ENC system reaches its best performance.

Based on the Wiener solution of the secondary path identified in Group 4 of Table 1 (as illustrated in Figure 8), the secondary path delay is 4 ms, with its energy concentrated in the first 60 taps. This indicates that a 128-tap filter is sufficient to fully characterize the secondary path. To avoid model distortion, the upper limit of delay_sec is set to 25 ms.

Figure 8.

Coefficient of secondary path.

In the subsequent experiments, delay_ref and delay_sec were incrementally increased in steps of 5ms (equivalent to 10 sampling points), to investigate their specific impacts on the performance of ENC system. Given that the test vehicle is equipped with a 4-cylinder engine, and engine noise is dominated by second-order harmonics, the simulation focuses on evaluating the noise reduction performance for the second-order harmonic component.

5. Result analysis

5.1. Impact of reference signal delay

To quantify the independent impact of reference signal delay on system performance, delay_sec is fixed at 0ms and delay_ref is adjusted using the control variable method. A key 4 second segment of WOT and POT acceleration process is selected, with an engine speed rise rate of 900 rpm/s (i.e., the engine speed increases by 900 revolutions per second). The initial noise waterfall plot of WOT condition is illustrated in Figure 9(a), which shows significant second-order noise energy concentrated in the rapid acceleration interval from 0.5 to 2 seconds.

Figure 9.

Simulation results of WOT condition: (a) Waterfall plots of noise with ANC off, (b) Waterfall plots of noise with ANC on with delay_ref = 0, (c) sound pressure level of second order with ANC off and on.

It should be noted that the reference signal collected in the experiment was directly extracted from the output of the hall-type crankshaft position sensor, and its transmission delay was negligible (<0.1 ms). In actual vehicle operating environments, the ENC module is typically integrated into the head unit controller. When the engine speed signal is forwarded to the ENC algorithm module via head unit controller, a forwarding delay is inevitably introduced, the magnitude of which depends on factors such as CAN bus load, data processing delay, and MCU parsing delay. Therefore, the essence of this study is to clarify the influence mechanism of engine speed signal forwarding delay on ENC performance under real operating conditions.

When delay_ref = 0, the residual noise signal after ENC is shown in Figure 9(b), the ENC algorithm can converge rapidly and stably, and the second-order noise reduction effect is obvious. For a more intuitive observation of the result, the second-order noise sound pressure level (SPL) before (ANC off) and after ENC(ANC on) is shown in Figure 9(c), where the overall second-order noise is reduced by 10-20 dB in the 1∼3s interval. Similarly, for the POT condition, Figure 10(a) and (b) show the primary and residual noise waterfall plots, the overall second-order noise decreases by 5-8 dB in the 1∼1.5 s segment.

Figure 10.

Simulation results of POT condition:(a) Waterfall plots of noise with ANC off, (b) Waterfall plots of noise with ANC on with delay_ref = 0, (c) sound pressure level of second order with ANC off and on.

By gradually increasing delay_ref, the noise waterfall plots after ENC are illustrated in Figure 11(a)∼(f) (WOT) and Figure 12(a)∼(f) (POT); the comparison of second-order sound pressure level noise reduction is presented in Figure 13. It can be seen from Figure 13 that as the delay of reference signal increases, the ENC noise reduction performance shows systematic deterioration. The waterfall plots in Figure 11 shows that the second-order noise frequency change rate $ζ$ of WOT condition is approximately 0.015 during the 1.7∼2.3 s interval. When delay_ref = 20 ms, the noise reduction performance deteriorates by less than 4 dB compared to delay_ref = 0 ms, and the system can still maintain effective noise reduction; but when delay_ref increases to 30 ms, the noise reduction effect begins to significantly degrade, and when delay_ref extends to 80 ms, the ENC system is basically invalid. This result clearly validates the relationship, identified in simulation, between the noise reduction level and the speed rise curve.

Figure 11.

Waterfall plots of noise with different delays in WOT and ENC on condition:(a) delay_ref = 10 ms, (b) delay_ref = 20 ms, (c) delay_ref = 30 ms, (d) delay_ref = 40 ms, (e) delay_ref = 60 ms, (f) delay_ref = 80 ms.

