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Abstract
To improve the receiver sensitivity of the digitized radio-over-fiber (DRoF) transmission system, a vector quantization scheme based on probabilistic quantization codeword shaping (PQCS) is proposed. The PQCS performs quantization bits (QBs) rematching on the original codebook to optimize the proportion distribution of level ‘0’ and level ‘2’ in 4-Pulse Amplitude Modulation (PAM-4) for improving system sensitivity. A 16-Quadrature Amplitude Modulation (16-QAM) DRoF transmission system using intensity-modulation/direct-detection is employed to experimentally verify the proposed scheme. The experimental results indicate that, compared to the traditional vector quantization scheme, the PQCS method offers 1.45 dB shaping gain for system sensitivity at a bit error rate (BER) of 5 × 10−4. Nevertheless, the error vector magnitude (EVM) can be obtained below 2% when 6 and 7 QBs are adopted for 64-QAM and 256-QAM, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of broadband wireless networks and the utilization of high-frequency spectrum resources, mobile internet continually demands higher transmission rate, larger capacity, and low latency communication [1,2]. At the same time, the centralized wireless access network with radio-over-fiber (RoF) mobile fronthaul becomes a potential candidate to support high-speed Internet, Internet of Things technology, and multimedia entertainment due to the inherent benefits of RoF technology, such as large bandwidth, low loss, flexibility, and immunity to electromagnetic interference [3]. RoF technology includes analog radio-over-Fiber (ARoF) and DRoF [4]. High spectral efficiency is an inherent advantage of ARoF, but it is susceptible to noise and nonlinearity during optical transmission. Compared to ARoF, DRoF can achieve excellent signal fidelity by applying high quantization bits [5,6], while suffering from low spectral efficiency. Therefore, the primary challenge for DRoF is improving its spectral efficiency.
There are various methods to improve the spectral efficiency, such as higher-order modulation, spatial multiplexing, data compression, etc. Signal quantization, a crucial component of lossy data compression methods, can effectively improve spectral efficiency. Signal quantization can be divided into two main categories according to the dimension of quantization. One is scalar quantization, which has been widely studied as a computationally simple quantization scheme. In particular, differential pulse coding modulation (DPCM) is frequently employed in voice and picture coding because it makes use of the correlation between nearby symbols to achieve a high signal-to-quantization-noise ratio [7,8]. However, as the quantization efficiency of this method is dependent on the correlation between the signals, dedicated quantization bits are required to mitigate the bit error under poor correlation. To decrease the number of quantized digits in DRoF, statistical data compression [9] and fast statistical estimation [10] are proposed. However, the fitting process in these methods is compute-intensive. Similarly, the Lloyd algorithm [11] requires numerous operations and results in longer delay since it uses thousands of iterations to establish quantization levels and thresholds. Delta-sigma modulation [12,13], as a scalar quantization, is used in mobile fronthaul to replace filters for digital-to-analog converters (DAC), but only for devices with high sampling rates. Compared to scalar quantization, vector quantization has better compression performance than scalar quantization for large high-dimensional data, which can further improve the spectral efficiency. Recently, several vector quantization schemes have been used for DRoF systems, including self-organizing feature map (SOFM) neural network clustering [14], K-means clustering [15], and Vector Linear Prediction [16]. These schemes utilize clustering algorithms to generate optimized codebooks, which can be used to quantize and compress data. However, the performance of these methods is extremely sensitive to the outliers in the initial cluster centroid [17], making the system unstable. Discrete Cosine Transform (DCT) [18,19] is also widely used as a common lossy compression method in mobile fronthaul, which can improve bandwidth efficiency. However, the quantization errors from DCT produce large number of artifacts in the processed signal, which is difficult to eliminate [20].
