Objection and Problem Statement

In this thesis, we will demonstrate the 60 GHz RoF system using 2 x 2 MIMO technology transmitting the Single Carrier vector signal to increase the spectrum efficiency in the 7 GHz unlicensed band. However, there are two main problems we will meet.

The first challenge is non-flat channel response with up to 10dB deviation within the 7 GHz spectrum. The 7 GHz SC signal will have a serious ISI problem. The complexity of the MIMO process in the time domain will rapidly increase. To overcome this problem, the SC frequency domain

equalizer (FDE) [9] is used. FDE not only can compensate the uneven channel response but also can well separate the MIMO signals in the frequency

domain.

The second one is the noise enhancement because of MIMO channel correlation. Channel correlation between different transmitted antennas is very important to the signal performance in the light of sight (LOS) MIMO

scenario. The channel correlation is related to the distance and the angles of received signals. The problem can be solved by increasing the antenna pairs or introducing the concept of the smart antennas where we don’t focus on this topic in this thesis. The channel correlation can also be decreased by well adjusting the antenna spacing.

5

Chapter 2

Multiple-Input Multiple-Output (MIMO) Technology

2.1 Preface

The RoF system is the possible solution of the high data rate wireless transmission in the future because of the property of the fiber which is low loss and have almost unlimited bandwidth. However, the bandwidth in wireless communication is constrained by the law. In order to raise the data rate in the fixed bandwidth, MIMO is the effective way to improve the spectrum

efficiency. Figure 2-1 shows the RoF system with the MIMO technology. In this chapter, we will introduce the basic concept of MIMO.

Figure 2-1 the concept of RoF system with MIMO technology.

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2.2 MIMO Technology for Improving Performance 2.2.1 Diversity

In the non-LOS wireless communication, we don’t know how the signal is received form transmitter to the receiver. The signal may be reflected, scattered, refracted and even blocked on the way to the receiver. If the signal performance is so poor that can’t be the reliable communication, we call this path is in a deep fade. When the path is in a deep fade, the communication will suffer from errors. A technique is called diversity, and it can significantly improve the performance over the fading channels.

There are many ways to obtain diversity, we introduce three diversity techniques in time, frequency and space in the chapter. Figure 2-2 shows the concept of the time diversity. H is a fading channel variously with time. When the time block 3 is in a deep fade, the signal at time block3 will suffer from error. Now, the same signal x is transmitted three times. Thus, even if the time block 3 is in deep fade, the signal x still could be detected correctly depending the received signals at other two time blocks. Similarly, one can also exploit diversity over frequency if the channel is frequency-selective which means the channel changes variously with the frequency. Multiple transmit and receive antennas will create the different channels from the different transmit antennas to receive antennas. The same signal can be received many times because of the different transmit paths, and the spatial diversity is obtained. The diversity technique is an important resource to the wireless communication, and we will introduce the Alamouti space-time code to implement the space diversity to improve the signal performance in next section.

7

2.2.2 Alamouti Space-Time Code

Spatial diversity which we can also call it antenna diversity, it involves both the receive diversity, using multiple receive antennas (single input multiple output, SIMO channels), and the transmit diversity, using multiple transmit antennas (multiple input single output, MISO channels). Channels with multiple transmit antennas and multiple receive antennas (multiple input multiple output, MIMO channels) provide more potential.

Alamouti scheme was proposed by Mr. Siavash M Alamouti in his landmark paper – A Simple Transmit Diversity Technique for Wireless Communication. This is the transmit diversity scheme proposed in several third-generation cellular standards. The Alamouti scheme is designed for two transmit antennas at the first, but more than two transmit antennas is possible.

For the discussion, we will assume that the channel is a flat fading Rayleigh multipath channel.

Figure 2-3 shows a 2 x 1 MISO scenario, and there are two transmit antennas and one receive antenna. Two transmitted signals x₁ and x₂ are

Figure 2-2 time diversity.

8

transmitted to the receive antenna and the received signal y is written as

𝑦,m- = ℎ₁,𝑚-𝑥₁,𝑚- + ℎ₂,𝑚-𝑥₂,𝑚- + 𝑤,𝑚- (Eq. 2-1) Where h_i is the channel gain from transmit antenna i, and w is the additive white Gaussian noise (AWGN).

