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We design a specific cascade least mean square (LMS) equalizer and to the best of our knowledge, it is the first time this kind of equalizer has been employed for 60-GHz millimeter-wave (mm-wave) radio over fiber (RoF) system. The proposed cascade LMS equalizer consists of two sub-equalizers which are designated for optical and wireless channel compensations, respectively. We control the linear and nonlinear factors originated from optical link and wireless link separately. The cascade equalization scheme can keep the nonlinear distortions of the RoF system in a low degree. We theoretically and experimentally investigate the parameters of the two sub-equalizers to reach their best performances. The experiment results show that the cascade equalization scheme has a faster convergence speed. It needs a training sequence with a length of 10000 to reach its stable status, which is only half as long as the traditional LMS equalizer needs. With the utility of a proposed equalizer, the 60-GHz RoF system can successfully transmit 5-Gbps BPSK signal over 10-km fiber and 1.2-m wireless link under forward error correction (FEC) limit 10−3. An improvement of 4dBm and 1dBm in power sensitivity at BER 10−3 over traditional LMS equalizer can be observed when the signals are transmitted through Back-to-Back (BTB) and 10-km fiber 1.2-m wireless links, respectively.
© 2016 Optical Society of America
1. Introduction
The formidable growth of various wireless communication services requires ever increasing data throughputs. The conventional microwave band below 10GHz, which is currently exploited by fourth-generation (4G) system, such as Long Term Evolution (LTE) and Mobile WiMAX, is extremely heavily utilized within just a few years [1–3]. Technologies such as orthogonal frequency-division multiplexing (OFDM), multiple-input multiple-output (MIMO), multi-user detection, advanced channel coding, adaptive coding and modulation, hybrid auto-matic repeat request (HARQ) and cell splitting have made the frequency efficiency very close to the theoretical limits. Looking into the future, 5G wireless technologies are on the horizon, which are characterized with higher data rate, excellent end-to-end performance and ubiquitous user coverage with lower latency, power consumption and cost [4]. In order to satisfy the 5G requirements, radio access networks (RANs) are evolving into two remarkable features, as Fig. 1 shows. The first is “cloudification” where large amounts of baseband units (BBUs) of conventional cells move to a cloud-centric site. Under the benefits of the cloud RAN (C-RAN), conventional complicated and power-hungry cells sites can be simplified as remote radio heads (RRHs) which requires less capital and operating expenditure (CAPEX and OPEX) related to power consumption and site maintainance. The other obvious characteristic is exploiting new frequency resources and forming micro-cells. Higher RF such as millimeter-wave (mm-wave) is a new frequency domain for 5G wireless communication and analog radio over fiber (RoF) has been widely studied [5,6]. Since the existing cellular systems under 10GHz have nearly reached their saturation points, network designers have been paying attention to higher segments of the frequency spectrum for the sake of larger transmission capacity.
In conventional wireless communication systems, the major sources of signal impairments are the imperfections of the components of the RF branch, particularly power amplifiers (PAs) and mixers [7,8]. Practical PAs own nonlinear transfer characteristics and bring distortions into the signal as well as out-of-band radiation. When it comes to the RoF link, additional signal impairments from optical link must be taken into consideration. The linear impairments of the optical signal are usually dominated by chromatic dispersion (CD) from fiber and amplified spontaneous emission (ASE) from erbium doped fiber amplifier (EDFA). The nonlinear distortion is usually originated from modulator and O/E converter. The electro-optical device nonlinearities often depend on the bandwidth and amplitude of input signal. Practically, frequency responses of these O/Es are not flatten with a wide bandwidth, which will also cause signal distortion and inter-symbol interference (ISI).
For 60-GHz RoF systems, the distortion phenomenon will be more sophisticated when the two kinds of impairments in optical and wireless links are connected in series. When the system works at high bit rates, estimation and subsequent equalization of the concatenated fiber-wireless channel become indispensable procedures at receivers. Various kinds of adaptive algorithms for equalization have been put forward to compensate the distortions of signal through transmission [9–12]. Among these proposed algorithms, LMS equalization is the most popular due to its better adaptability in practical systems. In [13], we proved that the LMS equalizer can significantly enhance the BER performance of 60-GHz RoF system when transmitting 5-Gbps BPSK signal. Later in [14], we introduced a variable step size LMS equalizer with fast convergence speed to improve the performance.