Similarly, probabilistic shaping is widely used in optical communication systems as a technique that can effectively improve spectral efficiency and system sensitivity. Constellation shaping [21] obtains the shaping gains by finding the optimized probability mass function (PMF) of the QAM symbols, with a 20% improvement in maximum system reach. However, obtaining the PMF requires a complicated Blahut-Arimoto algorithm for the optical channel, which increases the computational complexity significantly. Probabilistic constellation shaping [22] adaptively and iteratively updates the data constellation probability distribution to avoid the requirement of a channel model by feeding back the symbol error of each constellation point. However, this feedback method requires the construction of an error matrix to solve the optimization problem, which will cause a serious computational cost and increase the latency of the transmission system. Probabilistic shaping with Huffman code [23] is proposed to achieve better BER performance by using nonuniform 12-QAM. However, this method has lower spectral efficiency compared to uniform 16-QAM.
In this paper, a vector quantization scheme for DRoF transmission system is proposed and experimentally demonstrated based on PQCS. After rematching $QBs$ of the codewords according to quantization probabilities, the uniform proportion distribution of bit ‘0’ and bit ‘1’ in the $QBs$ stream changes to a nonuniform one. Therefore, the proportion distribution of PAM-4 levels can be greatly optimized by using the proposed method without increasing the quantization bits. To evaluate the system’s transmission performance, a proof-of-concept experiment is carried out through a 20 km single-mode fiber (SMF) using 5-Gbaud/λ PAM-4 signals. The experimental results indicate that a 1.45 dB sensitivity improvement is obtained from the implementation of the vector quantization scheme based on the PQCS.
2. Principle
Fig . 1 shows the schematic diagram of the DRoF transmission system based on the proposed PQCS method. The digital signal process (DSP) flow at the DU’s transmitter (Tx-DSP) and AAU’s receiver (Rx-DSP) are shown in Fig. 1. OFDM samples are first generated at the transmitter and then time-division-multiplexed (TDM) into frames for carrier aggregation. The new $QBs$ stream with nonuniform distribution is obtained through the PQCS procedure. Finally, the new $QBs$ stream is coded to generate nonuniformly distributed PAM-4 signals, which are subsequently modulated onto an optical source through intensity modulation. After the fiber transmission, the received signals are processed with the same procedure in reverse.
Fig. 1. The proposed DRoF technology for digital mobile fronthaul network. DU, distributed unit; AAU, active antenna unit; E/O, electro-optical converter; O/E, optical-electro converter.
There are primarily two stages in the vector quantization process. The K-means clustering algorithm is used in the first stage to produce an offline codebook. First, as shown in Fig. 2(a), all the OFDM samples are constructed into a 2-dimension (2-D) vector sequence $V = \{ {v_i},{v_{i + 1}}|i \in [1,L]\}$ where L is the total length of the OFDM samples. The vector signal ${v_i}$ is constructed with its in-phase (${v_{Ii}}$) and quadrature (${v_{Qi}}$) components. ${v_{Ii}}$ and ${v_{Qi}}$ components on the OFDM time domain approximately follow a 1-dimension (1-D) Gaussian distribution, as shown in Fig. 2(b) and 2(c). The blue filled part represents the amplitude probability distribution of the normalized OFDM components, and the orange line represents the gaussian distribution. The 1-D Gaussian distribution can be written as:
Fig. 2. (a) Voronoi diagram of signal quantization. (b) Diagram of probability distribution function of normalized OFDM samples (In-phase). (c) Diagram of probability distribution function of normalized OFDM samples (Quadrature).
To minimize distortion, the codebook needs to be updated until the distortion threshold is reached. Equations (3) and (5) are related to the update of the codebook. The conditions for the update can be written as:
where $\delta$ denotes the distortion threshold for stopping iterations and n denotes iteration number. The second stage is quantization. As shown in Fig. 2(a), each vector in the quantization space is clustered to the nearest codeword, and the clustering process can be written as Eq. (5). Finally, the vector signals are mapped to a codeword index sequence, while its binary form is a $QBs$ stream. As mentioned above, the vector signals approximately follow a 2-D Gaussian distribution in the quantized space, so the power required for each quantization subspace is nonuniform. Consequently, $QBs$ can be rematched to each codeword according to the quantization probability distribution of the codeword to improve the sensitivity of the system.The proposed PQCS method is utilized to rematch the $QBs$ according to each codeword’s quantization probability distribution. The rematch process is shown in Fig. 3. After the codebook generation, the codebook is used to quantize the training vector set to obtain the corresponding $QBs$ stream and codeword index sequence. Then the proportion counting is performed on the index sequence. As shown in Fig. 3(a), the proportion distribution of the codeword index is nonuniform. A higher codeword index proportion represents more vector signals in that quantization subspace and a higher quantization probability of the codeword, and vice versa.
