CN105610502A - Special visible light communication based integrated circuit for receiver - Google Patents
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Abstract
一种基于可见光通信的接收机专用集成电路,包括有依次连接的用于将得到的电流信号转化为电压信号并进行放大的跨阻放大器和用于将跨阻放大器输出的电压信号放大至数字电压水平的限幅放大器,所述跨阻放大器的输入端连接用于对从光电二极管接收到的电流进行补偿的前均衡单元的输出端,所述限幅放大器的输出端连接用于对从限幅放大器输出的电压信号进行二次补偿的后均衡单元的输入端,所述后均衡单元的输出端连接用作信号判决的比较器的输入端,所述比较器的输出构成基于可见光通信的接收机专用集成电路的输出。本发明有效地缩小了体积并减小了各模块级联时带入的误差。具有低功耗、集成度高、成本低、易于大规模生产等优点。
A receiver ASIC based on visible light communication, including a transimpedance amplifier connected in sequence for converting the obtained current signal into a voltage signal and amplifying it, and amplifying the voltage signal output by the transimpedance amplifier to a digital voltage A horizontal limiting amplifier, the input end of the transimpedance amplifier is connected to the output end of the pre-equalizing unit used to compensate the current received from the photodiode, and the output end of the limiting amplifier is connected for limiting the output from the photodiode. The input terminal of the post-equalization unit for secondary compensation of the voltage signal output by the amplifier, the output terminal of the post-equalization unit is connected to the input terminal of the comparator used for signal judgment, and the output of the comparator constitutes a receiver based on visible light communication ASIC output. The invention effectively reduces the volume and reduces the errors brought in when each module is cascaded. It has the advantages of low power consumption, high integration, low cost, and easy mass production.
Description
技术领域technical field
本发明涉及一种集成电路。特别是涉及一种基于可见光通信的接收机专用集成电路。The invention relates to an integrated circuit. In particular, it relates to a receiver application specific integrated circuit based on visible light communication.
背景技术Background technique
近年来,随着电子科技的高速发展,智能设备的用户总数和普及率逐年大幅度增加,随之增长的是人们对高速宽带多媒体通信的需求。此时传统射频通信出现频谱资源紧张的态势,加之电磁辐射干扰等因素的局限,以及人们日益重视辐射对身体健康的影响,促使产生了一种能够拓宽频谱的资源,通过绿色节能的LED灯为传输基站的通信方式——可见光通信。近几年,伴随着白光LED技术的发展,VLC技术应用于各种场景的潜力开始彰显,得到国内外愈来愈广泛地关注。In recent years, with the rapid development of electronic technology, the total number of users and the penetration rate of smart devices have increased significantly year by year, and people's demand for high-speed broadband multimedia communication has also increased. At this time, the traditional radio frequency communication has a shortage of spectrum resources, coupled with the limitations of electromagnetic radiation interference and other factors, and people's increasing attention to the impact of radiation on physical health, prompting the creation of a resource that can broaden the spectrum, through green and energy-saving LED lights. The communication method of the transmission base station - visible light communication. In recent years, with the development of white light LED technology, the potential of VLC technology in various scenarios has begun to show, and it has attracted more and more attention at home and abroad.
相比红外无线光通信系统,VLC系统中白光LED发出的光对人眼安全,因此发射功率可以很高,但由于LED的发光模式遵循朗伯发散模式,在离光源较远距离处,即便有较高的发射功率,光强依然很弱。VLC系统大多设计成光强度调制、直接检测系统(Intensitymodulation/directdetection,IM/DD),接收机光电检测器件接收到的光信号的强弱将直接决定整个系统能否正常的工作。同时LED发出的光是经过高速调制的,接收机的带宽与响应速率必须能够与调制信号光源相匹配。因此,设计出符合性能要求并且花费较低的接收机是可见光通信技术得以广泛应用的关键。Compared with infrared wireless optical communication systems, the light emitted by white LEDs in VLC systems is safe for human eyes, so the transmission power can be very high. Higher transmit power, the light intensity is still very weak. Most VLC systems are designed as light intensity modulation and direct detection systems (Intensity modulation/direct detection, IM/DD). The strength of the light signal received by the receiver photoelectric detection device will directly determine whether the entire system can work normally. At the same time, the light emitted by the LED is modulated at high speed, and the bandwidth and response rate of the receiver must be able to match the light source of the modulated signal. Therefore, designing a receiver that meets the performance requirements and costs less is the key to the wide application of visible light communication technology.
