Design Optimization of Feedforward Equalization for Mobile Fronthaul Based on Delta-Sigma Modulation With High-Order QAM Signals

Delta-sigma modulation can be used as a high spectral efficiency interface in place of conventional common public radio interface (CPRI) in mobile fronthaul (MFH) networks. However, inter-symbol interference (ISI) becomes more difficult to be mitigated in the networks due to bit quantization in delta-sigma modulation. In this paper, we propose a novel feedforward equalization (FFE) scheme based on the least mean square (LMS) algorithm for MFH networks employing 4th-order delta-sigma modulation technology with 1 and 2 bit quantization to alleviate the performance degradation caused by ISI. The performance of both 1-bit and 2-bit quantization systems employing the proposed FFE scheme with different tap lengths and step sizes has been systematically investigated. Our results show that, under the minimum computational complexity, the maximum transmission capacity can reach 8.98 Gbps when using the FFE scheme with 11 taps and step size of 3 × 10-5 or 3.5 × 10-5 and the average error vector magnitude (EVM) can be minimized to a level less than 0.032 with 19 taps and step size of 4 × 10-5 or 4.5 × 10-5 for 1-bit quantization system while for 2-bit quantization system, the maximum transmission capacity of 11.4 Gbps can be obtained when employing the FFE scheme with 19 taps and step size of 3.5 × 10-5 and the minimal average EVM less than 0.01 can be achieved with 19 taps and step size of 4 × 10-5. More hopefully, this work provides guidelines for optimizing the equalization scheme based on the requirements of EVMs, capacity, and computational complexity.

high-definition videos and virtual/augmented reality (VR/AR) in 5G and beyond, exponential growth of demands for data traffic are posing a great challenge with more strict requirements of higher capacity, lower latency, complexity and cost in mobile fronthaul (MFH) networks [1], [2].Radio-over-fiber (RoF) technique is widely considered as a promising solution to the challenge where the radio signals transmitted from the centralized baseband unit (BBU) to the cell-site remote radio heads (RRHs) are achieved via optical fronthaul transmission links [3], [4].Currently, RoF technique is mainly implemented in two major forms: analog radio-over-fiber (A-RoF) and digital radio-over-fiber (D-RoF).Compared to D-RoF, A-RoF has attracted more research attention in recent decade due to its inherent advantages of high spectral efficiency, high flexibility and low-complexity/cost implementation [5].However, a nonnegligible shortcoming of A-RoF is the vulnerability to the noise and the signal impairments and distortion caused by fiber nonlinearity [6].Despite D-RoF technique employing Common Public Radio Interface (CPRI) [7], [8], [9] is commonly considered as low bandwidth efficiency, which leads to the bottleneck of digital MFH to support massive mobile data transmission [10], theoretically it can achieve similar bandwidth efficiency as A-RoF under similar channel conditions, signal-to-noise ratios (SNRs) or error vector magnitudes (EVMs).
To realize bandwidth efficiency improvement for D-RoF and further increase the capacity of MFH networks, delta-sigma modulation technique was proposed for MFH networks [11], [12] where an analog-to-digital converter (ADC) with sampling rate much higher than conventional Nyquist ADC is applied to quantify the analog signals into digital ones, which enables the delivery of analog signals through digital ports and the data recovery of the received signals at RRHs using only a filters without expensive and high-linearity digital-to-signal converters (DACs) [13], [14].Moreover, a unique advantage of the deltasigma modulator is the functionalization of noise shaping which pushes the quantization noise out of the signal band [15].Due to the aforementioned advantages, delta-sigma modulation technique has attracted extensive research interest and various study has been carried out such as the combination of hierarchical and delta-sigma modulations [16], ultra-high-order delta-sigma modulator [17] and novel feedback structures [18] to further improve the system performance and increase the transmission capacity in recent years.Nevertheless, to explore the benefits enabled by delta-sigma modulation, inter-symbol interference (ISI) needs to be eliminated via digital signal processing (DSP) since it's recognized as the main challenge to high-speed transmission systems.Otherwise, strong ISI can lead to performance degradation, wrong data recovery and even link outage.To solve the issue, equalizers based on feedforward or decision feedback architectures for delta-sigma in digital domain have been proposed and demonstrated [19], [20].Despite, the proposed feedforward equalizers (FFEs) possess the advantage of low computational complexity, they fail to compensate the signal impairments caused by chromatic dispersion (CD) [21] via field information, which is attributed to the multipath effect when lightwave propagates along the fiber, since the original analog signals are usually quantified into intensity modulated (OOK or PAM-4) signals.To alleviate system performance degradation caused by ISI, a variety of equalization approaches such as constant modulus algorithm (CMA) [22], modified cascade multiple modulus algorithm (M-CMMA) [23], least mean square (LMS) [24], [25] and recursive least-square (RLS) [26], [27] equalization have been proposed for original high-order complex-valued signals and investigated extensively in recent decades.However, additional carrier phase estimation (CPE) employing the fourth power algorithm [28] within each equalization iteration is indispensable to recover the phase information of the received signals, which increases the computational complexity and the cost of training sequence significantly.
To further reduce the computational complexity of the FFE scheme for MFH networks employing delta-sigma modulation while preserving the capability of compensating CD-induced signal impairments, in this paper, we propose a novel FFE scheme based on LMS algorithm without CPE for improving the performance of MFH networks employing a 4th-order deltasigma modulator with both 1-bit and 2-bit quantization.We systematically investigate the system performance using the proposed FFE scheme with different tap lengths and step sizes.The simulation results show that, for the lowest computational complexity, the maximum transmission capacity of 8.98 Gbps can be obtained for 1-bit quantization system when employing the FFE scheme with 11 taps and step size of 3 × 10 -5 and 3.5 × 10 -5 and the minimum average EVM less than 0.032 can be achieved with 19 taps and step size of 4 × 10 -5 or 4.5 × 10 -5 .Meanwhile, for 2-bit quantization system, the maximum transmission capacity can reach 11.4 Gbps with the proposed FFE scheme of 19 taps and step size of 3.5 × 10 -5 and the minimal average EVM reaches below 0.01 when employing the proposed FFE scheme with lap length of 19 and step size of 4 × 10 -5 .The study indicates the system performance can be improved significantly by employing FFE.
The rest of this paper is organized as follows: Section II presents the principles of delta-sigma modulation and our proposed feedforward equalization scheme.Section III illustrates the simulation setup and results.Section IV concludes the paper.