Let $c = \{ {c_i}\} ,i \in [1,k]$ denote the real-valued codeword, represented by the random variable $C$. Moreover, ${P_C} = \{ {P_C}({c_1}),{P_C}({c_2}),\ldots ,{P_C}({c_k})\}$ denotes the quantization probability distribution of each codeword, represented by the proportion distribution. In the following, the ${P_C}$ are sorted in descending order (i.e., ${x_i} < {x_{i + 1,}}i = 1,2,\ldots ,k$) if:
The objective of the $QBs$ optimization is to rematch the codeword with higher quantization probability towards lower power $QBs$. There are three constraints on $QBs$ optimization. The first constraint states that $QBs$ with high power have a high proportion of bit ‘1’ and a low proportion of bit ‘0’, (e.g., the highest power $QBs$ are ‘111 111’) and vice versa. The second constraint states that $QBs$ with equal power such as ‘000 001’ and ‘000 010’, whose decimal index value is smaller, will be rematched first. The third constraint states that the $QBs$ optimization only rearrange the codeword indexes and does not change the components of codeword. Suppose a set of codeword with $QBs = 6$ is sorted in descending order by their quantization probabilities, as shown in Fig. 3(b), the codeword ‘47’ with highest quantization probability will be rematched to the new $QBs$ ‘000 000’, and its index will be updated to ‘0’. Correspondingly, the codeword ‘37’ will be rematched to the new $QBs$ ‘111 111’ as it has the lowest quantization probability.
After codeword optimization, the initial $QBs$ stream and codeword index sequence are remapped according to the new codebook. Since the PQCS method rematches the $QBs$ of codeword according to its quantization probability, the generated $QBs$ stream has a nonuniform distribution of bit ‘0’ and bit ‘1’, which increases the proportion of level ‘0’ and decreases the proportion of level ‘2’ in the PAM-4 coding. This nonuniform distribution of PAM-4 level offers an effective shaping gain to the system sensitivity.
Traditional probabilistic shaping technique uses distribution matcher to make the probability of each symbol obey a preset probability distribution before coding, and improves the error performance by increasing the occurrence probability of constellation points in the inner circle and decreasing the occurrence probability of constellation points in the outer circle. Compared to the traditional probabilistic shaping technique, the proposed PQCS is a new technique that does not require shaping based on a specific signal distribution, but rather the training sequence of the signal to obtain the quantization probability of the codeword and make an optimization, which provides a stable and efficient solution for the DRoF transmission link.
3. Experimental setup and results
The experimental setup of the DRoF transmission system is shown in Fig. 4. The K-means without the PQCS (wo-PQCS) was also utilized in the experiment as a comparison with the proposed scheme. Figure 4(a) shows a baseband OFDM signal with a bandwidth of 100 MHz at the Tx-DSP. The M-ary QAM orders for OFDM vary among 4, 16, 64, and 256. The number of subcarriers is 1600, with a subcarrier spacing of 60 kHz. A sampling rate of 122.88 MSa/s is obtained by using 2048 IFFT/FFT points. Carrier aggregation is then performed on three 100 MHz OFDM signals. The processed signals are quantized to generate the $QBs$ stream and quantization codebook. Then, the proposed PQCS method is performed on the codebook to rematch the $QBs$. The PAM-4 signals are transmitted at a baud rate of 5 Gbaud/λ. After that, the signals are generated by using an arbitrary waveform generator (AWG, 65-GSa/s). The amplified signals from the AWG are modulated by a light wave generated by a narrow linewidth laser (1550 nm, 12 dBm). And the optical signals are injected into a Mach-Zehnder modulator (MZM, 40 GHz). The optical signals are transmitted using a 20 km SMF, and a back-to-back (B2B) transmission is also experimentally demonstrated for comparison. The optical signals are then detected by a photodetector (PD, 15 GHz). The received optical power (ROP) is adjusted via a variable optical attenuator (VOA) situated before the PD. A digital storage oscilloscope (DSO, 40 GSa/s) captures the incoming signals. For PAM-4 signal recovery, the Rx-DSP employs a decision feedback equalizer (DFE) with 30 feedforward taps and 10 feedback taps. The PAM-4 signal is decoded and converted into a binary bit sequence, which is subsequently mapped to the corresponding codeword according to the codebook generated by the PQCS method. Then the data stream is recovered into an OFDM sample sequence and used to evaluate the EVM and BER performance.