Now, we have a transmission sequence such as {u₁, u₂, u₃, u₄, …} which are the data symbols. In the normal transmission, we will transmit u₁ in the first time slot, u₂ in the second time slot, u₃ in the third time slot and so on. However, The Alamouti scheme transmits two symbols u₁ and u₂ over two times. At time slot 1, x₁[1] = u₁, x₂[1] = u₂; At time slot 2, x₁[2] = -u₂^*, x₂[2] = u₁^*; We assume that the channel remain constant over the two symbol times which h₁ = h₁[1] = h₁[2], h₂ = h₂[1] = h₂[2], as the figure 2-4 shown, 2 x 1 Alamouti space-time code. Then, the receive signal can be expressed as

,𝑦,1- 𝑦,2-- = ,ℎ₁ ℎ₂- [𝑢₁ −𝑢₂^∗

𝑢₂ 𝑢₁^∗ ] + ,𝑤,1- 𝑤,2-- (Eq. 2-2)

The equation can be rewrote as

Figure 2-3 2x1 MISO

9 The estimate of transmit symbols are by inversing the diagonal matrix

(H^𝐻H)⁻¹ = [

Thus, the transmit diversity gain is 2 for the detection of each symbol. It is possible to provide diversity order 2M with two transmit and M receive

antennas. Figure 2-5 is the simulation result of 2 x 2 Alamouti scheme where

10

the channel is the flat fading Rayleigh channel, and the noise is AWGN. Clearly, 2 x 2 Alamouti scheme has better performance than the SISO channel.

2.3 MIMO Technology for Improving Capacity

We will see that under suitable channel conditions, MIMO channel provides an additional spatial dimension for communication and degrees of

Figure 2-4 2x1 Alamouti space-time code.

Figure 2-5 simulation result of Alamouti space-time code.

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freedom. These additional degrees of freedom can be exploited by spatial multiplexing several data streams on to the MIMO channel and the overall capacity is increased.

The time-invariant MIMO channel with n_t transmit and n_r receive antennas can be written as the n_r by n_t deterministic matrix H

𝐲 = 𝐇𝐱 + 𝐰 (Eq. 2-11) where x, y and w denote the transmitted signal, received signal and white

Gaussian noise at a symbol time.

This is a vector Gaussian channel. The capacity can be computed by decomposing the vector channel into a set of parallel, independent scalar Gaussian sub-channels. The matrix H has a singular value decomposition (SVD):

𝐇 = 𝐔𝛔𝐕^𝐻 (Eq. 2-12) where U and V are unitary matrices and σ is a rectangular matrix whose

diagonal elements are non-negative real numbers. The diagonal elements λ₁ ≥ λ₂ ≥ … ≥ λ_nmin are the ordered singular values of matrix H, number of non-zero singular values.

If we define

𝐱̃ = 𝐕^𝐻𝐱 (Eq. 2-14) 𝐲̃ = 𝐔^𝐻𝐲 (Eq. 2-15)

12

𝐰̃ = 𝐔^𝐻𝒘 (Eq. 2-16) then we can rewrite the channel as

𝐲̃ = 𝛔𝐱̃ + 𝐰̃ (Eq. 2-17)

Then, we have an equivalent representation as parallel Gaussian channel

𝑦̃_𝑖 = 𝜆_𝑖𝑥̃_𝑖+ 𝑤̃_𝑖, 𝑖 = 1,2, … , n_𝑚𝑖𝑛 (Eq. 2-18) Figure 2-6 shows the equivalence.

We can look the SVD decomposition as two coordinate transformations.

If the input is expressed in terms of coordinate system defined by the columns of V and the output is expressed in terms of a coordinate system defined by the column U, then the relationship between input and output can be very simple.

Thus, the property of MIMO channel will dominate how much data we can transmit.

在這裡鍵入方程式。

2.3.1 Spatial Multiplexing : Zero-Forcing Receiver

For a deterministic time-invariant MIMO channel, the capacity-achieving architecture is simple. Independent data streams are multiplexed in an

appropriate coordinate system. The receiver transforms the received vector into Figure 2-6 MIMO channel converts into parallel channel.

𝐱̃ 𝐱 𝐲 𝐲̃

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another appropriate coordinate system to separate the different data streams.

Figure 2-7 shows a 2 x2 spatial multiplexing MIMO scheme. Let’s rewrite it to the matrix form as: of the channel matrix is known, the transmitted data can be recovered by using the zero-forcing algorithm and written as

𝐲̃ = 𝐇⁻¹𝐲 = 𝐱 + 𝐇⁻¹𝐰 = 𝐱 + 𝐰̃ (Eq. 2-21) However, the noise w̃₁ and w̃₂ are correlated. The performance will decrease.

