About The Thesis - 多輸入/輸出正交分頻多工與多輸入/輸出多載波分碼多重進接系統之電腦模擬與效能鑑定

Chapter 1 Introduction

1.3 About The Thesis

This thesis is organized as follows. The MIMO-OFDM and MIMO MC-CDMA system models are described in Chapter 2. The details of the detection methods for the two systems are included in Chapter 3. The model for the different propagation impairments affecting the cellular environments is described in Chapter 4. The performance of the MIMO-OFDM and MIMO MC-CDMA systems are evaluated and compared through computer simulations in Chapter 5. Finally, some conclusions are drawn in the last chapter.

Chapter 2 System Model

In this chapter, the MIMO-OFDM and MIMO MC-CDMA system models are presented.

They both apply M antennas to transmit different data, so spectral efficiency becomes M times.

The details of system model are described and illustrated as follows.

2.1 MIMO-OFDM

Figure 2.1 shows a transmitter block diagram of the MIMO-OFDM system with M transmit antennas. The information source output is first encoded by a convolutional channel-coder, and interleaved by the interleaver Π . The encoded bits are then mapped into QPSK symbols and serial-to parallel (S/P) converted into M parallel data substreams. Each data substream is fed into an OFDM modulator, which induces N-point inverse discrete Fourier transform (IFFT) block followed by a parallel to serial (P/S) block and guard interval insertion (GI). The resultant M signals are transmitted simultaneously.

Π

TX1

TX^M

Figure 2.1: The transmitter block diagram of the MIMO-OFDM system

2.2 MIMO MC-CDMA

Figure 2.2 shows a transmitter block diagram of the MIMO MC-CDMA system with M transmit antennas. The information source output is first S/P converted into M parallel data

streams d^m, for 1 m M≤ ≤ .

MC-CDMA TX1

MC-CDMA TX^M

TX1

TX^M

d

Figure 2.2: The transmitter block diagram of the MIMO MC-CDMA system

Each data stream is then processed by an MC-CDMA transmission scheme and sent to the

corresponding transmit antenna. The MC-CDMA transmission scheme for the mth transmit

antenna is shown in Figure 2.3. After S/P conversion, the mth data stream is first mapped into QPSK symbols and multiplexed to

dm . Each data substream

1 l L≤ ≤ _,1, _,2, , _, ^T

m m m m

n = ⎣⎡bn bn bn N ⎤⎦

b is then spread by a group of Walsh codes, , for . The data modulated Walsh codes are summed up and the sum

can be expressed as , for 1

symbols are interleaved by the random interleaver Π to maximize the diversity gain and ^m avoid coherent IAI at the receiver side. The system load is and can be set to a value

from 1 to . As a result, the transmitted signal in frequency domain from the mth transmit antenna can be written as

After interleaving, the signals are fed into an OFDM modulator and the resultant M signals are transmitted simultaneously.

C

Figure 2.3: The MC-CDMA transmit scheme at the mth transmit antenna

For simplification, we assume that the synchronization and channel estimation at the receivers are perfect and the maximum multipath delay spread is fewer than T_g, the time

duration of GI. So receivers can obtain the accurate channel information and be ISI-free.

Chapter 3 Detection Methods for MIMO-OFDM and MIMO MC-CDMA Systems

In both MIMO systems, each transmitter is used to transmit different data stream that induces the inter antenna interference (IAI). The received signals for MIMO-OFDM systems and MIMO MC-CDMA systems all contain IAI. The data stream for individual transmitter must be detected from signals at J receivers. Each layer is considered in turn to be the desired signal, and the remainder is treated as interference (Successive Interference Cancellation, SIC). The signal processing chain related to each individual data substream from a transmit antenna is referred to as a layer. The signal processing of the Qth layer is called the Qth layered detection. For MIMO-OFDM systems, the ordering of layered detections gives effect to the performance of the SIC detector. On the other hand, for MIMO MC-CDMA systems the iterative multi-layered detection method is not sensitive to the order of the layer processing.

Therefore without loss of generality, the layered detection is started with the first layer and is done in a round robin fashion. In the following, we first describe the V-BLAST detection for MIMO-OFDM systems in subsection 3.1. In subsection 3.2, we describe the detection methods for MIMO MC-CDMA systems, which contain the layered antenna interference

cancellation (LAIC) concept, the adaptive MMSE equalizer, and the MPIC method. The iterative multi-layered detection method is summarized at the end of the section.