对可见光通信中接收机的研究在近两年来刚刚兴起。在设计工艺方面,以往多采用砷化镓或者双极性硅工艺来实现,但它们有成本高、功耗大、集成度低的缺点。此外,由于接收器件特性差异较大,系统整体结构所含模块较多,之间相互影响较为复杂,现有的研究主要是基于其可行性方面的研究,接收机搭建所用的也都是商用分立器件以实现功能。因此,设计用于可见光通信系统的整体独立接收机专用集成电路处于创新研发阶段,该方面还鲜有报道。The research on receivers in visible light communication has just started in the past two years. In terms of design process, gallium arsenide or bipolar silicon processes have been used to realize them in the past, but they have the disadvantages of high cost, high power consumption, and low integration. In addition, due to the large difference in the characteristics of the receiving devices, the overall structure of the system contains many modules, and the interaction between them is more complicated. The existing research is mainly based on the research on its feasibility, and the receivers are built using commercial discrete modules. device to perform the function. Therefore, the overall stand-alone receiver ASIC designed for VLC system is in the innovative research and development stage, and there are few reports on this aspect.
发明内容Contents of the invention
本发明所要解决的技术问题是,提供一种能够有效缩小体积并减小各模块级联时带入误差的基于可见光通信的接收机专用集成电路。The technical problem to be solved by the present invention is to provide a receiver application specific integrated circuit based on visible light communication that can effectively reduce the volume and reduce the error introduced when each module is cascaded.
本发明所采用的技术方案是:一种基于可见光通信的接收机专用集成电路,包括有依次连接的用于将得到的电流信号转化为电压信号并进行放大的跨阻放大器和用于将跨阻放大器输出的电压信号放大至数字电压水平的限幅放大器,所述跨阻放大器的输入端连接用于对从光电二极管接收到的电流进行补偿的前均衡单元的输出端,所述限幅放大器的输出端连接用于对从限幅放大器输出的电压信号进行二次补偿的后均衡单元的输入端,所述后均衡单元的输出端连接用作信号判决的比较器的输入端,所述比较器的输出构成基于可见光通信的接收机专用集成电路的输出。The technical solution adopted in the present invention is: a receiver ASIC based on visible light communication, including a transimpedance amplifier connected in sequence for converting the obtained current signal into a voltage signal and amplifying it; The voltage signal output by the amplifier is amplified to a limiting amplifier at a digital voltage level, the input terminal of the transimpedance amplifier is connected to the output terminal of the pre-equalizing unit used to compensate the current received from the photodiode, and the limiting amplifier The output terminal is connected to the input terminal of the post-equalization unit for performing secondary compensation to the voltage signal output from the limiting amplifier, and the output terminal of the post-equalization unit is connected to the input terminal of a comparator used as a signal judgment, and the comparator The output of constitutes the output of the receiver ASIC based on visible light communication.
所述的前均衡单元包括有:相并联的电流源和第一电容,所述电流源和第一电容的一端连接电压VDD,所述电流源和第一电容的另一端分别连接第一电阻的一端、电感的一端以及第一NMOS管的栅极,所述电感的另一端通过第二电阻接地,所述第一电阻的另一端和第一NMOS管的漏极共同连接第二NMOS管的源极,第一电阻的该端和第一NMOS管的漏极以及第二NMOS管的源极还共同构成前均衡单元的输出端连接跨阻放大器的输入端,所述第二NMOS管的漏极连接电压VDD,栅极通过第三电阻连接电压VDD。The front equalization unit includes: a current source and a first capacitor connected in parallel, one end of the current source and the first capacitor is connected to the voltage VDD, and the other end of the current source and the first capacitor is respectively connected to the first resistor One end, one end of the inductance and the gate of the first NMOS transistor, the other end of the inductance is grounded through the second resistor, and the other end of the first resistor and the drain of the first NMOS transistor are commonly connected to the source of the second NMOS transistor pole, this end of the first resistor, the drain of the first NMOS transistor and the source of the second NMOS transistor jointly constitute the output end of the pre-equalization unit connected to the input end of the transimpedance amplifier, and the drain of the second NMOS transistor The gate is connected to the voltage VDD, and the gate is connected to the voltage VDD through the third resistor.