Optical and wireless channels are entirely distinct in many aspects. For optical channel, chromatics dispersion effect is the main factor that broadens the pulse of the signal which will cause signal interference. When using EDFA in optical link, ASE is the main distortion in devices. For wireless channel, it will be another group of factors that degrade signal. Multipath effect is the essential factor that distorts signal and sometimes it will produce zero transmission points on channel amplitude-frequency characteristic curves. This effect causes serious signal interference. For wider bandwidth, PA memory effects as a kind of nonlinear effect can no longer be ignored [15]. Especially for mm-wave system, amplifiers with higher gain exhibit memory effects. In conclusion, the two kinds of impairments caused by optical and wireless channels connected in series increase the degree of the distortions degree in the whole RoF system by summation. The wireless channel is always regarded as a time variant system because of the random locations and movements of the wireless devices while for the optical link, the channel can be seen as relatively static. So contrast to the relative stable optical channel, wireless channel needs repeated equalization to track the channel status. In [16], authors studied adaptive predistortion of nonlinear distortion induced by RoF link and PAs in series and the results show that the consecutive scheme can achieve the best performances in which the RoF optical link and wireless link are compensated successively.
In this paper, we for the first time introduce a cascade LMS equalizer dedicated for 60-GHz mm-wave RoF system. The equalizer is composed of two cascaded secondary LMS equalizers, the optical equalizer and the wireless equalizer. Consecutively, the two parts separately estimate the optical and wireless channels. Experimental results show that in 60-GHz RoF system, the proposed cascade equalizer prominently increases the BER performance and has an obvious advantage over traditional LMS equalizer. Further more, with appropriate parameters setting, the cascade equalizer also has a faster convergence speed than its counterpart. With the help of the proposed cascade LMS equalizer, the 60-GHz RoF system can successfully transmit BPSK signal at bit rate 5Gbps under FEC limits 10−3 with more than 1dB improvement in power sensitivity.
2. Operation principle
2.1 Principle of the cascade LMS equalizer
For generally, there exist two kinds of algorithms to adjust the taps of equalizer, zero forcing criterion and minimum mean square error (MMSE) criterion. However, the defect of zero-forcing criterion on noise amplication limits its applications. The MMSE is more widely used in wireless and fiber communications for it takes both ISI and noise into consideration in taps updating. Among many structures used for equalization, the transversal (tapped-delay-line or nonrecursive) equalizer shown in Fig. 2 is the simplest one. The conventional LMS algorithm can be given by the following equations [17]:
where W(n) = [w0(n),w1(n),…wN(n)]T is the taps weight vector. N is taps number of the equalizer. Y(n) = [y(n), y(n-1),…y(n-N)]T is the feedback signal vector for adaption. μLMS denotes the step size, and z(n) represents the desired signal. The step size μLMS is directly proportional to convergence speed. However, there is a tradeoff between the convergence speed and equalizer taps misadjustment which is the main limitation of the LMS algorithm [18]. The misadjustment of the tap coefficients is called excess mean-square error power, which is the part of error power goes beyond the minimum attainable MSE (with tap gains frozen at their optimum settings).In order to make the analysis tractable, we introduce a following simplifying assumption that the system is assumed to be a discrete linear time invariant system and we can get the z-transformation version of the channel response of the whole system as
In general, in discrete linear time invariant system, the orders of numerator and denominator of the system response H(z) is not equal. For causal system, the order of numerator is equal to or smaller than the order of denominator (M>N). In practice, the ISI is limited to a finite number of samples in real channels [19]. Therefore, the channel response can be approximated by a finite duration impulse response (FIR) with symbol-spaced or fractionally-spaced taps. For finite sequence is convergence at the whole z-plane (|z|>0), response H(z) should not have pole points, that is to say all ak in H(z) must be zero, so we can get
In RoF system, the factors causing linear or nonlinear distortion can be mainly classified in two categories, optical link factors and wireless link factors. In Eq. (4), br contains the distortion of the cascade opti-wireless channel which will be so complicated that traditional LMS equalizer unable to completely compensate. What’s more, long orders of equalizer require a small step size, which in turn slows the adaption process [20]. To counteract these problems, we present an alternative structure for adaptive linear equalization based on least mean squares minimization in which the equalizer is formed by a cascade of smaller-order independently adapting linear filters. The channel response H(z) can be factored into a cascade of two smaller sections shown as follows:
where N1 + N2 = M. The first section H1(z) represents the response of optical channel and the second section H2(z) is the wireless channel response. To compensate the distortion, we introduce an equalizer with response of G(z). When the noise is small, the equalizer is the channel inverse.It is clear that we have H(z) = G(z)−1 if Z(z) = X(z). In this case, H(z)G(z) = 1. We also can divide the equalizer response G(z) into two sections, G(z) = G1(z)G2(z), where The two sections are designated to compensate the optical and wireless channels in RoF system respectively. In this method, we reformulate the equalization technique to estimate the parameters of the filter in cascade form rather than in direct form. The parameters of the cascade sections can be estimated by minimizing the given MSE in successive.According to the analyses above, we design a specific equalizer which contains two sub-equalizers in cascade, as shown in Fig. 2. The first sub-equalizer is utilized for optical channel equalization, and the tap values W1m(k) are adapted after each iteration in training period to make the response of the equalizer approximate to G1(z) in Eq. (7). The second sub-equalizer is employed for wireless channel compensation. After training period of optical channel, the output of the first sub-equalizer will be utilized to train the second sub-equalizer. After the two-stage training period, the cascade equalizer is ready to be used for RoF system transmission.
