Concept of Pre-coded Technique - Hybrid Access Network with Frequency Quadrupling

Chapter 6 HYBRID ACCESS NETWORK

6.3 Hybrid Access Network with Frequency Quadrupling

6.3.3 Concept of Pre-coded Technique

Figure 6-15 schematically depicts the concept of the millimeter-wave generation using single-electrode MZM. The single drive Mach-Zehnder modulator (MZM) used to modulate optical field. The optical field at the input of MZM is given by ^{E t}_in^{( )}^E_o^cos(_o^t⁾, where Eo and _o are the amplitude and angular frequency of the optical field, respectively. The driving signal V(t) consisting a DC biased voltage and RF signal at frequency _RF is

( ) _bias _m( )cos( _RF ( ))

V t V V t  t t , where Vbias is the dc biased voltage, ( )V_m t and ( )t are the amplitude and phase information of RF signal, respectively.

The optical field at the output of the MZM is then given by

 . Using Bessel function expansion, the

output optical field at the output of the MZM can be rewritten as



Due to the power of optical sidebands with the order of higher than J2 are smaller than J2 term and the generated optical signal would filter by optical band pass filter, the high order optical sidebands can be neglected with

significant errors. The output optical can be further simplified to After square-law photo detection the photocurrent of the generated RF signal can be express as where R is the responsivity of photodiode. This result is proposed frequency doubling system, the phase information of signal need pre-coded form 2 ( ) t to ( )t . Because the frequency doubling system is less arrange type can choose. In this work, the frequency quadrupling system is used to analysis pre-code method.

If the MZM is biased at the full point (Vbias = 0 ), the output field at the output of the MZM is become



0 2



( ) J ( ( )) cos( ) J ( ( )) cos( 2 2 ( )) ,

out o o o RF

E t E  m t  t  m t  t  t  t (6-17) where m(t) is the modulation index defined as ^V_m( )t  ²^V_ , Jn() is the nth order.

After the modulation, the strong optical carrier at _o would decade the signal sensitivity. Therefore, the strong optical carrier can be suppress by notch fiber bragg grating and the output optical can be further simplified to

( ) 2( ) cos( 2 2 ( ))

out o o RF

E t  E J m  t  t  t (6-18) This result is the same with previous proposed frequency quadrupling result.

The amplitude and phase information of two optical sidebands at _o ²_RF are

2( )

J m and 2 ( ) t , respectively. After square-law photo detection the photocurrent of the generated RF signal can be express as

2 The frequency of the generated RF signal (4_RF) is four times that of the driving signal (_RF). The amplitude and phase information of generated RF signal are J m t₂²[ ( )] and 4 ( ) t , respectively. Since the amplitude and phase information of generated RF signal is different with driving signal, the driving signal needs to be pre-coded to achieve the desired information. By properly pre-coded driving signals, the proposed scheme can support various kinds of vector signals, including amplitude-shift keying (ASK), phase-shift keying (PSK), and quadrature amplitude modulation (QAM). The pre-coded V t_m( ) is related to the second order of Bessel function, and the phase information of the generated vector signal is four times of ( )t .

For the QPSK signal, since the phase information will change after the proposed system, the original signal need to pre-code. Figure 6-16 shows the standard and pre-coded QPSK signals, the standard QPSK have four constellation points at ⁄4 ∙ ⁄ , where n = 0,1,2, and 3. For every point 2 has four different points will reach same constellation points after frequency quadrupling system. For example, the previous result use four points in first

quadrant and get standard QPSK constellation points after receiver. In fact, there are many different arrange types will get the same signal. However, the signal shows different performance with different arrange type.

In this work, we discuss pre-coded QPSK signal with twelve different arrange types and compare their performance. The twelve different arrange type shows in Table 6-1. The different arrange type that has different RF spectrum is show in Fig. 6-17. The constellation point would transfer to each other. If the constellation has centralized points, it causes constellation points have lower variation and the signal energy would centralize at the carrier frequency as show in Fig. 6-17. In other words, if the constellation points have large variation, it also needs more energy in high frequency to provide constellation point transfer. Therefore, the bandwidth of 97% of electrical power in how much symbol rate could calculate form electrical spectrum as shown in the Table 6-1. Because the electrical spectrum of generation RF signal has centralized bandwidth, the signal suffers less band limit channel effect.

