Chapter 3 DIGITAL MODULATION TECHNIQUES
3.4 Multiple-Input Multiple-Output
The data throughput of communication system proportions to the bandwidth of wireless and the SNR. However, the bandwidth of wireless system is limited and it is hard to increase the SNR of a system. One of powerful techniques to improve data throughput is the MIMO technology. For the wireless communication system, the MIMO use multiple antennas at both the transmitter and receiver to improve system performance.
Figure 3-18 shows the principle of a MIMO technology [76, 77]. There are M transmitter antennas, and N receiving antennas. The xi is the transmit signal from transmitter antenna i and the yj is the receive signal from receiver antenna j. The H is the channel matrix. The hij is the channel response from transmitter antenna i to receiver antennal j. The signals from different transmitter antennas go through different path and are received by different receiver antennas. The received signal Y is written as
Y
The advantages of MIMO communication can be divided into three categories, beam-forming, spatial diversity and spatial multiplexing. The beam-forming technology is like a spatial filter. Based on control the phase and gain of each antenna which transmits identical waveform, the direction of antenna beam would change because of constructive or destructive interferences in different directions. Therefore, this technology could increase the gain of transmitter and receiver antenna and reduce the multipath fading effect from channel.
The purpose of spatial diversity is to enhance the quality of signal [77].
Since the signal may be reflected, scattered, refracted and even blocked on the way to the receiver, the signal suffered different fading effect at different frequency and time. Because each transmitter antenna locates in different position, the signal transmission path from each antenna is also different. Since multiple transmitter antennas will create different channels, the signal from different antenna has different channel response. If different transmitter antennas send relational signal, the signal can be recovered when one path is blocked.
One of the powerful techniques is spatial multiplexing [76]. The spatial multiplexing means that different transmitter antenna send different signal at the same frequency in the same time. The signals transmit over the wireless channel and received by the receiver antenna array. If multiple transmit signals can be recover in the receiver side after demodulation, the system capacity can
be improved by this technique. This thesis focuses on the spatial multiplexing.
For the 2x2 MIMO scheme, the system could be express as this equation, y The transmitted signals could be recovered from received signals by multiply suitable matrix W. The target of W is to have highest quality of recovered signals. The recovered signal could be express as this equation,
x
x W y
y (3-15) The recover matrix W could be calculate form receiver signals and train signals and express as this equation,
W x
x y
y (3-16) The channel matrix is very important in the MIMO system. From mathematics, the condition number of the matrix is a good parameter for analyzing system the performance. The condition number is:
c (3-17) Where λ and λ are maximal and minimal singular value of matrix, respectively. The higher condition number means the recovery signal is susceptible to noise. The maximal condition number and minimal condition number are infinity and one, respectively.
If channel matrix H equals to 100
1 , the system could be separated to two independent SISO system. If the signal power from each transmitter antenna is the same, the system have double data throughput. The condition number equals to one in this matrix. On the other case, the channel matrix H equals to
110
0 . The condition number is infinity. The system could not find the recovery
matrix W and the data throughput equals zero.
Figure 3-18 MxN MIMO channel model with M transmitter antennas and N receiver antennas.
3.5 Summary
This chapter introduces four digital modulation formats. The properties of these formats are shown in table 3-1. Single carrier signal has low PAPR, but easily suffer ISI. The OFDM signal robust to ISI, but has high PAPR issue.
Therefore, the SC-FDE is proposed to provide easily equalization in frequency domain and reduce ISI by adding CP. However, the complex receiver is needed to demodulate signals. Moreover, the SC-FDE could not provide bit-loading for signal generation. Therefore, the SC-FDM is proposed to solve these problems.
However, the SC-FDM system has complex transmitter and receiver. The adaptive bit-loading algorithm and I/Q imbalance compensation algorithm were investigated. The bit-loading algorithm could increase the total data-capacity with the same communication system by adjusting power and bits per symbol
for each subcarrier/group. The I/Q imbalance compensation algorithm could reduce the impairment of I/Q imbalance effect from non-ideal I/Q mixer. This chapter also introduces MIMO technology that could increase total data throughput by adding transmitter and receiver antennas.
Chapter 4
OPTICAL I/Q UP-CONVERSION RADIO-OVER-FIBER SYSTEM
4.1 Preface
In the previous chapter, we have introduced RoF systems, digital modulation format, and digital signal processing. The generation of optical RF vector signals, using an external Mach–Zehnder modulator (MZM) based on double-sideband (DSB) modulation scheme have been demonstrated [42].