所述的后均衡单元包括有相并联的第二电容和第四电阻,所述第二电容和第四电阻的一端共同连接所述限幅放大器的输出端,所述第二电容和第四电阻的另一端通过一个负载电阻接地,所述第二电容和第四电阻的该端还构成后均衡单元的输出端连接比较器的输入端。The post-equalization unit includes a second capacitor and a fourth resistor connected in parallel, one end of the second capacitor and the fourth resistor is commonly connected to the output end of the limiting amplifier, and the second capacitor and the fourth resistor The other end of the second capacitor and the fourth resistor are connected to the ground through a load resistor, and the output end of the post-balance unit is connected to the input end of the comparator.
本发明的一种基于可见光通信的接收机专用集成电路,通过新的系统拓扑结构,同时使用前均衡和后均衡技术提升带宽,将光接收机整体集成于一片,有效地缩小了体积并减小了各模块级联时带入的误差。整体采用标准的CMOS工艺单片集成,实现在可见光光照环境下高速数据的接收机功能,同时具有低功耗、集成度高、成本低、易于大规模生产等优点。本发明具有如下优点:A receiver application specific integrated circuit based on visible light communication of the present invention, through a new system topology, simultaneously uses pre-equalization and post-equalization techniques to increase bandwidth, integrates the optical receiver as a whole, and effectively reduces the volume and reduces the The error introduced when each module is cascaded is eliminated. The overall use of standard CMOS process monolithic integration realizes the receiver function of high-speed data in the visible light environment, and has the advantages of low power consumption, high integration, low cost, and easy mass production. The present invention has the following advantages:
1.基于新兴的可见光通信技术,实现了可见光环境下的数据接收功能,与传统的射频通信技术相比,具有适用性广,抗干扰保密性强,无电磁辐射对人体无害等优点,在危险品存放和特殊场所物品检测方面有诸多优势。1. Based on the emerging visible light communication technology, the data receiving function in the visible light environment is realized. Compared with the traditional radio frequency communication technology, it has the advantages of wide applicability, strong anti-interference and confidentiality, and no electromagnetic radiation is harmless to the human body. There are many advantages in dangerous goods storage and item detection in special places.
2.可见光接收机芯片化。使用较为成熟的CMOS工艺进行制造,代替现有的各部分分立器件系统结构,实现了高度集成化,减小体积,降低了成本。为研发微型可见光探测设备及大面积推广提供了可能。2. Visible light receiver chip. Manufactured using a relatively mature CMOS process, replacing the existing discrete device system structure of various parts, achieving high integration, reducing volume and cost. It provides the possibility for the research and development of miniature visible light detection equipment and large-scale promotion.
3.在电路结构中同时加入了前均衡和后均衡电路结构,使接收机的整体带宽得到了提升,提高了接收机的信息数据传输能力。为整体的可见光通信集成化系统进行大数据传输提供了基础。3. The circuit structure of pre-equalization and post-equalization is added to the circuit structure at the same time, which improves the overall bandwidth of the receiver and improves the information and data transmission capability of the receiver. It provides a foundation for the overall visible light communication integrated system to carry out big data transmission.
4.本电路采用低功耗的设计方式,有效地控制整体光接收机芯片的能耗,与现有接收机相比仅需要提供毫瓦级别的能量便可工作,提高了接收系统的持续工作能力,显著减轻了在实际运用中的能源消耗问题。4. This circuit adopts a low-power design method to effectively control the energy consumption of the overall optical receiver chip. Compared with the existing receiver, it only needs to provide milliwatt-level energy to work, which improves the continuous operation of the receiving system ability, significantly reducing the energy consumption problem in practical use.
综上所述,本发明提出的基于可见光通信的接收机专用集成电路结构和实施方法具有良好的应用前景。To sum up, the VLC-based receiver ASIC structure and implementation method proposed by the present invention have good application prospects.