A. Principle of Delta-Sigma Modulation
The operation principle of conventional CPRI is shown in Fig. 1(a), where Nyquist sampling scheme is employed.By contrast, in delta-sigma modulation scheme, the input analog signals are sampled with oversampling rate of where f s is the sampling rate and B is the signal bandwidth.Consequently, the quantization noise is extended over a wide frequency area, which is shown in Fig. 1 The designed 4th-order delta-sigma modulator based on cascade-of-resonators feedforward (CRFF) structure is shown in Fig. 2(a), in which the reciprocal of the noise transfer function (NTF) can be expressed as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where z = e 2πf /f s .a-f represent the feedback coefficients of the delta-sigma modulator, which can be obtained using R. Schreier's toolbox [29] or genetic algorithm [30], [31].Based on the aforementioned principles, we obtain the NTF curve and the pole-zero diagram of the delta-sigma modulator which is illustrated in Fig. 2(b) (c) respectively.Fig. 2(d) shows the spectrum of the output of the delta-sigma modulator.It can be observed from both NTF curve and the output spectrum that more than 30 dB SNR gain can be obtained by using the delta-sigma modulator, which enables the recovery of the received signals at low received optical power after filtering the quantization noise.

B. Principle of Feedforward Equalization
The quantized signal R(t) is firstly split into In-phase (I) and Quadrature (Q) sequences by a pair of orthogonal matched filters m I (t) and m Q (t), which can be written as where f c is the central frequency of the received signal spectrum.After band-pass filtering, the obtained data sequences are combined to recover the original high-order complex-valued signals, which can be expressed as ) where H BPF (t) represents the responsitivity of the band-pass filter.Therefore, the recovered complex-valued signal in frequency domain is illustrated as where ω c = 2πω c .Assume the pulse shape of the transmitted OOK or PAM-4 symbols can be defined as g(t) with amplitude of a n and the symbol interval is T s , then the transmitted symbols can be written as [32] where E and ω 0 represents the amplitude and the angular frequency of the electrical field of the lightwave, respectively.V c and ω c is the amplitude and the angular frequency of the RF clock.Assume only one symbol interval is considered for ease of calculation and analysis, then the transmitted signals in frequency domain can be expressed as where Sa(x) = sin(x)/x, ω f = ω c -ω 0 and ω p = ω c +ω 0 .τ is the pulse width.After propagation in the fiber, the received signals can be expressed as where μ is the amplitude attenuation coefficient.β and z t represents the propagation constant and the transmission length in the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
fiber.Then the received signals are detected by the photodetector (PD) with square-law detection, which can be expressed as where α is the responsitivity of the PD.Substitute ( 10) into ( 6), the final expression of the recovered signal in frequency domain can be written as We can further write (10) as where H(ω) is the transfer function that results in ISI in the system because of CD.To eliminate ISI caused by CD, the recovered signal is required to be multiplied by 1 H(ω) , which can be written as 1 where w n are tap coefficients which can be obtained using FFE based on LMS [24], [25] and RLS [26], [27] algorithms et al.For conventional FFE scheme based on LMS algorithm, the output of the equalized complex-valued symbols can be expressed as where s(k) represents the k-th symbol of the received signal s and w(k) is the k-th symbol of the tap coefficient vector w and is updated as where η is the step size and 0<η<1.d(k) is the k-th symbol of the desired output.θ(k) represents the k-th symbol of the estimated phase information via CPE using the fourth power algorithm [28], which can be expressed as where M is the length of the received signal s in frequency domain.
In this paper, to relax the dependence on carrier phase estimation within the equalization of the recovered complex-valued symbols and further reduce the computational complexity, we propose a novel FFE scheme based on LMS algorithm, where the output of the equalizer is written as Different from conventional FFE based on LMS algorithm, here w is initialized with complex values to enable the equalization for complex-valued signal directly.w * denotes the conjugation of w, which is updated as Here to obtain quick and sufficient convergence, the tap coefficient vector is updated using the training sequence with length of 6000.After convergence, the update of the tap coefficient vector stops and the received signals are equalized by multiplying the latest tap coefficient vector directly.which is driven by a distributed feedback (DFB) laser with central wavelength of 1550 nm to generate optical signals for 30 km standard single-mode fiber (SSMF) transmission.The dispersion parameter of the SSMF is set as 17 ps/nm/km.At the optical network unit (ONU), the received signals are converted into photocurrent by a photodetector (PD).Prior to the RRH, the converted photocurrent is first split by a pair of matched filters m I (t) and m Q (t).After that low-pass filtering (LPF) is performed to filter out the quantization noise at the high-frequency domain.Next, the obtained data sequences are combined to format the original QAM symbols.The later DSP stage consists of a carrier de-aggregation process that de-aggrates the 32 CCs of digital signals for baseband processing followed by the FFE based on Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.LMS algorithm to mitigate the ISI.Finally, EVM calculation is operated to evaluate the whole system performance.