However, the DSB signal undergoes performance fading due to the fiber dispersion. Furthermore, to generate an RF vector signal in a high frequency band, an electrical mixer with a typical conversion loss of more than 8 dB is required to up-convert vector signals to an inter-medium or radio frequency, which degrades the performance of the up-converted RF vector signals, especially at the higher frequency. Recently, the generation of optical RF signals by all optical up-conversion has been extensively investigated [78-83].
However, the corresponding system requires at least two modulators to up-convert the in-phase (I) and quadrature phase (Q) signals, and occupies much more optical bandwidth than traditional DSB modulation schemes [80-83].
This investigation proposes a novel optical RF vector signal generation approach using optical up-conversion and studies its performance both numerically and experimentally. The advantage of this architecture is that it requires no electrical mixer with a typical conversion loss of more than 8 dB to generate the electrical vector RF signal. Furthermore, since the proposed
system generates only one un-modulated optical subcarrier and one modulated optical subcarrier, i.e. optical single sideband (SSB) format, the system does not suffer from RF fading. Since the generated optical signal has one modulated subcarrier and one un-modulated subcarrier, the proposed system can generate not only OOK signals but also PSK, QAM and OFDM signals.
Additionally, the relative powers of un-modulated and modulated subcarriers can be easily tuned by adjusting the individual intensities of the electrical sinusoidal waves and data signals to optimize the performance of the RoF system.
However, an important factor that significantly affects system performance is the precision of controlling the amplitude and phase of the input I/Q signals.
Therefore, the I/Q imbalance compensation algorithm that compensates for the I/Q imbalance is proposed and demonstrated numerically and experimentally.
With I/Q imbalance compensation, both simulation and experimental results verify a significant increase in the tolerance of both amplitude mismatching and conjugate misalignment. In this experiment, a 32.65-Gb/s bit-loading OFDM signal with I/Q imbalance compensation in frequency domain is generated, and the power penalty is negligible after 25km standard single-mode fiber transmission.
4.2 The Concept of Proposed System
Figure 4-1 schematically depicts the proposed frequency quadrupling system employing all-optical up-conversion. The proposed 60-GHz RoF transmitter consists of two dual-parallel MZMs for optical up-conversion and frequency quadrupling, respectively. For all-optical up-conversion, OFDM I and Q signals are sent to MZ-a and MZ-b of the first dual-parallel MZM,
respectively. Next, both MZ-a and MZ-b are biased at the null point to achieve high optical modulation depth and operate in the optical field linear region of MZM. Additionally, direct-detection vector signals are realized by inserting an optical subcarrier as a remote heterodyne scheme through the use of optical single side band modulation with carrier suppression [84]. The electrical sinusoidal signals which have 90o phase difference are sent to MZ-a and MZ-b of the first dual-parallel MZM, respectively. When MZ-c of the first dual-parallel MZM is biased at the quadrature point, the optical phase of LSB would be opposite between the output of MZ-a and MZ-b. The LSB will be cancelled and the USB is still obtained. Therefore, according to inset (a) of Fig.
4-1, the generated optical vector signal consisting of an un-modulated subcarrier and an modulated subcarrier, which can be converted into electrical RF vector signals by square-law photo-diode (PD) detection, can be produced.
Unfortunately, the bandwidth of typical dual-parallel MZM is less than 25GHz.
The second dual-parallel MZM is needed to provide high frequency application.
Next, the generated optical vector signal is up-converted by using the frequency quadrupling method [85] (inset (b) of Fig. 4-1). When the MZ-a and MZ-b of the second dual-parallel MZM are biased at full point, the optical phase of the odd order sidebands are suppressed. The electrical sinusoidal signals which have 90o phase difference are sent to MZ-a and MZ-b of the second dual-parallel MZM, respectively. When MZ-c of the second dual-parallel MZM is biased at the null point, the optical phase of the zero, fourth, etc order sidebands are opposite between the output of MZ-a and MZ-b.
The pure second order sidebands could be obtained.
Following an interleaver to filter out the unwanted sideband, the proposed optical SSB signal is generated, as shown in inset (c) of Fig. 4-1. Notably, the relative intensity between the un-modulated and modulated subcarriers can be modifying by varying the individual power of the electrical sinusoidal and vector signals to optimize the performance of the optical RF signals [86].
Figure 4-1 Conceptual diagram of the 60-GHz RoF system using all-optical
up-conversion.
4.3 Theoretical Calculations and Simulation Results
4.3.1 The Generated Optical Signal
Figure 4-1 presents the proposed optical transmitter to generate a direct-detection wideband optical vector signal. For optical up-conversion, the optical field is modulated by an dual-parallel MZM, which consists of three sub-modulators: two sub-modulators for in-phase modulation (MZ-a) and quadrature-phase modulation (MZ-b), and another sub-modulator (MZ-c) for
controlling the phase difference between MZ-a and MZ-b. The optical field at the input of the dual-parallel modulator is given by cos , where and are the amplitude and angular frequency of the optical field, respectively. MZ-a and MZ-b are both biased at the null point, and MZ-c maintains a 90o phase shift between the output signals of MZ-a and MZ-b. The optical field at the output of the transmitter is given by
sin cos sin sin (4-1) where I(t) and Q(t) are the in-phase and quadrature-phase data of the vector signal, respectively.