附图说明Description of drawings
图1是本发明在可见光接收端系统应用的结构示意图;Fig. 1 is a schematic structural diagram of the application of the present invention in a visible light receiving end system;
图2是本发明基于可见光通信的接收机专用集成电路构成框图;Fig. 2 is a block diagram of a receiver application specific integrated circuit based on visible light communication in the present invention;
图3a是本发明中前均衡单元的电路原理图;Fig. 3 a is the circuit schematic diagram of front equalization unit in the present invention;
图3b是本发明前均衡单元中并联谐振回路的等效电路;Fig. 3 b is the equivalent circuit of the parallel resonant circuit in the front equalization unit of the present invention;
图3c是本发明前均衡单元中RLC网络等效电路图;Fig. 3c is the equivalent circuit diagram of the RLC network in the front equalization unit of the present invention;
图4是本发明中后均衡单元的电路原理图。Fig. 4 is a schematic circuit diagram of the post equalization unit in the present invention.
图中in the picture
1:蓝色滤波片2:集成电路芯片1: blue filter 2: integrated circuit chip
3:数字端或示波器21:前均衡单元3: Digital terminal or oscilloscope 21: Front equalization unit
22:跨阻放大器23:限幅放大器22: Transimpedance amplifier 23: Limiting amplifier
24:后均衡单元25:比较器24: Post equalization unit 25: Comparator
具体实施方式detailed description
下面结合实施过程和附图对本发明的一种基于可见光通信的接收机专用集成电路做出详细说明。A VLC-based receiver ASIC of the present invention will be described in detail below in conjunction with the implementation process and the accompanying drawings.
图1给出了本发明所应用的可见光接收端系统结构示意图。如图1所示使用硅PIN光电二极管PD作为可见光探测器,将前端白光LED发射的加载有0/1信号的可见光透过蓝色滤波片1转化为电流信号,再通过本发明的基于可见光通信的接收机专用集成电路芯片2将该微小电流信号转化为数字电压水平的电压信号。FIG. 1 shows a schematic structural diagram of a visible light receiving end system applied in the present invention. As shown in Figure 1, the silicon PIN photodiode PD is used as a visible light detector, and the visible light loaded with the 0/1 signal emitted by the front-end white light LED is converted into a current signal through the blue filter 1, and then through the visible light communication based on the present invention. The receiver ASIC chip 2 converts the tiny current signal into a voltage signal at a digital voltage level.
如图2所示,本发明的一种基于可见光通信的接收机专用集成电路,包括有依次连接的用于将得到的电流信号转化为电压信号并进行放大的跨阻放大器22和用于将跨阻放大器22输出幅度很小的电压信号放大至数字电压水平的限幅放大器23,所述跨阻放大器22的输入端连接用于对从光电二极管PD接收到的电流进行补偿的前均衡单元21的输出端,所述限幅放大器23的输出端连接用于对从限幅放大器23输出的电压信号进行二次补偿的后均衡单元24的输入端,所述后均衡单元24的输出端连接用作信号判决的比较器25的输入端,所述比较器25的输出构成基于可见光通信的接收机专用集成电路的输出端连接到数字端调制或连接示波器3。As shown in FIG. 2, a receiver ASIC based on visible light communication of the present invention includes a transimpedance amplifier 22 connected in sequence for converting the obtained current signal into a voltage signal and amplifying it, and for converting the transimpedance Impedance amplifier 22 outputs a voltage signal with a very small amplitude and amplifies it to a limiting amplifier 23 at a digital voltage level, and the input terminal of said transimpedance amplifier 22 is connected to the pre-equalizing unit 21 for compensating the current received from photodiode PD Output terminal, the output terminal of described limiting amplifier 23 is connected to the input terminal of the rear equalization unit 24 that is used to carry out secondary compensation to the voltage signal output from limiting amplifier 23, and the output terminal of described rear equalization unit 24 is connected as The input terminal of the comparator 25 for signal judgment, the output of the comparator 25 constitutes the receiver ASIC based on visible light communication. The output terminal is connected to the digital terminal for modulation or connected to the oscilloscope 3 .