B. Results and Discussion
We first investigate the performance of the MFH network with delta-sigma modulator with 1-bit quantization.Fig. 4 shows the maximum achievable capacity of different tap coefficients and iteration step sizes for the MFH network with delta-sigma modulator.The maximum achievable capacity can be expressed as where B c represents the bandwidth of each CC.Since the required multiplications and additions/subtractions for LMS-based equalizer is 2N+1 and 2N respectively within each iteration [34], where N is the tap length of the LMS-based equalizer, the computational complexity of the FFE scheme can be written as O(N).The minimum average value of EVM with the minimum computational complexity can be achieved when employing the FFE scheme with 19 taps and step size of 4.5 × 10-5 or 4 × 10-5 as the computational complexity of FFE increases with the taps.
The performance of the MFH network employing delta-sigma modulator with 2-bit quantization is also investigated, where the maximum achievable capacity of different tap coefficients and iteration step sizes is presented in Fig. 6.Similarly to the case of 1-bit quantization, here the maximum achievable capacity can be written as where N 3 is the number of the CCs of which the EVM meets the 3GPP specification for 1024QAM.We can observe that the maximum transmission capacity of 11.4 Gbps corresponding to the case of N 2 = 14 and N 3 = 18 can be obtained when the cases of (a) tap number: 19, step size: 3.5 × 10 -5 ; (b) tap number: 23, step size: 4.5 × 10 -5 ; and (c) tap number: 27, step size: 4 × 10 -5 are employed.We also illustrate EVM distribution of the CCs of the aforementioned cases in the respect inserts in Fig. 6.Since the computational complexity of FFE increases with the taps, the maximum transmission capacity with the minimum computational complexity can be obtained when the tap length of the FFE scheme is 19 and the step size is 3.5 × 10 -5 .
The EVM performance of different tap coefficients and iteration step sizes for the MFH network employing delta-sigma modulator with 2-bit quantization is depicted in Fig. 7, where the minimum average value of EVM less than 1% can be obtained when the cases of (I) tap number: 19, step size: 4 × 10 -5 ; (II) tap number: 23, step size: 4.5 × 10 -5 ; (III) tap number: 27, step size: 4 × 10 -5 and (IV) tap number: 27, step size: 3 × 10 -5 are adopted.Also shown is the constellation diagrams of the recovered signals of CC 10 , CC 15 , CC 22 and CC 27 with the cases (I)-(IV) respectively.The minimum average value of EVM with the minimum computational complexity can be obtained when case (I) is adopted, since the computational complexity of FFE increases with the tap length as described previously.