3.1 V-BLAST Detection Methods for MIMO-OFDM Systems

The received signal vector in frequency domain for the ith subcarrier and all J receive antennas can be expressed as r_i

i = i i+ i

r H x n (3.1)

where H_i, x_i, and n_i are the J×M channel matrix with element h_i^{j m}^, representing the

channel frequency response between the mth transmit antenna and the jth receive antenna at the ith subcarrier, the M×1 vector for the transmitted signal form all M transmit antennas, and the J×1 noise vector at J receive antennas.

In [4], a V-BLAST architecture is proposed which can be used for MIMO-OFDM systems.

Signals for different layers are detected by the successive interference canceller combined with MMSE criterion. As mentioned in [13], when symbol cancellation is used, the system performance is affected by the order in which the components are detected. Because the operations are the same for all subcarriers, the subcarrier index i is omitted below. The

matched signal is z H r H Hx H n^H = ^H + ^H . The full MMSE V-BLAST detection algorithm

(see Appendix A) can now be described compactly as a recursive procedure, including determination of the optimal ordering, as follows:

Initialization It should be noticed that the V-BLAST architecture described above is a modified version of [4]. We have added a matched filter at the receiver to improve the system performance. By

rewriting Eq. (3.3) as G1=H⁺ inv

(

H H^H +σn²IM

)

H^H and removing the matched filter, we can obtain the original V-BLAST architecture proposed in [4].

After the V-BLAST detection is done, the decision results are deinterleaved and decoded by a Viterbi decoder, as shown in Figure 3.1.

RX1

RX^J ₋₁

Π

Figure 3.1: The receiver block diagram of the MIMO-OFDM system

3.2 Iterative Multi-layered Detection Methods for MIMO MC-CDMA Systems

The notation for MIMO-CDMA systems is slightly different from that for MIMO-OFDM systems. The received signal in frequency domain at the jth receive antenna can be written as:

the received signal vector, channel frequency response matrix from the mth transmit antenna to the jth receive antenna ( diagonal matrix), and noise vector at the jth receive antenna, respectively. The matrix can be expressed as

N×N

where P is the total number of paths. H_p^{j m}^, is the channel frequency response of the pth path, which is diagonal with each element αp^{j m}^, ^{exp 2}

{

j π

(

i−¹

)

τp^{j m}^, ^/N

}

, for 1≤ ≤i N, where

, j m

αp and τ_p^{j m}^, are the complex fading gain and the excess delay of the pth path, respectively.

The N elements of are modeled as independent complex Gaussian random variables with zero mean and variance

nj 2

σn.

3.2.1 Layered Antenna Interference Cancellation and Adaptive MMSE Equalization

From Eq. (3.14), it is apparent that the orthogonality of Walsh codes will be destroyed when the channel is frequency selective. Under such circumstances, the system encounters not only severe IAI but also severe MPI which together degrade the system performance.

At the Qth layered detection, the hard decision results of the previous layers, for can be used to generate the IAI replicas. After subtracted from the

received signal of the jth receive antenna, the resulting signal is ˆ^m

Then, we apply a simple frequency domain adaptive MMSE equalizer G^{j Q}^, without matrix inversion to the signal r^{j Q}^, [14]. It can be formulated by G^{j Q}^, =diag g

{

1^{j Q}^, ,g2^{j Q}^, , ,g_N^{j Q}^,

}

. Assume that the hard decision results of the previous layers are all correct, i.e. the IAI is perfectly removed. Besides, due to the use of the interleaver at the transmitter side, we can treat the unprocessed IAI us noise. Therefore, the coefficients of the adaptive MMSE

equalizer can be expressed as

, *

The uth code channel output after despreading and receiver diversity combining is , where

3.2.2 Multipath Interference Cancellation

After first iteration, hard decision results of all layers are available. At the jth receive

antenna and the Qth layered detection, a signal r^{j Q}^, can be obtained by subtracting the IAI

from the received signal r^j, that is,

With the hard decision results of the Qth data substream, the MPIC method can be used to suppress the MPI and to achieve multipath diversity gains [9]-[12]. The details operations of the MPIC method are summarized as follows. First, the MPI replicas of all interfering signal

paths can be generated and subtracted from the signal r^{j Q}^, to extract the signal from each path r_v^{j Q}^,