所接收到的可见光信号以微弱的电流形式从PIN光电二极管PD流出,经过前均衡模块的补偿进入跨阻放大器中,由电流转化为电压小信号。再经过多级的限幅放大器进行信号放大,将得到的较大摆幅电压信号经过后均衡进行二次补偿。由于探测器自身结电容往往相对较大,加上电路各级产生的寄生影响,此时所得到的信号已经产生变形,不利于后端数字模块进行调制处理,因此在后均衡后加入迟滞比较器,对波形进行处理,达到调整波形的目的,使输出恢复为数字电压水平的原有信号,完成可见光信号的传输目的。输出端也可接入示波器来观测所接收到的信号。The received visible light signal flows out from the PIN photodiode PD in the form of a weak current, and enters the transimpedance amplifier after being compensated by the pre-equalization module, where the current is converted into a small voltage signal. Then, the signal is amplified through multi-stage limiting amplifiers, and the obtained larger swing voltage signal is post-equalized for secondary compensation. Since the junction capacitance of the detector itself is often relatively large, coupled with the parasitic effects generated by all levels of the circuit, the obtained signal has been deformed at this time, which is not conducive to the modulation processing of the back-end digital module, so a hysteresis comparator is added after post-equalization , to process the waveform to achieve the purpose of adjusting the waveform, so that the output can be restored to the original signal at the digital voltage level, and the transmission of the visible light signal can be completed. The output terminal can also be connected to an oscilloscope to observe the received signal.
前均衡是指在光电探测器产生的光生输入电流信号进入跨阻前置放大器前,通过采用补偿的手段,提高输入信号的电带宽,以恢复信号中的高频成分,避免高频信号经放大电路后因损失过大而无法恢复。本发明中的前均衡模块采用并联谐振回路峰化技术来实现。Pre-equalization means that before the photo-generated input current signal generated by the photodetector enters the transimpedance preamplifier, the electrical bandwidth of the input signal is improved by means of compensation to restore the high-frequency components in the signal and prevent the high-frequency signal from being amplified. The circuit cannot be restored due to excessive loss. The pre-equalization module in the present invention is realized by using parallel resonant circuit peaking technology.
如图3a所示,所述的前均衡单元21包括有:相并联的电流源Is和第一电容Cpd,所述电流源Is和第一电容Cpd的一端连接电压VDD,所述电流源Is和第一电容Cpd的另一端分别连接第一电阻RfA的一端、电感Leq的一端以及第一NMOS管nA1的栅极,所述电感Leq的另一端通过第二电阻Req接地,所述第一电阻RfA的另一端和第一NMOS管nA1的漏极共同连接第二NMOS管nA2的源极,第一电阻RfA的该端和第一NMOS管nA1的漏极以及第二NMOS管nA2的源极还共同构成前均衡单元21的输出端连接跨阻放大器22的输入端,所述第二NMOS管nA2的漏极连接电压VDD,栅极通过第三电阻RdA连接电压VDD。As shown in FIG. 3a, the front equalization unit 21 includes: a current source I s and a first capacitor C pd connected in parallel, one terminal of the current source I s and the first capacitor C pd is connected to a voltage VDD, and the The other end of the current source I s and the first capacitor C pd are respectively connected to one end of the first resistor R fA , one end of the inductor L eq and the gate of the first NMOS transistor n A1 , and the other end of the inductor L eq passes through the second The resistor R eq is grounded, the other end of the first resistor R fA and the drain of the first NMOS transistor n A1 are jointly connected to the source of the second NMOS transistor nA2, and this end of the first resistor R fA is connected to the drain of the first NMOS transistor nA1. The drain of A1 and the source of the second NMOS transistor n A2 also together form the output end of the pre-equalization unit 21 connected to the input end of the transimpedance amplifier 22, the drain of the second NMOS transistor n A2 is connected to the voltage VDD, and the gate The voltage VDD is connected through the third resistor RdA .
其中光电二极管PD、电流源Is和第一电容Cpd相互并联构成光电探测器的等效电路,它们分别为理想光电二极管、光电探测器的光生电流和结电容。电感Leq和第二电阻Req分别为片上电感与电阻,它们与跨阻前置放大器的输入电容Cin(约等于NMOS管nA2的栅源电容Cgs,A2)、输入电阻Rin,A构成一个并联谐振回路(如图3b)。The photodiode PD, the current source I s and the first capacitor C pd are connected in parallel to form an equivalent circuit of the photodetector, which are respectively the ideal photodiode, the photogenerated current and the junction capacitance of the photodetector. The inductance L eq and the second resistance R eq are the on-chip inductance and resistance respectively, and they are related to the input capacitance C in of the transimpedance preamplifier (approximately equal to the gate-source capacitance C gs,A2 of the NMOS transistor n A2 ) , the input resistance R in, A constitutes a parallel resonant tank (as shown in Figure 3b).
