Sigma-delta RoF system realization

Figure 3(a) shows the structure of a ΣΔ-modulator. It is obtained by replacing the quantizer, the 1-bit ADC, in the first-order ΣΔ-modulator with a copy of a first-order ΣΔ-modulator. Considering again ideal components, the output, y(kT), takes the form:

(1)$$y( {kT} ) = x( {k-1} ) T) + Q_e( {kT} ) -2Q_e( {( {k-1} ) T} ) + Q_e( {( {k-2} ) T} ) .$$

Fig. 3.

Block diagram representing the second-order ΣΔ modulation (a) structure and (b) its Z transfer domain model.

Equation (1) represents that output is a delayed quantized input signal with a second-order differencing of the quantization noise. Figure 3(b) shows its linear z-domain model, from which the NTF and the STF can be obtained:

(2)$$\eqalign{V_{out}( z ) = & \;STF( z ) V_{in}( z ) + NTF( z ) Q_e( z ) \cr V_{out}( z ) = & z^{{-}1}V_{in}( z ) + ( {1-z^{{-}1}} ) ^2{\rm \;}Q_e( z ) , \;} $$

where V _out(z) and V _in(z) are output and input, respectively, while Q _e(z) represents the quantization noise. The integrator blocks I ₁ and I ₂ are expressed, respectively, by I ₁ = 1/(1 − z ⁻¹) and I ₂ = z ⁻¹/(1 − z ⁻¹). In (2), STF is the signal transfer function, while NTF is the noise transfer function.

The magnitude of the NTF is evaluated as follows:

(3)$$\vert {NTF( {e^{\,j2\pi f}} ) } \vert ^2 = ( {2\sin ( {\pi f} ) } ) ^4\approx ( {2\pi f} ) ^4, \;{\rm for}\;f\ll 1.$$

Similarly, the in-band noise power of the output for the second-order SDM can be calculated as:

(4)$$\sigma _{in}^2 = \smallint \vert {NTF} \vert ^2.S_p( f ) df = \displaystyle{{\pi ^4} \over {15 \times {( {OSR} ) }^5}}, \;$$

where S _p(f) is the power spectral density (PSD) and OSR is over sampling ratio. If we consider again a sin wave as the input with amplitude A, the output becomes:

(5)$$\sigma _{out}^2 = \displaystyle{{A^2} \over 2}.$$

Since |STF|² = 1.

The signal to noise ratio (SNR) is computed as follows:

(6)$$\eqalign{SNR = & 10\log _{10}\left({\displaystyle{{\sigma_{out}^2 } \over {\sigma_{in}^2 }}} \right)\cr \;\; = & 15\;A^2\displaystyle{{{( {OSR} ) }^5} \over {2\pi ^4}}\;{\rm \;\;}( {{\rm dB}} ) .} $$

The frequency response of the second-order $\sum \Delta M$ is given in Fig. 4(a) in linear scale and in dB scale in Fig. 4(b). It also shows that the quantization noise is highly attenuated in the band of signal near 0 and is eminently invigorated in high, out of band frequencies, more than it undergoes in case of first-order $\sum \Delta M$ [Reference Wang, Liu, Zhang, Zhu, Xu, Lu, Cheng and Chang23].

Fig. 4.

Frequency response of second-order $\sum \Delta M$: (a) magnitude in linear scale, (b) magnitude in dB.

From Eq. (6), the doubling of the OSR leads to an increase of the SNR by 15 dB, which means that to achieve the same value of SNR, the second-order $\sum \Delta M$ needs a lower OSR, leading to a lower sampling frequency, when compared with the first-order $\sum \Delta M$. The downside is the increased total noise power, as stated previously.

The details of the ΣΔ-M model implied can be found in [Reference Fouto and Paulino40–Reference Hadi, Nanni, Venard, Baudoin, Polleux and Tartarini43].

Figure 5 shows the experimental test bed utilized for this work. Let us consider an in-phase denoted as I and quadrature represented by Q baseband signals. This pair of baseband signals is sigma-delta converted by 1-bit ΣΔ modulators at 6 GSa/s. The unwanted and relatively high quantization noise will be filtered out at the receiver. The sigma-delta modulated baseband signals are then up-converted with carrier frequency f _c = 3 GHz. This is followed by the electrical-optical conversion according to the typical A-RoF approach.

Fig. 5.

Experimental test bed for real-time implementation of sigma-delta radio over fiber system. I-BB, Q-BB, in-phase and quadrature baseband, respectively; ΣΔMOD, sigma-delta modulator; Optical Tx, optical transmitter; SMF, single mode fiber; LNA, low noise amplifier; BPF, band-pass filtering; RTO, real-time oscilloscope; VSA, vector signal analyzer; Param. Eval., parameters evaluation.