First, we focus on the detection of symbol form transmit antenna 1. The noise become:

14

ỹ₁ = x₁+√|ℎ₂₁|²+ |ℎ₂₂|² ℎ₁₁ℎ₂₂− ℎ₁₂ℎ₂₁ 𝑧₁

(Eq. 2-24) Then we define

y₁^′ = ℎ₁₁ℎ₂₂− ℎ₁₂ℎ₂₁

√|ℎ₂₁|²+ |ℎ₂₂|²ỹ₁ = (𝜙₂^𝐻𝐡₁)x₁+ 𝑧₁

(Eq. 2-25) where

𝐡₁ = [ℎ₁₁

ℎ₁₂] , 𝜙₂ = 1

√|ℎ₂₁|²+ |ℎ₂₂|²[ ℎ₂₂^∗

−ℎ₂₁^∗ ]

(Eq. 2-26) The h₁ can be seen as the direction of the signal from transmit antenna 1, and the ϕ₂ is the direction orthogonal to h₂. Equation 2-25 represents that the signal form transmit antenna 1 is detected by projecting the received signal y to the direction perpendicular to the direction of the transmit antenna 2, h₂. Hence, the interference from transmit antenna 2 can be eliminated. However, if the h₁ and h₂ are not orthogonal in the beginning, the vector of h₁ orthogonal to the h₂ will be smaller than h₁ itself as figure 2-8 shown.

Figure 2-7 2x2 spatial multiplexing MIMO.

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Figure 2-9 is the simulation result of 2x2 MIMO channel with

Zero-Forcing receiver where the channel is the flat fading Rayleigh channel, and the noise is AWGN and the transmit antennas transmit two independent symbols at once. We only use the one dimension to decode the signal by the projection, so we don’t have any diversity gain in this scheme. Thus, the performance is not better to the SISO channel, but the capacity is double.

Figure 2-8 the correlated channel.

Figure 2-9 simulation result of MIMO with ZF receiver.

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2.3.2 Spatial Multiplexing : Maximum-Likelihood Receiver

Maximum-Likelihood (ML) receiver is the very directly way to detect the independent data streams. The core idea of the ML detection is to compare all of the possible transmitted symbols to find the maximum likely one. Figure 2-7 is the 2x2 spatial multiplexing MIMO scheme. Equation 2-19 and Equation 2-20 is the matrix form of this scheme, where H is the channel matrix, and x = [x₁ x₂]^T is the input vector is consist of two independent symbols x₁, x₂, w = [w₁ w₂]^T is white noise. The ML detection bases on the following equation:

𝐬 = arg min_x‖𝐲 − 𝐇𝐱̂‖² (Eq. 2-27) Assume the channel matrix H is known, and we also know what kind of the symbol 𝐱̂ the transmit antenna may sent. Then, the receiver can decision what kind of symbol it is.

For an example, the 2x2 MIMO scheme is like figure 2-7, and the modulation is BPSK. The ML receiver tries to find 𝐱̂ which minimizes 𝐊 =

‖𝐲 − 𝐇𝐱̂‖², and the possible value of the BPSK symbol is +1 or -1. So we need to find the minimum from all four possible combinations.

𝐊_+1,+1 = ‖[y₁ all of the dimensions are considered, the performance is better than the SISO channel by the diversity gain. Figure 2-10 shows the simulation result.

However, the complexity of the ML receiver will exponentially grow with

17

increasing the number of antennas and the order of data format of symbols.

Figure 2-10 simulation result of MIMO with ML receiver.

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Chapter 3

Single Carrier Frequency Domain Equalizer

3.1 Preface

In this thesis, we want to apply the MIMO antenna technology to the 60 GHz RoF system with 7 GHz broadband bandwidth doubling the data rate.

However, such high carrier frequency signal (60 GHz) has very high propagation losses rendering it more suitable for short-range wireless links (~10m). The wideband 60 GHz RoF system has an uneven frequency

response of up to 12 dB within 7 GHz license-free band. These two properties make the MIMO channel in 60 GHz RoF system is a time-invariant and frequency-selective channel. Hence, it is the different situation from the assumption in the chapter 2. We assume the MIMO channel is a flat fading Rayleigh channel in the chapter 2. In this chapter, the complexity will highly increase by using the ZF detector due to the frequency-selective channel, but we will introduce the frequency domain equalizer (FDE) to MIMO

technology which is simple method to double the data rate.

3.2 Inter-Symbol Interference

Inter-symbol interference is an important issue in digital communication.

It is a form of distortion of signal where the symbols interfere to the symbols each other. That’s just like the noise to the decision samples, and that will make the communication less reliable. ISI usually comes from two different situations. One is the multipath propagation, and the other one is the uneven

19

frequency response of the system.