2.2 Theoretically analysis
The analyses above are given under an assumption that the RoF system is a linear system. However, in practice, RoF channel is very complicated. In optical link, the CD and ASE are the main sources of linear distortion. Optical channel also suffers from much nonlinear distortion. Imperfect intensity modulation and photodetector distortion are often nonlinear. In wireless link, multipath effect is the essential linear factor that distorts signal. For mm-wave system, PA memory effects can no longer be ignored, especially for amplifiers with higher gain and wider bandwidth. The memory effect is a kind of nonlinear distortion in wireless communications.
As we can see that LMS equalizer is a kind of linear equalizer which is designed to compensate linear distortion in transmission systems. LMS equalizer can perfectly solve the linear problems in the system. But in practice when it is applied to nonlinear signal sequence, people find that it’s still effectual. If the nonlinear response of the system is differentiable and time invariant, the LMS equalizer can also handle nonlinear signal with low nonlinearity order by dividing the nonlinear signal into small pieces and each piece can be regarded as a linear signal [21]. In other words, LMS equalizer can process nonlinear problem with low low degree of distortion. When the nonlinear distortion becomes severe, LMS equalizer is unable to cope with it well. So it is very important and necessary to simplify the nonlinearity of the system.
Separately processing the distortion from optical link and wireless link can greatly reduce the nonlinear degree of the RoF system and improve the performance of the system. This conclusion can be explained by two aspects. We take the memory effect in PA as an example. Both the linear and nonlinear distortion of optical link will make memory effect more complex. In the first aspect, we consider the linear distortion of optical link. So the channel response can be explained as
where x(n) and y(n) are the input and output of the optical link. According to [15], the memory polynomial model for PA nonlinearities in wireless link can be given byw(n) and z(n) are the input and output of the amplifier, respectively. K is the nonlinearity order, Q is the length of the memory. If the output of the optical link is injected into the wireless amplifier, the expression isObviously, we can see that the linear effect in the optical link will extend the length of the memory in PA, from Q to Q + N. The enlargement of memory effect will make the nonlinear distortion more complicated and bring challenges for LMS equalizer. In the second aspect, we consider the nonlinear distortion in the optical link. In this case, the optical channel can be expressed as Volterra series without the time delay [22]N is degree of optical link nonlinearity. We also consider the memory effect in PA and put Eq. (12) into Eq. (10) and we can obtainFrom Eq. (13), we can draw a conclusion that the nonlinearity order of the system will increase from K to NK. The nonlinear degree of the whole RoF system will greatly increase if the optical link nonlinearity is not properly coped with. Therefore, compensating the distortion from optical link and wireless link separately is very necessary and it is an efficient method to decrease the complexity of the distortion, especially nonlinear distortion. Compared to the single-stage LMS equalizer, the cascade LMS equalizer can better improve the RoF channel BER performance by avoiding the interaction between the two groups of distortion.3. Experimental setup and results
The experimental setup is illustrated in Fig. 3. In the IM-DD based RoF system, a distributed feedback laser device (DFB) with the center wavelength and power at 1552.08nm and 10.02dBm is utilized as a light source. A high-speed phase modulator (PM) with bandwidth larger than 40GHz is driven by a microwave source working at frequency 30GHz to produce two sidebands, illustrated in Fig. 3(a). An interleaver is utilized to suppress the central wavelength of the optical signal. The intensity modulator (IM) is driven by a 5-Gbps electrical rectangular NRZ PRBS (Pseudo-Random Binary Sequence) signal, which is generated from a signal quality analyzer. The optical spectrum of the two modulated sidebands is given in Fig. 3(b). Considering our experiment conditions, the distortion from optical link are mainly caused by CD from fiber and ASE from EDFA. These two kinds of distortion are linear. The nonlinear distortions from MZM modulation can be ignored because we adjusted the signal in modulator’s optimal linear zone and the format of modulated signal is simple (BPSK).