To realize the direct-detection optical vector signals, an un-modulated optical subcarrier is generated at , as shown in Fig. 4-1. Two sinusoidal waves with the same RF frequency ( ) but a 90o phase difference are sent to the MZ-a and MZ-b after being combined with the electrical I/Q signals. Since the bias points of MZ-a and MZ-b are set at the null point, one un-modulated optical subcarrier with carrier suppression is generated at the angular frequency of . The high-order terms and the interference between the un-modulated and modulated subcarriers caused by the nonlinear transfer function of an MZM can be neglected when the modulation depth is small. Accordingly, the optical field at the output of the transmitter can be approximated as,
≅ sin cos sin sin
2 cos (4-2)
where m is (V/2Vπ)π and V is the amplitude of electrical sinusoidal driving signal. From equation (4-2), the un-modulated subcarrier at and modulated subcarrier at will be obtained after first dual-parallel modulator.
For frequency quadrupling, the optical field at the input of the second modulator is cos . MZ-a and MZ-b are both biased at the maximum transmission point, and MZ-c maintains a 180o phase shift between the output signals of MZ-a and MZ-b. Two sinusoidal waves with the same RF frequency ( ) but a 90o phase difference are sent to the MZ-a and MZ-b.
The optical field at the output of the MZ-a and MZ-b of second dual-parallel modulator are given by
√ ∙ ∙ cos
∑∞ ∙ cos 2 (4-3)
√ ∙ ∙ cos
∑∞ ∙ cos 2 (4-4) The high-order terms caused by the nonlinear transfer function of an MZM can be neglected when the modulation depth is small. Accordingly, the optical field at the output of the second dual-parallel modulator can be approximated as,
√ √
≅ ∙ cos 2 (4-5) If the optical field at the input of the second modulator is , the optical field at the output of the second dual-parallel modulator can be express as
∙ ∙ ∙ sin cos 2
∙ ∙ ∙ sin sin 2
2 ∙ ∙ ∙ cos 2 (4-6)
where m1 and m2 are the modulation index of first and second MZM,
respectively. From equation (4-2), Four subcarriers will be obtained after second dual-parallel modulator as shown inset (b) of Fig. 4-1.
4.3.2 The Generated Electrical Signal
First, we calculated generated electrical RF signal from equation (4-2). As determined by square-law photo-detection, the beating terms of the modulated and un-modulated signals generate the desired RF vector electrical signal at the frequency of , and can be expressed as,
sin cos sin sin (4-7)
where R is the responsivity of the photodiode. Since the modulation depth is small, the equation can be further simplified as
cos sin (4-8)
However, the I/Q data transmit over different paths to the modulator, resulting in amplitude mismatch and conjugate misalignment. These mismatches will significantly degrade the system performance. The possible origins of the amplitude mismatch can be the difference between the powers of the I/Q signals, the different Vπ of MZ-a and MZ-b, and the imperfect splitting ratio between MZ-a and MZ-b. Furthermore, conjugate misalignment arises from that the MZ-c does not provide an exact 90o phase shift between the output signals of MZ-a and MZ-b. The amplitude mismatch can cause signal distortion, and the conjugate misalignment causes interference between the I/Q signals as shown in Fig. 4-2. These effects can be expressed analytically:
cos sin (4-9)
where a and are the amplitude mismatch and the conjugate misalignment parameter, respectively. The GSOP algorithm which is based in time domain
can be used to reduce the imbalance effect [70], and it will be revealed by both the simulation and the experimental results.
The VPI WDM-TransmissionMaker™ is used to simulate the effects of I/Q imbalance and the compensation using the GSOP. Figures 4-3 (a) and (b) present the simulation results concerning a QPSK signal. In our simulation, 3 dB amplitude mismatch and 15° conjugate misalignment result in 3.2 dB and 2.3 dB SNR degradation, respectively. The SNR is defined by
SNR = –20 log (EVM/100%) (4-10) where EVM is defined as the noise power from constellation over the signal power from constellation. The SNR degradations of ~0.6 dB and ~0.4 dB corresponding to 3 dB amplitude mismatch and 15° conjugate misalignment, respectively, are achieved by the GSOP compensation. Figures 4-4 (a) and (b) present the cases of 16-QAM signals. While 3 dB amplitude mismatch and 15°
conjugate misalignment result in 8 dB and 6.4 dB SNR degradation, the degradation is suppressed to 0.6 dB and 0.9 dB by using the GSOP compensation, respectively. The results clearly reveal the criticality of the I/Q imbalance for the QPSK format and the 16-QAM format and the great performance improvement by the GSOP. The simulation results reveal that the GSOP can remove most penalties caused by the I/Q imbalance for different modulation formats.