, for 1 v P≤ ≤ . After RAKE combining and deinterleaving, the signal becomes

( )

The uth code channel output z_u^Q after despreading and receiver diversity combining is

3.2.3 Iterative Multi-layered Detection

The iterative multi-layered detection method is summarized as follows. Figure 3.1 shows the first iteration of our multi-layered detection method. The signal is processed according to the LAIC concept and the adaptive MMSE equalization method as described in subsection 3.2.1. Note that at the first layered detection, the received signals are passed only through the adaptive MMSE equalizer to obtain the hard decision results for the first data substream.

Figure 3.2 shows the second and subsequent iterations of the iterative multi-layered detection method. For illustration purpose, we focus on the Qth layered detection for the jth receive antenna for the second iteration. Because we have the hard decision results of all the data substreams, the LAIC eliminates all the other data substreams (excluding the Qth data

substream) according to Eq. (3.19) to obtain the signal r^{j Q}^, . Afterward, we use the adaptive MMSE equalizer with coefficients of ^gⁱ^{j Q}^, ⁼⁽^hⁱ^{j Q}^, ⁾^*

(

^hⁱ^{j Q}^, ²⁺^σⁿ² ²^L

)

^{, for 1} ^{, to}

equalize the signal

i N

≤ ≤

rj Q and obtain more reliable decision results of the Qth data substream.

At this point, the MPIC method mentioned in subsection 3.2.2 is excuted according to Eq.

(3.20) and Eq. (3.21) to obtain the decision results of the Qth data substream. In general, the decision result is much more accurate by fully exploiting the gains from both the spatial diversity and the multipath diversity. The process can be repeated in several iterations until

reliable data estimates of all the data substreams are obtained. Note that for the last few iterations, because the adaptive MMSE equalizer can not have further improvement in BER performance, the MPIC can be executed alone without the help from the adaptive MMSE equalizer to accelerate the convergence process.

Figure 3.1: The first iteration of the multi-layered detection method

Ant #J

Ant #1 Ant #j Despreading SC-MMSE

{ }

1Q− ΠHARD DEC

1ˆ b ²ˆ b

1ˆQ− b

Spreading1 Π

,1j ih 1Q=2QM≤≤ ,* , 2 2,() 2

jQ jQi i jQi i u

h g h Nσ= +

,jQ i

h

,jM ih −

1 subcarrierth subcarrierNth

subcarrierith

IAI Reconstruction ,1

c

Ant #1 Ant #j Ant #J

j i

r

1 i

r

J i

r

Q u

z ˆ

Q u

b

,uNc μ moduuNμ

× × ×

Figure 3.2: The second and latter iterations of the multi-layered detection method

Ant #J

Ant #1 Ant #j Despreading SC-MMSEHARD DEC

ˆ b

ˆ

Q−

b

1ˆQ+ b

Spreading1

Π

,* , 2 2,() 2

jQ jQi i jQn i u

h g h Nσ= +

−

1 subcarrierth subcarrierNth subcarrierith

IAI Reconstruction Ant #1 Ant #jQ u

z

ˆ

Q u

b

ˆM b

MPIC

ˆ

b ˆ

Q N

b

Q u

b

Ant #j

Ant #1 HARD DEC

ˆ

Q u

b

Q u

b

c

μ ,uN

c

μ moduuNμ

× × ×

,1j ih j i

r

¹ ⁱ

r

J i

r

Ant #J

{ }

1Q− Π

Chapter 4 Multi-cell Environment

Here we present a cellular network. Furthermore, a propagation model for the path loss is introduced and described in detail.

The cellular network is based on a typical hexagonal structure where all cell sizes are assumed to he equal. A base station is located in the center of each cell. The multi-cell environment consists of base stations where the center base station, denoted as , is surrounded by interfering base stations, denoted as , for

(I+ )1 BS₍₀₎

BS( )_i 1 i I≤ ≤ .