The optical converted signals are transmitted over standard single mode fibers (standard SMFs). At the receiver, the photodiode converts the optical signal back to electrical domain followed by a reconstruction BPF which filters out most of the quantization noise.

The module has a capacity to implement 4x parallel transmitters, and 4 ΣΔ-RoF links of the kind of the one represented in Fig. 5 have consequently been realized to fully exploit its potentiality. To bring the optical signal to the respective RRHs, a cable composed of SMFs is utilized, terminated with MTP connectors. For simplicity, the results referred to only one lane proof will be shown.

The baseband signal generation, its sigma-delta modulation, and up-conversion represented in Fig. 5 are implemented on Xilinx Virtex Ultrascale VCU108 FPGA Evaluation Kit. After the FPGA performs sigma-delta modulation followed by up-conversion, the 1-bit modulated stream is fed to Module QSFP28-PIR4-100G (1310 nm distributed feedback (DFB) laser) employed for the electrical-optical conversion to transmit over SSMF. The module used has allowed min power = −9.4 dBm, max power = 2.0 dBm in the transmitting mode and min power = −12.66 dBm, max power = 2 dBm in the receiving mode, however, it can be pushed below the safe limits for seeing the trend. The received signals are then fed to respective RRH units having a low noise amplifier that amplifies the received signal and sends it to an analog BPF tuned at the RF signal center frequency. A properly designed BPF eliminates the out-of-band quantization noise shaped by the SDM and guarantees that the spectral mask requirements are met. The band-pass filtered signals are fed to UXR1004A Infiniium UXR real-time oscilloscope that runs the vector analysis software for post processing of data and parameters evaluation. The noise current spectral density around f _c is 16 ${\rm pA/}\sqrt {{\rm Hz}}$. The module QSFP28-PIR4-100G has four transmitters where each one has a clock data recovery to resample the data if needed. The parameters and values are given in Table 1.

Table 1.

System parameters

Table 1 below shows the detail of setup and parameters utilized.

Experimental results and discussion

Firstly, the performance of the system is measured by estimating the ACLR. ACLR is defined as follows [44]:

(7)$$ACLR{\rm \;}( {{\rm dB}} ) = \displaystyle{{{\rm Power}\;{\rm in}\;{\rm the}\;{\rm adjacent}\;{\rm channel}} \over {{\rm Power}\;{\rm in}\;{\rm the}\;{\rm transmitted}\;{\rm channel}}} = 10\log _{10}\left[{\displaystyle{{\mathop \smallint \nolimits_{B_{Al}}^{B_{Au}} S( f ) {\rm \;}df} \over {\mathop \smallint \nolimits_{B_{Ul}}^{B_{Uu}} S( f ) {\rm \;\;}df}}} \right].$$

Here B _Al represents the lower and B _Au are the upper frequency limits of one of the adjacent channel bands. Similarly, B _Ul is the lower and B _Uu are the lower and upper frequency limits of the useful channel bands. S(f) represents the measured PSD of the output signal.

One of the most important measurements is the leakage power in the adjacent channels. ACLR is considered as a critical specification for digital communication systems corresponding to signal distortion leaking in the neighbor channels. Leakage power influences the system capacity as it interferes with the transmission in adjacent channels. Therefore, it must be rigorously controlled to guarantee a stable system capacity. ACLR limits are given in standards for the whole system. As defined in 3GPP TS 34.122, ACLR should not be more than −33 dB at the offsets of ±1.6 MHz.

The adjacent channel power ratio of a wireless communication system is the integrated power in the carrier channel relative to the adjacent channel. The non-linearity distortion in the link can downgrade the transmission performance of an RoF system since the non-linearity can generate spurious cross-talks that may overlap with the transmitted RF signal and leak the power into the adjacent RF channels. Among all the non-linear spurious products, the third-order intermodulation distortion attracts more attention because it probably falls into the passband of a multicarrier system and is difficult to be filtered out. Excessive non-linearity limits the power of the input signal, therefore degrading the dynamic range performance. Usually, we use robust distortion measure called as ACPR when we study the non-linearity-induced cross-talk in an RoF system. ACPR is the wideband equivalent to the input intercept point of order 3 case.

Figure 6 represents the experimental evaluation of ACLR with respect to changing fiber length L and input RF power P _IN, respectively. It can be appreciated that for a given P _IN, ACLR increases with increasing L. Conversely, for a given L, higher values of P _IN lead to higher ACLR values. The worst value reported in Fig. 6 is therefore the one corresponding to P _IN =  0 dBm and L = 10 km, for which it is ACLR = −29.59 dBc. Figure 6 refers to the transmission of a 256 − QAM signal, with symbol equal to 400 MBd. Note however that the ACLR evaluation has been performed transmitting a 256 − QAM signal, with the symbol rate that ranged from 100 to 400 MBd, and the behavior of ACLR resulted to be substantially the same regardless of the symbol rate considered.