IV. CONCLUSION
In conclusion, to mitigate ISI issue in MFH networks based on delta-sigma modulation technology, we have proposed a novel LMS based FFE scheme for MFH networks employing 4th-order delta-sigma modulator with both 1-bit and 2-bit quantization.The number of taps and step size of the FFE has been systematically studied to achieve the optimal performance.Results show that, for the lowest computational complexity, the maximum transmission capacity of 8.98 Gbps can be obtained when employing the FFE scheme with 11 taps and step size of 3 × 10 -5 or 3.5 × 10 -5 and the minimum average EVM less than 0.032 can be achieved with 19 taps and step size of 4 × 10 -5 or 4.5 × 10 -5 for 1-bit quantization system.For 2-bit quantization system, the maximum transmission capacity reaches 11.4 Gbps when the tap length of the FFE is 19 and step size is 3.5 × 10 -5 while the minimum average EVM less than 0.01 can be obtained with 19 taps and step size of 4 × 10 -5 .Based on the results, we believe our study can provide guidelines for selecting an optimal equalization scheme based on the integrated requirements of EVMs, capacity and computational complexity.
(b).After 1-or-2-bit quantization, the sampled signals are converted into on-off keying (OOK) or 4-level pulse amplitude modulation (PAM-4) signals.Meanwhile, noise shaping is performed to push the quantization noise out of the signal bandwidth.As shown in Fig.1(c), the noise is mainly concentrated at the high-frequency domain while the signal is located at low-frequency domain.At the receiver, the original data stream can be retrieved from the quantified OOK or PAM-4 signals by filtering the quantization noise out of the signal bandwidth using a low-pass filter without digital-to-analog convertors (DACs) as shown Fig.1(d).

Fig. 3
Fig. 3 illustrates the simulation setup of the MFH network using delta-sigma modulation.At the baseband unit (BBU), 32 component carriers (CCs) of mobile signals with each bandwidth of 20 M are aggregated for DSP, in which respective 16 CCs1of 64QAM and 256QAM for 1-bit quantization and 10 CCs of 1024QAM and 22 CCs of 256QAM for 2-bit quantization are accommodated and all EVMs of them meet the specifications for 3GPP (1024QAM 1%, 256QAM 3.5% and 64QAM 8%) [33].After that, the signals are fed into a delta-sigma modulator and up-sampled with sampling rate of 10.5 Gsa/s, in which the OSR of 8 is employed and digitalized into 10 Gbaud OOK signals by 1-bit quantization or PAM-4 signals by 2-bit quantization after noise shaping.Next, the generated PAM-4 signals are loaded onto a Mach-Zehnder Modulator (MZM)which is driven by a distributed feedback (DFB) laser with central wavelength of 1550 nm to generate optical signals for 30 km standard single-mode fiber (SSMF) transmission.The dispersion parameter of the SSMF is set as 17 ps/nm/km.At the optical network unit (ONU), the received signals are converted into photocurrent by a photodetector (PD).Prior to the RRH, the converted photocurrent is first split by a pair of matched filters m I (t) and m Q (t).After that low-pass filtering (LPF) is performed to filter out the quantization noise at the high-frequency domain.Next, the obtained data sequences are combined to format the original QAM symbols.The later DSP stage consists of a carrier de-aggregation process that de-aggrates the 32 CCs of digital signals for baseband processing followed by the FFE based on

Fig. 4 .
Fig. 4. Contour map for the maximum achievable capacity of different tap coefficients and iteration step sizes for the MFH network using delta-sigma modulator with 1-bit quantization and corresponding EVM distribution of the CCs.

Fig. 5 .
Fig. 5. Contour map for the EVM performance of different tap coefficients and iteration step sizes for the MFH network using delta-sigma modulator with 1-bit quantization and corresponding constellation diagrams of the recovered signals of the CCs.

Fig. 6 .
Fig. 6.Contour map for the maximum achievable capacity of different tap coefficients and iteration step sizes for the MFH network using delta-sigma modulator with 2-bit quantization and corresponding EVM distribution of the CCs.
N 1 and N 2 is the number of the CCs of which the EVM meets the 3 GPP specification for 256QAM and 64QAM respectively.It can be found that the maximum transmission capacity of 8.98 Gbps (N 1 = 19 and N 2 = 13) can be achieved when the cases of (a) tap number: 11, step size: 3 × 10 -5 ; and (b) tap number: 11, step size: 3.5 × 10 -5 are adopted.Also shown is the EVM distribution of the CCs of the aforementioned cases.We also investigated the EVM performance of different tap coefficients and iteration step sizes for the MFH network with delta-sigma modulator with 1-bit quantization, which is shown in Fig.5.It can be seen that the minimum average value of EVM less than 3.2% can be obtained when the cases of (I) tap number: 19, step size: 4.5 × 10 -5 ; (II) tap number: 19, step size: 4 × 10 -5 and (III) tap number: 23, step size: 4 × 10 -5 are adopted.Also shown is the constellation diagrams of the recovered signals of

Fig. 7 .
Fig. 7. Contour map for the EVM performance of different tap coefficients and iteration step sizes for the MFH network employing delta-sigma modulator with 2-bit quantization and corresponding constellation diagrams of the recovered signals of the CCs.