Fig. 3 Experimental setup for the 60-GHz RoF system employing the proposed cascade LMS equalizer. (a) and (b) are the optical sprectrums of the signals after phase modulator and intensity modulator. (c) Picture of the real experimental setup. DFB-LD: distributed feedback laser device. PM: phase modulator. IL: interleaver. EDFA: erbium doped fiber amplifier. IM: intensity modulator. PD: photodiode. EA: electrical amplifier. LPF: low-pass filter. OSC: oscilloscope. CO: central office. RAU: remote antenna unit. UE: user equipment
After the two sidebands detected by a high-speed PD (Photodiode), a pair of rectangular horn antennas with a gain of 20dBi, frequency range of 50-70GHz are used to broadcast the mm-wave component of the electrical signal at base stations (BS). The two antennas can also act as two band-pass filters to remove the baseband unused components. Two amplifiers are utilized before transmitting antenna and after received antenna respectively to compensate the great loss of the 60-GHz wireless signal in air. Limited by the gain of 60-GHz radio amplifiers, the transmission distance of 60-GHz wireless signal is limited to 1.2m. The two rectangular horn antennas’ radiation patterns are line-shape and the space between the transmitting and receiving antennas is clear, as shown in Fig. 3(c). So the multipath effect in our experiment can be ignored. However, the memory effect as a kind of nonlinear distortion in PA is severe in the experiment because we totally use three broadband amplifiers (two amplifiers with bandwidth more than 65GHz and one more than 20GHz). The signal will be inevitably distorted when bitrate up to 5Gbps. The received baseband data is then captured with a 20-GS/s real-time scope (ADC) and passed on to a computer for further analysis in Matlab.
The block diagram of offline processing is also given on the right side in Fig. 3. After synchronization, down-sampling and normalization, the captured signal will be sent into the proposed cascade LMS equalizer. The equalization algorithm is based on LMS adaption to maximize the eye-opening at the decision points. The training of the cascade LMS equalizer will be divided into two steps. At the first step, the sub-equalizer for optical link which is illustrated at the top of Fig. 3 is trained to adjust taps values to reach convergence state. At the training period, the received signal is captured at the output of PD which is defined as the end of optical link. The oscilloscope can directly detect the signal at the output of PD because after O/E conversion, the baseband of the electrical signal is also loaded with downstream information. In this method, the received signal for training the first sub-equalizer is not degraded by the distortion of wireless channel. In real RoF system, we can suppose that the optical channel is not time varying compared to wireless one. So the optical link can be estimated at the remote antenna units (RAU) initially, and after optical taps values approaching the optimal status, these values will be broadcast to user equipments (UE) under coverage through wireless links to adjust the first sub-equalizers. These values for optical equalizers will keep constant until the optical fiber distribution is changed.
At the second step, we should try to train the second sub-equalizer. In ideal condition, the distortion originated from optical channel is completely compensated at the output of the first sub-equalizer. Therefore, we can draw a conclusion that after the whole optical-wireless transmission and digital processed by the first equalizer, the received signal is only distorted by the nonlinear factors derived from the wireless link which is illustrated at the top of Fig. 3. So we can directly use the received signal at the output of first sub-equalizer to estimate the response of wireless channel. In practice, the locations of UEs are not stable. So the wireless channel is time varying and it needs frequently training to adjust the changing channel conditions. The calculation of this process is completed in UEs. After the two-step training of the cascade LMS equalizer, the output can be sent for decision and BER calculation operations.