ISI of the multipath propagation occurs because of the wireless signal from the transmit antenna to the receive antenna via different paths. The same signal will arrive to the receiver at different time due to the various paths, so the signals are going to distort the amplitude and phase which cause

interference between symbols at different time. The phenomenon of fiber dispersion also results in ISI. The reason is similar to the multipath propagation.

Compared to the ISI of the multipath propagation, the ISI because of the uneven frequency response of the system is presented in both wired and wireless communication. Every component in the communication system has its own frequency response, so the frequency response of the entire system is non-flat and will cause ISI.

3.3 Linear Convolution and Circular Convolution

The concept of the circular convolution plays an important role to the SC FDE. In this section, we will introduce form the linear convolution to the circular convolution [11].

20

1)-point to do the circular convolution, x₄,n- becomes

x₄,n- = x₁,n- ⨂ x₂,n- = ∑ x₁ Thus, the circular convolution is the aliased version of the linear convolution.

On the other hand, if we pad the number of zeros to make x₁,n- and x₂,n- become a (N₁ + N₂ – 1)-point sequence, the result of circular convolution is equal to the result of linear convolution.

3.4 Single Carrier Frequency Domain Equalizer

The traditional method to compensate for ISI is to use a time domain equalizer at the receiver. One or more transversal filters are main components

21

where the number of adaptive tap coefficients is on the order of number of the data symbols spanned by ISI. An SC system transmits a single carrier

modulated with QAM at high symbol rate suffering a serious ISI problem. The complexity and digital processing speed become exorbitant, and the time domain equalizer becomes unattractive.

Frequency domain equalizer compensates the channel response in the frequency domain. Figure 3-1 shows the basic idea of FDE. When a signal x into the system which the channel impulse response is h, we know that it is the convolution of the signal x and the channel h in the time domain. The

convolution process becomes the simple multiplication in the frequency

domain where F{} and F^-1{} are the fast Fourier transform and inverse Fourier transform, and we can easily use one tap equalizer to compensate the signal in the frequency domain. For channel with severe ISI, frequency domain

equalization is computationally simpler than the time domain equalizer. Figure 3-2 is the block diagram of FDE. At first, the received signal passes the fast Fourier transform (FFT) operation transforming the time domain SC signal to frequency domain, and then the compensated signal transfer to the time domain signal by inverse fast Fourier transform (IFFT) after equalization. However, we can’t do FFT to all of the data and process all of the data at once, because the memory of the digital circuit has its limitation. Thus, we want to process the signal in the block form which every M symbols (M = 64, 128, 256… and so on) a block. Then, the concept of cyclic prefix (CP) is introduced. CP length is L symbols which is added form the end of the data block and the length of data block becomes M + L symbols at transmitter. CP makes every data block

circular, and we can lead into the conception of circular convolution to equalize

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M symbols at receiver after removing CP.

Figure 3-1 the basic ideal of FDE.

3.5 MIMO Technology with Frequency Domain Equalizer

Figure 3-3 shows the fundamental concept of 2 x 2 MIMO RoF System.

Two antennas, Tx1 and Tx2, transmit two different signals to the receive

antennas, Rx1 and Rx2. The receive signals will be the summation of these two transmitted signals with different channel coefficient s due to the different transmitting paths and can be expressed as

[y₁ appropriate training symbol, the transmitted data can be recovered by using the

Channel

Figure 3-2 the block diagram of FDE.

23

zero-forcing algorithm and written as [x̂₁

x̂₂] = [ℎ₁₁ ℎ₂₁

ℎ₁₂ ℎ₂₂]⁻¹[y₁

y₂] (Eq. 3-6)

However, since 60 GHz RoF system has uneven frequency response of up to 12 dB within 7 GHz license-free band, the system would encounter the serious inter-symbol interference (ISI) problem. The complexity of MIMO processing in the time domain would significantly increase with the number of signal taps causing by ISI. Thus, we want to find a suitable way avoiding the highly complex matrix calculation. The proper answer is the FDE, and the received signal y transformed to the frequency domain by FFT can be expressed as

[𝐹*y₁,𝑚-+ same as the previous mentioned, the transmitted data can be recovered by using the zero-forcing algorithm, if the channel coefficients in frequency domain are estimated. Figure 3-3 2x2 MIMO RoF system.