Figure 12.

Waterfall plots of noise with different delays in POT and ENC on condition:(a) delay_ref = 10 ms, (b) delay_ref = 20 ms, (c) delay_ref = 30 ms, (d) delay_ref = 40 ms, (e) delay_ref = 60 ms, (f) delay_ref = 80 ms.

Figure 13.

Sound pressure level of second order with ENC off and on in condition of different reference signal delays:(a) WOT, (b) POT.

For the POT condition in Figure 12, The value $ζ$ is approximately 0.012 during the 2 s∼2.5 s interval, delay_ref varies from 0 ms to 20 ms ( $Δ_{r e f}$ = 40), resulting in a maximum noise reduction difference of approximately 2.5 dB. When delay_ref varies from 0 ms to 40 ms ( $Δ_{r e f}$ = 80), maximum noise reduction difference is approximately 4.6 dB. With increasing delay_ref, the noise reduction performance exhibits no further significant deterioration, which also aligns with the relationship between noise reduction and $Δ_{r e f}$ shown in Figure 6(a).

For the idle steady-state condition at 4000 rpm, the study found that the reference signal delay has almost no impact on ENC noise reduction performance, as shown in Figure 14(a)∼(c). For periodic signals, the controller has a sufficiently long impulse response to generate a phase-matched cancellation filter without causality effects.²⁸ Therefore, even with certain reference signal delay, the system can still achieve good noise reduction effects.

Figure 14.

Waterfall plots of noise at 4000 RPM static condition:(a) ENC off, (b) ENC on with delay_ref = 0, (c) ENC on with delay_ref = 50 ms.

It can be seen that the impact of reference signal delay is strongly correlated with the dynamic variation of the engine speed. For conditions with rapid engine speed changes (like WOT or POT), an increase in reference signal delay leads to severe degradation of the ENC system’s noise reduction performance, and its tolerance for delay is significantly lower than that under steady-state conditions.

Therefore, in the design of ENC systems for actual vehicles, strict control of the engine speed signal forwarding delay is essential (a maximum delay no more than 20 ms is recommended) to ensure effective noise reduction under dynamic operating conditions.

5.2. Impact of secondary path delay

To quantify the independent impact of secondary path delay on system performance, this subsection fixes the reference signal delay to 0ms, and adjusts the secondary path delay through the method of controlling variables. Similarly, taking a key segment of WOT and POT acceleration process lasting 4s, the results when delay_sec = 0ms are consistent with the baseline group in Section 5.1 (i.e., the results shown in Figure 9(a) and Figure 10(a)).

It should be particularly noted that the two signals collected in the experiment for identifying the secondary path are directly connected to data acquisition system, the circuit delay can be ignored, and is essentially the physical propagation delay of the sound wave. In actual vehicle environment, the ENC module is generally integrated in the head unit controller, which will introduce audio bus loop delay (including ADC/DAC conversion, audio bus and algorithm buffer delay, etc.). Therefore, the essence of this section is to reveal the influence mechanism of the loop delay of the domain control audio bus on the performance of ENC.

With a gradual increase in the parameter delay_sec, the noise waterfall plots with ENC on are illustrated in Figure 15(a)∼(f) (WOT) and Figure 16(a)∼(f) (POT), while the comparative analysis of ENC effect in terms of the second-order sound pressure level is presented in Figure 17. It can be observed that the increase of secondary path delay induces a remarkable deterioration in noise reduction performance, and secondary path delay plays a more decisive role than the reference signal delay on the final noise reduction performance. Specifically, under the same delay, the noise attenuation rate ranges from 30% to 60%. When delay_sec is set at 5 ms, the system maintains a stable noise reduction performance. As the delay increases to 10 ms, the noise reduction starts to decline, with a performance reduction of less than 5 dB relative to the case of delay_sec = 0 ms, and the system still retains its effective noise reduction capability. However, once delay_sec reaches 25 ms, the ENC system essentially becomes invalid.

Figure 15.

Waterfall plots of noise in WOT condition with different secondary path delay: (a) delay_sec = 5 ms, (b) delay_sec = 10 ms, (c) delay_sec = 15 ms, (d) delay_sec = 25 ms.