Compared to the single traditional LMS equalizer in which the parameters includes step size, convergence speed and taps number, the parameters of the cascade LMS equalizer are much more complex. Firstly, we discuss the step size of the equalizers, which affects the BER performance and convergence speed. Usually, there is a tradeoff between the convergence speed and misadjustment. Larger step size means faster convergence speed but results in bigger misadjustment. When the step size is small, it means we can obtain a good BER performance but the convergence speed is slow. For the proposed cascade LMS equalizer, we should consider the impacts of two sub-equalizers at the same time. Figure 4(a) gives contour of the BER performance of the 60-GHz RoF system employing the proposed cascade LMS equalizer when transmitting 5-Gbps BPSK signal with received power at −28.2dBm versus values of step sizes of the two sub-equalizers. μ1 and μ2 represent the step sizes of optical and wireless equalizers, respectively. As illustrated in Fig. 4(a), in order to obtain a sufficient improvement, both the two step sizes of sub-equalizers are required to be small enough. The upper limit of the μ1 (<0.12) is much larger than μ2 and this phenomenon can be described by the fact that at first step of equalization, convergence speed is more important and the size of misadjustment is not so significant because the misadjustment will be adjusted to smaller value through second step of equalization. The μ2 must be small enough (<0.005) to ensure the misadjustment is tiny after the wireless equalizer reaches stable state. Figure 4(b) shows the iterations the equalizers need to improve the system’s BER performance when the step size of the two sub-equalizers are μ1 = 0.001 and μ2 = 0.0005. To achieve a satisfactory improvement status, enough training sequences are indispensable for both equalizers. For the system to reach BER under 10−3, the training sequence required for optical equalizer is less than 1.5 × 104, shorter than the wireless one that requires almost 2.5 × 104 training iterations. The reason is that the required step size of wireless equalizer is often smaller than the optical one. Compared to wireless link, optical link is simpler because the distortion is linear in the experiment.
Fig. 4 BER performances of the 60-GHz RoF system when transmitting 5-Gbps BPSK signal with received power at −28.2dBm versus (a) values of step sizes of the two sub-equalizers and (b) training iterations for two sub-equalizers.
In order to further study the convergence process of the cascade equalizer, MSE value as a function of iterations is investigated. To make the data smooth enough to be observed, the curve is the average value of MSEs after 200 times running. To make the experimental data more convincible, we introduce traditional LMS algorithm proposed in [18], as a reference for the cascade method. In the first experiment, the step sizes of the two sub-equalizers are set to be μ1 = 0.001 and μ2 = 0.0005 and the step size of traditional LMS equalizer is μ = 0.0005 and μ = 0.001. When μ = 0.0005, the traditional LMS equalizer can obtain its best BER performance. The MSE results are given in Fig. 5(a) in which the optical equalizer takes nearly 10000 iterations to reach convergence status and the wireless equalizer consumes about 15000 iterations to reach stable status and obtain optimal BER performance. The MSE jump between the two training stages is caused by the remaining distortion of wireless link in the second group of training sequence. In the first part, the optical link, the convergence for the consecutive equalizer is faster compared to the traditional. However, this phenomenon does not completely depend on the size of step size. When the traditional LMS equalizer and optical equalizer in cascade scheme have the same step size μ1 = μ = 0.001, the traditional LMS equalizer still converges slower than the cascade one because the traditional LMS equalizer need to compensate more complex distortion. The division of the distortion factors between optical and wireless channels simplified the compensation difficulty compared to simultaneously compensating the whole optical-wireless link. Therefore, we can observe that the cascade one can achieve a smaller MSE value than the traditional one which means better compensation efficiency. What’s more, as analysis in Fig. 4(a), the μ1 do not need to be very small because the misadjustment will be minimized in the second stage. In our second experiment, the step size of the optical sub-equalizers are modified to be μ1 = 0.01. In Fig. 5(b), it is joyful to observe that without sacrificing the BER improvement, the convergence speed is greatly promoted since the optical equalizer only needs about 1000 iterations to appropriate convergence state.
Fig. 5 Results of the MSE of the cascade equalizer when the step size of traditional LMS equalizer is μ = 0.0005 and μ = 0.001 (a) step size of optical and wireless equalizers are μ1 = 0.001, μ2 = 0.0005 and (b) μ1 = 0.01, μ2 = 0.0005, respectively.
The BER performances of system versus iterations with received power at −28.2dBm at bitrate 5Gbps are shown in Fig. 6. In this experiment, in the case μ1 = 0.001, μ2 = 0.0005, the iterations allocation for optical and wireless channels is 1:1. In the case μ1 = 0.01, μ2 = 0.0005, the iterations for optical channel are set be 1000 constantly, because after 1000 iterations, the optical equalizer can reach its convergence state which can be observed in Fig. 5(b). From Fig. 6, we can draw a conclusion that with suitable parameters, the cascade scheme not only has a greater improvement for BER performance of the RoF system, but also has a faster convergence speed. The cascade scheme takes 10000 iterations to achieve its optimal status which is only half number of the traditional scheme.