4.1 Propagation Loss Model

The propagation attenuation is generally modeled as the product of the ρ power of th

distance and a log-normal component representing shadowing loss [15]. Shadow variations

are caused by large terrain features between the base station and the mobile station such as buildings and hills. These represent slowly varying variations even for users in motion and apply to both downlink and uplink. Thus for a user at a distance d from a base station, the received signal energy E_r can be modeled as

(4.1) 10 /10

r t

E =E ×d⁻^ρ× ^η

where E_t is the transmitted signal energy. Furthermore, the shadowing factor η is a normally distributed random variable with zero mean and standard deviation σ and is given _p in dB. In [16], the standard deviation σ and the distance decay factor ρ are set to 8 dB _p

and 4, respectively, as suggested by experimental data. These values are used throughout this paper unless further mentioned.

4.2 Distributions of Signal-to-Noise Ratio

The following is a list of assumptions from which we depart to establish a multi-cell environment.

1). Our system performance is limited by interference coming from users within the same frequency band.

2). The information data signaling rate is low enough such that ISI can be neglected.

3). Uplink transmission and downlink transmission have to be separated.

4). Each base station transmits at the same power level in its downlink channels.

5). Every mobile station transmits at a power level such that its home base always receives at the same power level, i.e., power control is executed in uplink transmissions.

6). The uplink and downlink channel are reciprocal from propagation loss point of view.

7). A mobile station always chooses its home base station to be the one provides the largest received signal power level.

Here we use computer simulation to calculate SIR [17]. The propagation loss model is used as described in subsection 4.1.

0/10 independent distributed random variable with zero mean and standard deviation σ for all i. _p

Figure 4.2 shows the simulated cumulative distribution of downlink SIR when the whole system consists of 2~61 cells. In the simulation, a candidate mobile station is randomly located within the central cell and the received signal power level from each base station is calculated according to the mentioned propagation loss model. The base associated with the

largest received signal power level is regarded as the home base and the signals from all the other bases are regarded as interference. In order to examine the distribution curves more closely, we expand the initial portion of curves in Figure 4.1 in Figure 4.2. From Figure 4.2 we observe that downlink SIR is better than -5.0, -4.5, and -3.4 dB for more than 99 percent of the simulated cases when the number of tiers is 4, 2, and 1, respectively.

The simulation of uplink SIR is trickier than the downlink case. Take the 4 tiers case as an example, we first generate a table of size 60 × 10000 from the downlink simulation. During

each run of downlink simulation we found a home base for a candidate mobile randomly located in the central cell. Each row of the table was then generated such that it consists of normalized interference power received at the mobile from 60 bases around the home base.

By normalization we mean the dividing of the received power from each surrounding base by the power received from the home base. As a result, each item in the table is less than or equal to one. The table can be interpreted as a sample space of normalized interference from each of the 60 surrounding bases to a user associated with the home base. Due to power level reciprocity the table can also be interpreted as a sample space of normalized interference from a user associated with the home base to its 60 surrounding bases when uplink power control is in effect. Figure 4.3 shows the simulated cumulative distribution of uplink SIR under the assumption that a candidate home base station is located at the central cell and each base station has a mobile station in communication with it. The wanted signal comes from the

mobile associated with the central home base and the interference comes from all other mobiles associated with surrounding bases. Figure 4.4 expands the initial portion of the distribution curves in Figure 4.3. From Figure 4.4 we see that uplink SIR is better than -3.1, -2.9, and -2.2 dB for more than 99% of the simulated cases when the number of tiers is 4, 2, and 1, respectively. The simulation results indicate that uplink SIR is better than the downlink case.

-10 0 10 20 30 40 50 60

60 interfering cells (4 tiers) 18 interfering cells (2 tiers) 6 interfering cells (1 tier) 4 interfering cells

2 interfering cells 1 interfering cell

Figure 4.1: Simulated distribution of Downlink SIR

Figure 4.2: Initial portion of Figure 4.2

-10 0 10 20 30 40 50 60 SIR, dB

0 0.2 0.4 0.6 0.8 1

Prob. SIR<Abscissa

Uplink

60 interfering cells (4 tiers) 18 interfering cells (2 tiers) 6 interfering cells (1 tier) 4 interfering cells

2 interfering cells 1 interfering cell

Figure 4.3: Simulated distribution of Uplink SIR

Figure 4.4: Initial portion of Figure 4.4

4.3 Cellular Interference Modeling

The cellular interference can be modeled as depicted in Figure 4.5. We assume the synchronization between the base station and the mobile station is perfect.