Figure 16.

Time-frequency spectrogram of noise in POT and ENC on condition with different secondary path delay: (a) delay_sec = 5 ms, (b) delay_sec = 10 ms, (c) delay_sec = 15 ms, (d) delay_sec = 25 ms.

Figure 17.

Sound pressure level of second order with ENC off and on with different secondary path delays:(a) WOT, (b) POT.

For the steady-state idle condition of 4000 rpm, the research found that the secondary path delay has almost no effect on the noise reduction performance of ENC, as shown in Figure 18(a)∼(c).

Figure 18.

Time-frequency spectrogram of noise at 4000 RPM static condition: (a) ENC off, (b) ENC on with delay_sec = 0; (c) ENC on with delay_sec = 20 ms.

It can be seen that the influence mechanism of secondary path delay on system performance is similar to that of reference signal delay, with both being highly dependent on the dynamic variations of engine speed. For example, during the 1s∼1.5s interval, when delay_sec varies from 0ms to 10ms ( $Δ_{r e f}$ = 20), the maximum noise reduction difference is about 3.5dB under WOT condition and 1.2dB under POT condition. When delay_sec varies from 0ms to 25ms ( $Δ_{r e f}$ = 50), maximum noise reduction difference under WOT and POT conditions both exceed 6dB. This phenomenon, similarly, aligns with the correlation observed in simulation results shown in Figure 6(b).

Therefore, to ensure the noise reduction effectiveness of the ENC system under the dynamic operating conditions of actual vehicles, the total delay of the audio bus must be strictly controlled at a low level (a maximum delay no more than 10 ms is recommended), so as to guarantee effective noise reduction in dynamic scenarios. ms) to ensure effective noise reduction under dynamic working conditions. Notably, the experimental results reveal that the maximum secondary path delay is significantly lower than the maximum reference signal delay. This phenomenon occurs because reference signal delay can typically be partially compensated through the controller’s adaptive algorithms. In contrast, the secondary path delay directly disrupts the phase cancellation model built by the controller and couples with the system’s physical response (from the speaker to the error microphone), preventing the adaptive filter from accurately reconstructing the inverse waveform at the cancellation point.

6. Conclusions

This study quantitatively analyzed the impact of time delay on the performance of the vehicle-mounted ENC system through theoretical modeling, simulation and experiments, providing a clear introduction for optimizing system design (e.g., reducing signal transmission and processing latency). The main conclusions are as follows: (1) Increases in both reference signal delay and secondary path delay lead to attenuation in the system’s noise reduction magnitude under dynamic acceleration conditions, while having a negligible impact under static steady-state conditions; (2) The simulation results indicate that a higher intensity of the speed rise curve leads to a more pronounced impact on noise reduction performance. In the vehicle test, dynamic operating conditions with rapid engine speed variation (e.g., WOT or POT) are significantly more sensitive to delay than static steady-state conditions, which corresponds well with results derived from the simulation.; (3) Reference signal delay primarily simulates the delay introduced by the speed signal forwarding process in head unit controller, while secondary path delay mainly models the loop delay induced by the audio bus (including ADC/DAC conversion, bus transmission, and buffer processing). To ensure effective noise reduction under dynamic operating conditions, system design must strictly control the reference signal delay to no more than 20 ms and the secondary path delay to no more than 10 ms. This conclusion is combined with the experimental data and the maximum delay in the hardware system, which can be used as a reference for the design of the actual system.

Based on this research, we will develop delay compensation algorithms to enhance system robustness in dynamic conditions in subsequent work to solve the performance degradation problem caused by the time delay of ENC system. Furthermore, the subsequent work will cover the common multi-channel, nonlinear and road noise interactions in vehicle systems.

Footnotes

Acknowledgment

The individual contributions of each author: Yuhui Hu: Writing - original draft. Kang Ding: Experiment, Software. Xiaofan Huang: Conceptualization, Methodology. Yuting Xu: Writing - review & editing. Xu Zhong: Funding acquisition, Formal analysis, Validation. Additionally, the technical assistance of Tao Jin, Lin Yao and Yi Yang is gratefully acknowledged.

ORCID iD

Yuting Xu

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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