24

By using the inverse fast Fourier transform F^-1{}, we can get the transmitted signals in the time domain and can be expressed as

x̂_𝑖,m- = 𝐹⁻¹{𝐹*x̂_𝑖,m-+} 𝑖 = 1,2 (Eq. 3-9) Figure 3-4 shows the block diagram for 2 x 2 MIMO systems with FDE. The bit data stream after the encoder is mapped to different data symbols. The on-off training sequence is used to estimate the channel coefficients. Each block for FDE consists of M+L symbols. Every block includes M data symbols and L symbols as cyclic prefix (CP). The data streams are transmitted to the receiver through the two transmit antennas. After other two antennas receive the transmitted data, MIMO processing is employed to compensate for uneven frequency response and recovery the data. MIMO processing includes FFT, FDE, zero-forcing algorithm, IFFT, and symbol decoder.

Figure 3-4 the block diagram of 2x2 MIMO with FDE.

25

Chapter 4

The Theoretical Calculation of Proposed System

4.1 Introduction Mach-Zehnder Modulator

Figure 4-1 shows a Mach-Zehnder Modulator (MZM), the output E-filed of upper arm is

The output E-filed for lower arm is

E_𝐿 = E₀∙ √1 − a²∙ e^𝑗∆𝜑2 (Eq. 4-3)

∆𝜑₁ is the optical carrier phase difference that is induced by V₂,

∆𝜑₂ ≜ V₂ V_𝜋 ∙ 𝜋

(Eq. 4-4) The output E-filed for MZM is

E_T = E₀∙ {𝑎 ∙ 𝑏 ∙ e^𝑗∆𝜑1+ √1 − a²∙ √1 − b²∙ e^𝑗∆𝜑2} (Eq. 4-5) where a and b are the power splitting ratios of the first and second Y-splitters in MZM, respectively. The power splitting ratio of two arms of a balanced MZM is 0.5. The electrical field at the output of the MZM is given by

E_T =¹

2∙ E₀∙ *e^𝑗∆𝜑1 + e^𝑗∆𝜑2+ (Eq. 4-6)

26 For single electro x-cut MZM, the electrical field at the output is given by

E_out = E₀∙ cos (∆𝜑 − (−∆𝜑)

2 ) ∙ exp (𝑗 ∙∆𝜑 + (−∆𝜑)

2 )

(Eq. 4-8) Add time component, the electrical field is

E_out = E₀∙ cos (∆𝜑) ∙ exp (𝜔₀t) (Eq. 4-9) where E₀ and 𝜔₀ denote the amplitude and angular frequency of the input optical carrier, respectively; V t( ) is the applied driving voltage, and  is the optical carrier phase difference that is induced by V t( ) between the two arms of the MZM. The loss of MZM is neglected. V t( ) consisting of an electrical sinusoidal signal and a dc biased voltage can be written as

𝑉(𝑡) = 𝑉_{𝑏𝑖𝑎𝑠}+ 𝑉_𝑚cos (𝜔_𝑅𝐹𝑡) (Eq. 4-10) where 𝑉_{𝑏𝑖𝑎𝑠} is the dc biased voltage, 𝑉_𝑚 and 𝜔_𝑅𝐹 are the amplitude and the angular frequency of the electrical driving signal, respectively. The optical carrier phase difference induced by 𝑉(𝑡) is given by

∆𝜑 =𝑉(𝑡)

2𝑉_𝜋 =𝑉_{𝑏𝑖𝑎𝑠}+ 𝑉_𝑚∙ cos (𝜔_𝑅𝐹𝑡)

𝑉_𝜋 ∙𝜋

2

(Eq. 4-11) Equation 4-10 can be written as

E_out = E₀∙ cos (𝑉_{𝑏𝑖𝑎𝑠}+ 𝑉_𝑚∙ cos(𝜔_𝑅𝐹𝑡)

27 Expand Equation 4-12 by Bessel functions, as detailed in Equation 4-13, 14, 15 and 16. The electrical field at the output of the MZM can be written as

E_out = E₀∙ cos(𝜔₀𝑡) ∙ where J_n is the Bessel function of the first kind of order n. the electrical field of the mm-wave signal can be written as

E_out = E₀∙ cos(𝑏) ∙ 𝐽₀(𝑚) ∙ cos(𝜔₀𝑡)

+E₀∙ cos(𝑏) ∙ ∑ 𝐽_2𝑛(𝑚) ∙ cos((𝜔₀− 2𝑛𝜔_𝑅𝐹)t + 𝑛𝜋)

∞

𝑛=1

28

4.2 Theoretical calculation of single drive MZM 4.2.1 Bias at maximum transmission point

When the MZM is biased at the maximum transmission point, the bias

When the MZM is biased at the maximum transmission point, the bias

在文檔中 單載波調變與多天線輸入多天線輸出傳輸技術應用於60 GHz光載微波無線訊號系統 (頁 13-0)