Second, we calculated generated electrical RF signal from equation (4-6).
The individual square term of this equation will generate the baseband signal, and the cross terms will generate the RF signal. Since the modulation depth is small, these signals can be expressed as
cos sin
∙ cos 4 sin 4
∙ cos 4 sin 4
(4-11) The RF signal will generate at , 4 , and 4 . Since the RoF want to use low frequency components to generate high frequency RF signal, the desire frequency of generated RF signal is 4
. Moreover, the optical filter can be used to remove some of subcarriers that do not contribute for RoF system. Therefore, the filter will use to filter out
optical subcarriers at 2 and 2 in experiment.
The optical filed after filter can be expressed as
∙ ∙ ∙ sin cos 2
∙ ∙ ∙ sin sin 2
2 ∙ ∙ ∙ cos 2 (4-12)
Figure 4-2 Concept of proposed optical I/Q up-conversion system.
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Figure 4-3 Simulation results of QPSK signal of amplitude mismatch and
conjugate misalignment.
-3 -2 -1 0 1 2 3
Figure 4-4 Simulation results of 16-QAM signal of amplitude mismatch and conjugate misalignment.
4.3.3 Consider Dispersion Effect
The dispersion will contribute different phase delay for different subcarriers. For optical I/Q up-conversion RoF system, the generation of only
one copy of the desired RF signal after photodiode could eliminate the possibility for fading. Therefore, dispersion does not induce RF fading problem in the proposed RoF system.
4.4 Experimental Demonstration without Frequency Quadrupling
4.4.1 Experiment Setup
Figure 4-5 presents the experimental setup of the proposed system. Since the baseband QPSK and 16-QAM signals are complex, the real and imaginary parts are sent from channel one and channel two of a Tektronix® AWG7102 arbitrary waveform generator (AWG). The sampling rate and the digital-to-analogue converter resolution of the AWG are 10 GHz and 8 bits, respectively. The QPSK and 16-QAM signal symbol rates are 2.5 GSymbol/s, as shown in inset (i) of Fig. 4-5. The data rate is 5 Gb/s for the QPSK signal and 10 Gb/s for the 16-QAM signal. To realize optical direct-detection, a new optical subcarrier is generated in one sideband at the frequency of 8 GHz higher than the original optical carrier. The generated photonic vector signal is then amplified using an EDFA and filtered through a 0.4 nm optical filter to suppress the ASE noise, as shown in inset (ii) of Fig. 4-5. An optical attenuator is used to set the optical launching power to be 0 dBm before transmission to prevent fiber nonlinearity. A 50km standard single-mode fiber is used to evaluate the transmission penalty of the system. Following square-law detection, an electrical 2.5GSymbol/s signal at 8 GHz is generated and captured by a Tektronix® DPO 71254 with a 50Gb/s sampling rate and a 3dB bandwidth of 12.5 GHz, as shown in the inset (ii) in Fig. 4-5. The off-line DSP program is used to demodulate the vector signal. The bit error rate (BER)
performance is calculated from the measured SNR.
Figure 4-5 Experimental setup of the proposed optical I/Q up-conversion system.
4.4.2 Results and Discussions
Figure 4-6 and Fig. 4-7 present the experimental results obtained using GSOP compensation. Since the frequency response of AWG is uneven, the feedforward equalizer is used to reduce the ISI effect. The experimental results in Figs. 4-6 (a) and (b) reveal that 3 dB amplitude mismatch and 15° conjugate misalignment correspond to ~5.9 dB and ~3.6 dB SNR degradation, respectively. However, the GSOP greatly improves performance, such that SNR degradation becomes only 0.6 dB and 0.2 dB, respectively. Figures 4-7 (a) and (b) present experimental results concerning the 16-QAM signal, and the GSOP compensation can decrease the SNR degradation from 8.3 dB to 0.6 dB (from 6.6 dB to 0.6 dB) due to 3 dB amplitude mismatch (15° conjugate misalignment). The results also verify the criticality of the I/Q imbalance for both the QPSK format and the 16-QAM format. Because the spacing of 16-QAM constellation points is closer than that of QPSK, the 16-QAM signal has more penalty than the QPSK signal with the same I/Q imbalance.
Furthermore, the experimental results agree with the simulation results well.
Furthermore, the experimental results agree with the simulation results well.