Fig. 4. Experimental setup of the proposed DRoF system. (a) Spectrum of the OFDM signal with 100 MHz bandwidth. (b) Eye diagram of PQCS under 20 km SMF transmission. AWG: arbitrary waveform generator; MZM: Mach-Zehnder modulator; SMF: single-mode fiber; VOA: variable optical attenuator; PD: photodetector; DSO: digital storage oscilloscope; Tx-DSP/Rx-DSP: digital signal processing at the transmitter/ receiver.
The length of the training vector set and the $QBs$ per sample affect system EVM performance. It can be seen from Fig. 5(a) that with the training sequence length of 9600, the EVM decreases as the $QBs$ increases because high $QBs$ can reduce the signal distortion. As illustrated in Fig. 5(c) and 5(d), the recovered constellation graphs with $QBs$ of 6 is more distinct than that with $QBs$ of 4. Nevertheless, unnecessary quantization bits will increase the quantization time and the system delay. Similarly, it can also be seen from Fig. 5(b) that though the l is critical for maintaining the quality of the codebook, its marginal effect on the EVM diminishes as it reaches above 9600. The recovered constellation graphs with l of 1200 and 9600 are shown in Fig. 5(e) and 5(f), respectively, while $QBs = 5$. Therefore, excessive training vectors cannot significantly trade the performance with raised computational complexity. To reduce the quantization time and computational complexity, the $QBs$ and l are set as 5 and 9600, which are enough to satisfy the requirements in the DRoF transmission system.
Fig. 5. (a) The EVM performances versus the $QBs$ per sample. (b) The EVM performances versus the length of the training vector. The recovered constellation graphs at (c)$QB\textrm{s} = 4,\textrm{ }l = 9600$, (d) $QB\textrm{s} = 6,\textrm{ }l = 9600$, (e) $QB\textrm{s} = 5,\textrm{ }l = 1200$, (f) $QB\textrm{s} = 5,\textrm{ }l = 9600$.
The system’s receiver sensitivity is related to the proportion distribution of each PAM-4 signal. The PAM-4 level proportion distribution using K-means with PQCS and wo-PQCS has been calculated in the DRoF system. After OFDM modulation and TDM aggregation, the same codebook is used to quantize the four random data sets using PQCS and wo-PQCS, respectively. The ratio is of number of ‘1’s to number of ‘0’s is 1:1, 2:1, 3:1, and 4:1 in data set 1, 2, 3, and 4, respectively. As shown in Fig. 6, 4 different data sets are processed by wo-PQCS to produce the uniformly distributed PAM-4 levels. The reason for this is that in order to reduce the signal distortion when using the K-means clustering algorithm for vector quantization, 10 bits (i.e.,5bits for OFDM in-phase and quadrature component sample, respectively) are used as $QBs$ the of the OFDM signal, and the signals can enter each quantization subspace relatively uniformly, thus producing uniformly distributed PAM-4 levels. In contrast, the proportion distribution of PAM-4 levels after processing by the PQCS method is nonuniform. In particular, the proportion of level “0” increased by 9.26%, 10.61%, 12.83%, and 15.05% for the four data sets, while the proportion of level “2” decreased by 9.36%, 10.35%, 12.34% and 13.65%, respectively. Since the PQCS method optimizes the $QBs$ of signal, it changes the ratio of ‘0’ and ‘1’ in the $QBs$ stream and produces nonuniformly distributed PAM-4 levels. Furthermore, the shaping effect is achieved for all four data sets using the same codebook, which proves that the codebook is universal for different patterns of data and improves the system robustness.