Fig. 6.

Measured ACLR at the receiving end of the SD-RoF system, versus input power and for varying values of L.

In order to keep ACLR at lower values, which means lower detriment given to adjacent channels from the creation of undesired distortion terms, it should be then appropriate to keep P _IN as low as possible, within the range allowed.

To better specify this requirement, the system performance is measured by EVM. EVM can be mathematically expressed as [Reference Hadi, Aslam and Jung39]:

(8)$$EVM\;( \% ) = \sqrt {\displaystyle{{1/N\mathop \sum \nolimits_{\,j = 1}^N [ {{( {{\tilde{I}}_j-I_j} ) }^2 + {( {{\tilde{Q}}_j-Q_j} ) }^2} ] } \over {1/N\mathop \sum \nolimits_{\,j = 1}^N [ {{( {{\tilde{I}}_j} ) }^2 + {( {{\tilde{Q}}_j} ) }^2} ] }}} , \;$$

where N is the total number of symbols received, I _j is the received in-phase component of the j − th received symbol, while $\tilde{I}_j$ is the ideal in-phase component of the same symbol. Similarly, Q _j is the quadrature component of the j − th received symbol, while $\tilde{Q}_j$ is its ideal quadrature component. The 3GPP standard has set an EVM limit for LTE signals modulated by 256 QAM format to be 3.5% [Reference Vieira and Gomes28].

The EVM is then evaluated for varying values of P _IN and for different link lengths L. For this estimation, the symbol rate was marked as 400 MBd. The obtained results are summarized in Fig. 7, where it can be seen that for a given value of L, increasing the values of the input power allows to obtain the EVM to fall below the values of 3.5%. For a given P _IN, an EVM increase is observed for L going from 0.1 to 10 km, due to the increasing path loss undergone by the transmitted signal.

Fig. 7.

EVM with changing input power for different lengths at 400 Mbd.

In Fig. 8, the received constellation diagram is compared when a 256 QAM signal is transmitted with 400 MBd and with P _IN = 0 dBm through the minimum and maximum ΣΔ-RoF link lengths, respectively. It is observable that for L = 100 m the received constellation diagram is clean, while for L = 10 km it is rather noisier. However, looking again at Fig. 6, it can be observed that in the two cases, the EVM is respectively 1.01 and 2.48%, i.e. both configurations fall below the threshold of 3.5% set by 3GPP.

Fig. 8.

Constellations corresponding to the received signal EVM with input power P _IN = 0 dBm, for different lengths at 400 Mbd.

A behavior similar to the one reported in Fig. 9 is also observable for the other values of L considered. In order to summarize all the measured performances, Fig. 10 reports for each considered value of L value minimum value P _{IN,min, EVM<3.5%} below which P _IN cannot fall in order to guarantee EVM < 3.5%. It can be appreciated that when transmitting at 400 Mbd it is P _{IN,min, EVM<3.5%} = −12  dBm for L = 0.1 km, while it is P _{IN,min, EVM<3.5%} = −6  dBm for L = 10 km.

Fig. 9.

Reports the EVM for 10 km link length with symbol rates ranging from 100 to 400 MBd, at different values of input power P _IN. It is visible that performing an increase from the value P _IN = −16  dBm, for which it is EVM>3.5% for all the symbol rates considered, the EVM monotonically decreases and, starting with the 100 MBd and ending with the 400 MBd case, the transmission is gradually attainable while respecting the EVM limit.

Fig. 10.

Minimum RF input required to achieve a determined baud rate for different link lengths.

In line with the considerations developed above, the values of P _{IN,min, EVM<3.5%} can be identified as the optimized ones, since they maintain the ACLR at the lowest possible value, while allowing the received EVM to accomplish the 3GPP requirement. As far as the range of the power of the optical transceiver QSFP28-PIR4-100G is concerned, the minimum power allowed is −12.66 to 2 dBm (receiving mode) and −9.4 to 2 dBm (transmitting mode)[Reference Hadi, Nanni, Polleux, Traverso and Tartarini45]. In our experiments, we pushed the device below this threshold, however, we only report the results in the range mentioned in the data sheet for which device is supposed to work.

Table 2 summarizes this result in the case of transmission of a 256 QAM signal at 400 MBd.

Table 2.

Optimized RF input powers for different lengths of the SD RoF system considered when transmitting a 256 QAM LTE signal at 400 MBd, with the corresponding values of EVM and ACLR