由于串联和并联的LR部分阻抗相等,有如下关系:Since the impedances of the LR parts connected in series and in parallel are equal, the relationship is as follows:
其中Q=RP/ω0LP=ω0LS/RS,则可得:Where Q=R P /ω 0 L P =ω 0 L S /R S , then:
RP=RS(Q2+1)R P = R S (Q 2 +1)
将该电路等效为典型的RLC网络(图3c),其中:Equivalent this circuit to a typical RLC network (Figure 3c), where:
R=[Req(1+Q2)]||Rin,A R=[R eq (1+Q 2 )]||R in,A
C=Cpd+Cgs,A2 C=C pd +C gs,A2
则该谐振回路的谐振频率为 Then the resonant frequency of the resonant circuit is
此外,跨阻前置放大器的负载第一NMOS管nA1和第三电阻RdA构成一个有源电感,它们与下一级的输入电容和输入电阻也构成一个并联谐振回路。通过参数优化调整使这两个谐振回路产生的谐振峰相互交叠,可有效提高前置跨阻放大器的带宽。此外,通过大幅增加用作跨阻的第一电阻RfA和用作前置电阻的第二电阻Req的阻值还可以增加光接收机的输入电阻,减小第一电阻RfA和第二电阻Req引入的噪声电流。In addition, the first NMOS transistor n A1 and the third resistor R dA of the load of the transimpedance preamplifier form an active inductance, and they also form a parallel resonant circuit with the input capacitance and input resistance of the next stage. The resonant peaks generated by the two resonant circuits overlap each other through parameter optimization and adjustment, which can effectively improve the bandwidth of the pre-transimpedance amplifier. In addition, the input resistance of the optical receiver can be increased by greatly increasing the resistance values of the first resistor R fA used as a transimpedance and the second resistor Req used as a pre-resistance, and the first resistor R fA and the second resistor R eq can be reduced. Noise current introduced by resistor R eq .
如图4所示,所述的后均衡单元24包括有相并联的第二电容C和第四电阻R,所述第二电容C和第四电阻R的一端共同连接所述限幅放大器13的输出端,所述第二电容C和第四电阻R的另一端通过一个负载电阻RL接地,所述第二电容C和第四电阻R的该端还构成后均衡单元24的输出端连接比较器25的输入端。As shown in Figure 4, the post equalization unit 24 includes a second capacitor C and a fourth resistor R connected in parallel, one end of the second capacitor C and the fourth resistor R are commonly connected to the limiting amplifier 13 The output terminal, the other end of the second capacitor C and the fourth resistor R is grounded through a load resistor RL , and this end of the second capacitor C and the fourth resistor R also constitutes the output terminal of the post-equalizing unit 24 to connect to the comparison The input terminal of device 25.
该均衡器的频率响应传输函数为The frequency response transfer function of this equalizer is
其中,1/k=RL/(R+RL),T=RC,RL是负载电阻,1/k是均衡器的直流系数(ω=0)。则其的幅值响应为Among them, 1/k= RL /(R+ RL ), T=RC, RL is the load resistance, and 1/k is the DC coefficient of the equalizer (ω=0). Then its magnitude response is
此均衡器的3dB点计算结果为The 3dB point calculation for this equalizer is
当时,此3dB点存在。在此3dB点附近,|He(ω)|近似为线性。均衡器频率响应的斜率se可以近似表示为when , this 3dB point exists. Around this 3dB point, |He (ω)| is approximately linear. The slope s e of the equalizer frequency response can be approximated as
为了使蓝光分量高频段和低频段的增益平衡,均衡器的响应要求se=-sb,sb为未加均衡时蓝光分量的频率响应曲线斜率,近似为-0.24dB/MHz。采用均衡而获得的期望带宽可以近似估计为In order to balance the gains of the high-frequency band and low-frequency band of the blue light component, the response of the equalizer requires s e = -s b , where s b is the slope of the frequency response curve of the blue light component without equalization, which is approximately -0.24dB/MHz. The expected bandwidth obtained by equalization can be approximated as
由(4)式和(5)式可以看出,T和k的选择将会决定均衡带宽以及均衡信号的增益。选择一个较大的k值,将会获得更高的调制带宽。It can be seen from (4) and (5) that the choice of T and k will determine the equalization bandwidth and the gain of the equalized signal. Choosing a larger k value will result in a higher modulation bandwidth.
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