After frequency quadrupling system, the phase information would change to four times than original phase information. The stander QPSK signal would appear after square-law photo detection. However, the constellation transfer path would different form different arrange type, as shown in Fig. 6-18. Figure 6-18 (a) shows the constellation transfer path of first arrange type. The original four points are at π/16, 3π/16, 5π/16, and 7π/16. After frequency quadrupling system and square-law photo detection, the four points would at π/4, 3π/4, 5π/4, and 7π/4. Moreover, the transfer path of phase information from π/16 to 7π/16 is counterclockwise. Due to the path of original driving signal, the path of generated signal is also counterclockwise. This reason cause the receive

constellation transfer path is different between with regular QPSK signal and the signal with different arrange type also have different constellation transfer path. The length of constellation transfer path could calculate form original pre-code constellation point. If we don’t consider the amplitude variation, the length of constellation transfer path after system is proportion to original driving signal. Table 6-1 shows the length of constellation path that calculate from pre-code driving signal. Normally, the nearest distance between two points is the length of straight line between two points. Because the generated signal comes from different pre-code signal, the generated signal would have different transfer path. When the length of the constellation transfer path becomes more and more, this signal need more bandwidth to provide the constellation point transfer or provide more time to transfer. Therefore, the signal with large bandwidth would suffer channel response very serious. The worse channel response would cause signal performance decrease a lot especially in the signal with large bandwidth. Therefore, the complex transfer path needs more bandwidth for the constellation point transfer. If the channel bandwidth is limited, the signal would distortion after demodulator. For other arrange type, like Fig. 6-18 (b). The original four points are at π/16, 3π/16, 5π/16, and 15π/16. After frequency quadrupling system and square-law photo detection, the four points would at π/4, 3π/4, 5π/4, and 15π/4. This signal path between π/4, 3π/4, and 5π/4 are the same with pervious case. The different are points to 15π/4 point and form 15π/4 point to other points. For example, the phase information continues change from the π/16 point to 15π/16 point. After the receiver, the phase information from π/4 to 15π/4 would pass 2π and then reach 7π/4. This phase change is large fluctuations, an undesirable quality in

communication systems. This work would discuss different arrange type and compare performance each other.

For the start 8-QAM signal generation, it would include amplitude information. Due to the analysis result of the optimal condition is four points closely that have lowest bandwidth and the lowest constellation length path.

Therefore, the simulation condition of star 8-QAM signal would fix inner and outside four points is closely and change the position between inner and outside as shown in Fig. 6-19. The star 8-QAM signal can be divided into eight different arrange type, as shown in Table 6-2. Figure 6-20 shows the electrical spectrum before send into MZM. The 500-Msymbol/s 8-QAM signal is used to demonstrate.

Figure 6-20 shows the electrical spectrum that inner and outside point from small to large. The figure shows that the points are centralization would have higher carrier power and lower sideband power. The 97% power in how much bandwidth is show in Table 6-2. The length of transfer path could calculate form pre-code signal, as shown in Table 6-2. In this work, we would give detail analysis and experimental demonstration of direct-direction RF QPSK and 8-QAM signals using frequency quadrupling.

VBias MZM LD

DC f

(a)

(b) 2f

O/E

DC 2f

(d)

Null point Full point

DC 4f

(e) 4

Full point Null point

Figure 6-15 The concept of the millimeter-wave generation using single-electrode MZM.

Figure 6-16 The principle of pre-coded scheme of the QPSK format with

frequency quadrupling system.

Table 6-1 Comparison of 12 pre-coded QPSK signals.

Arrange type n, ( π) Path Length Power(97%)(Symbo l rate)

1 0, 1, 2, 3 1 0.523

2 0, 1 ,2, 7 1.84084 1.379

3 0, 1, 6, 7 2.12475 1.452

4 0, 1, 3, 6 1.80687 1.259

5 0, 1, 6, 11 2.38026 1.521

6 0, 1, 3, 10 2.10828 1.457

7 0, 1, 7, 10 2.39219 1.536

8 0, 1, 3 ,14 1.52295 0.752

9 0, 2, 5, 7 2.07987 1.391

10 0, 2, 5, 11 2.36379 1.503

11 0, 5, 7, 14 2.38128 1.533

12 0, 3, 6, 9 2.35823 1.489