Fig. 6. Proportion distribution of PAM-4 levels generated by using PQCS and wo-PQCS for 4 different sets of random data.
Next, the performance of the vector quantization scheme with PQCS and wo-PQCS are investigated in the DRoF transmission system. The EVM versus ROP of the recovered OFDM baseband digital signals with PQCS and wo-PQCS is measured, as shown in Fig. 7(a). It can be observed that the EVM reduces with increasing ROP. However, the receiver sensitivity of the PQCS method is different from wo-PQCS. For instance, to obtain an EVM below the 9%, the required ROP of the PQCS method and wo-PQCS are higher than -4.5 and -1.5 dBm, respectively. When compared to the traditional scheme, the PQCS method improves receiver sensitivity by 3 dBm, which can be further enhanced with greater ROP. At the EVM of 12.5%, the threshold specified by 3GPP, the receiver sensitivity improvement reduces from 3 dBm to 1.45 dBm. Figure 7(b) shows the BER versus the ROP of the recovered OFDM baseband digital signals transmitted over 20 km. To achieve BERs below the RS-FEC 528/514 threshold (5 × 10−4), the needed ROP with PQCS and wo-PQCS is greater than -4 dBm and -3 dBm, respectively. Receiver sensitivity of the PQCS method can be increased by 1 dBm. Furthermore, the EVM of the PQCS method under the impact of bit errors is around 6.5%, which is 4.3% lower than the EVM of wo-PQCS.
Fig. 7. The EVM (a) and the BER(b) of the PAM-4 signals employing PQCS and wo-PQCS in 16-QAM versus ROP for B2B and 20 km SMF transmission.
Finally, Fig. 8(a) and 8(b) depict the EVM performances and the BER curves of the OFDM baseband digital signals versus the ROP for B2B and 20 km transmission, respectively. For 4, 16, 64, and 256-QAM orders, the $QBs$ are 4, 5, 6, and 7, respectively. The EVM changes slightly when the ROP is greater than -3 dBm. When the ROP is less than -3 dBm, the EVM rapidly increases. According to the 3GPP specification (17.5% for 4-QAM, 12.5% for 16-QAM, 8% for 64-QAM and 3.5% for 256-QAM, respectively), the ROP for 4, 16, 64, and 256-QAM orders in 20 km DRoF transmission system is restricted to roughly -5.65dBm, -4.78 dBm, -4.8dBm, -3.5dBm, respectively.
Fig. 8. The EVM (a) and the BER (b) of the OFDM baseband digital signals versus ROP for B2B and 20 km SSMF transmission by using four different modulation formats (4-QAM, 16-QAM, 64-QAM, and 256-QAM).
4. Conclusion
We have proposed a vector quantization scheme employing PQCS method for mobile fronthaul to improve the system receiver sensitivity. The proposed method was experimentally demonstrated in an OFDM-modulated system with 4, 16, 64, and 256-QAM. Compared to the traditional scheme at EVM of 12.5%, the receiver sensitivity can be improved by 1.45 dBm in the DRoF system. In addition, when $QBs = 6$ and $QBs = 7$ are adopted for 64-QAM and 256-QAM, respectively, an EVM below 2% can be obtained when the received optical power is less than -2 dBm. Therefore, our proposal is expected to offer a viable solution for the DRoF mobile fronthaul system with improved receiving sensitivity.
Funding
National Key Research and Development Program of China (2019YFB1803500); National Natural Science Foundation of China (61860206006, 62075185); Sichuan International Science and Technology Innovation Cooperation Project (2021YFH0013).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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