Fig. 6 The BER performances of system versus the number of iterations with received power at −28.2dBm at bitrate 5Gbps.
The impact of taps number over the proposed cascade equalizers and traditional single LMS equalizer is illustrated in Fig. 7. In practice, the first stage should use a low-order filter as a pre-convergence equalizer to compensate optical channel. The second stage should adopt a longer filter, which works well for general signals and can reach a better convergence state [23]. So we can set the proportion of optical and wireless equalizer as 1:2. As illustrated in Fig. 7, as the taps number growing, both the two kinds of equalizers can improve their performances. When the total number of the cascade equalizer is 60 with taps proportion of 1:2 (taps number of optical and wireless equalizers are 20 and 40 respectively), the BER performance reaches its optimal point −3.47dB with received power at −24.2dBm.
Fig. 7 BER performances of 60-GHz RoF system employing cascade equalizer or single LMS equalizer versus taps number when the optical received power is −24.2dBm.
The BER performances versus received power of the system at bitrate 5Gbps are demonstrated in Fig. 8(a) and (b). The traditional LMS equalizer with taps number 120 is introduced as a reference, which has been illustrated in our previous works [13, 14]. Step sizes of the cascade equalizer are μ1 = 0.01, μ2 = 0.0005 and taps number of optical and wireless equalizers are set at 20 and 40. Both schemes are trained by sufficient amount of training sequence to achieve optimum status. Using the cascade equalization scheme discussed above, the BER performance is improved significantly as indicated by the eye diagrams placed at the right side of figures. In fiber Back-to-Back (BTB) and wireless 1.2-m transmission case, shown in Fig. 8(a), the required power under BER 10−3 using cascade scheme is −28.2dBm which has an increment about 4dBm in power sensitivity over the traditional LMS equalization scheme. When it comes to the case fiber 10-km and wireless 1.2-m transmission, illustrated in Fig. 8(b), an 1dBm power sensitivity improvement over traditional one can be observed. Compared to the fiber BTB case, the advantage of the proposed cascade scheme over its counterpart decreases. The reason for this phenomenon is that after long fiber transmission, the compensation of optical channel by optical equalizer is not ideal.
Fig. 8 Comparisons of different equalization schemes for 60-GHz RoF system with (a) BTB and (b) 10-km SMF and 1.2-m wireless link when transmitting 5-Gbps BPSK signal.
To sum up, compared to the traditional direct LMS equalizer, the cascade of short filters allows larger step sizes which results in a faster and more agile route to convergence. The cascade form also divides the distortion factors from optical and wireless channels and alleviates the degree of compensation difficulty. Smaller MSE can be obtained, which means a better BER performance. In view of engineer, the cascade form need less storage units and be less susceptible to zero points drifting, so it will be easy to implement in practice.
4. Conclusions
We proposed a special cascade LMS equalization scheme suitable for 60-GHz RoF system transmission. With the help of the proposed equalizer, the 60-GHz RoF system can successfully transmit 5-Gbps BPSK signal over 10-km fiber and 1.2-m wireless link under FEC limit 10−3. Firstly, we theoretically discuss the advantage of cascade LMS equalizer and it can decrease the complexity of the RoF link. Then we study the impact of the parameters of the proposed cascade LMS equalizer including step size, convergence speed and taps number. We draw conclusions that to reach optimal convergence status, the step size of optical equalizer can be much bigger than the wireless one, μ1 = 0.01, μ2 = 0.0005. What’s more, the taps number of optical equalizer should be smaller than wireless one. Compared to the traditional direct LMS equalizer, the cascade scheme means faster convergence speed and greater BER improvement. The cascade equalizer needs a training sequence with length of 10000 to reach its stable status which is only half long of the traditional LMS equalizer needs. An improvement of 4dBm and 1dBm in power sensitivity at BER 10−3 when transmitting through BTB and 10-km fiber 1.2-m wireless transmission can be observed, respectively. The experiment shows that the 60-GHz RoF system with cascade equalization scheme can satisfied the required multi-gigabit capacity for mobile backhauling transmission and with a faster convergence speed. It can timely adapt to the sophisticated optical-wireless channel.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant No. 61431003, and 61372038 and the Fund of the State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Post and Telecommunications), China.
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