Figure 4.5: Model of the cellular MIMO-OFDM and MIMO MC-CDMA system

By including the interfering base stations the received signal in frequency domain becomes (for similarity, we omit the subcarrier index)

(4.3)

transmitter and the receiver, M×1 transmitted signal vector from the ith transmitter, J× 1 received signal vector, and noise vector, respectively. The signal energy of the ith transmitter can be modeled according to Eq. (4.1).

J×1

4.3.1 Gaussian Approximation

For system level simulations, the simulation of all interfering signal paths is very complex.

Thus, a simplification of the interference model is done by assuming the entire interference as Gaussian noise [18]. Hereby, the noise variance has to be scaled appropriately. By Gaussian approximation, Eq. (4.2) can be rewritten as

(4.3)

0 (0) (0) I

≈E +

y H x n +n

If all path gains have unit mean, the variance of the Gaussian approximated interference

will be

1 I i i

∑

₌ E . With the Gaussian approximation, no information about the interfering

signal is needed, except for their average signal strength. Thus, a multi-cell environment can be implemented very efficiently. The Gaussian approximation is suitable because is Gaussian. is not Gaussian since it is randomly taken from a finite set

( )i

{

^{± ±}^{1 j}

}

Chapter 5 Simulation Results

5.1 Simulation Environments

We verify and compare the performance of the MIMO-OFDM and MIMO MC-CDMA systems by computer simulations. A frequency selective channel is modeled and the equivalent baseband impulse response of the multipath channel between the mth transmit and

the jth receive antenna is represented by

( ) (

complex fading gain of the pth path, which is complex Gaussian random variable, and δ( )t

denotes a delta function. The fading patterns of each temporally resolvable path from each transmit antenna to the receive side are generated independently. It is assumed that the channel is stationary over each transmission. Two channel models are selected for our simulations. One is a two-path channel with relative path power profiles: 0, 0 (dB). The other

is a Universal Mobile Telecommunication System (UMTS) defined six-path channel with relative path power profiles: -2.5, 0, -12.8, -10, -25.2, -16 (dB) [19].

Table 5.1 shows the simulation parameters commonly used for both MIMO-OFDM and MIMO MC-CDMA systems. The entire simulations are conducted in the equivalent baseband.

We assume symbol synchronization, carrier synchronization, and channel state information are perfectly estimated. The noise and interference power are also assumed to be known at the receiver end. The excess delay of the paths is uniformly distributed between 0μs and 12.3μs.

In the multi-cell environment, all interfering cells have the same parameters as the desired cell.

Table 5.2 shows the MIMO-OFDM system-specific simulation parameters. We choose the convolutional codes with fixed rate R=1/ 2. The encoders are listed in Table 5.3. Each code is chosen to has maximum free distance [20].

Table 5.4 shows the MIMO MC-CDMA system-specific simulation parameters. The number of Walsh codes is equivalent to the length of each Walsh code. Therefore, when there are N_u active users, the system load will be N_u L which can be set to a value ranging

from 1 to 1/ L.

# transmit antenna M 4

# receive antenna J 4

Modulation QPSK

Carrier frequency f c 2GHz

Total Bandwidth B w 5.12MHz

# subcarriers N 256

Guard interval Tg 12.5μs

# resolvable paths P 2 or 6

Table 5.1: Simulation parameters common for both MIMO-OFDM and MIMO MC-CDMA systems

Channel coding Convolutional code

Channel coding rate R 1/2

Table 5.2: Simulation parameters for MIMO-OFDM system

free free

d Upper bound on d Constraint length K Generators in octal

3 5 7 5 5

4 15 17 6 6

6 53 75 8 8

7 133 171 10 10

9 561 753 12 12

Table 5.3: Rate 1/2 maximum free distance codes

# Walsh codes L

{

4,8,16,32,64,128, 256

} {

^{1, 2, , L}^…

}

# active users N u

Table 5.4: Simulation parameters for MIMO MC-CDMA system

5.2 The Performance of MIMO-OFDM System

Figure 5.1 shows the BER performance of the MIMO-OFDM system in the two-path channel.

在文檔中多輸入/輸出正交分頻多工與多輸入/輸出多載波分碼多重進接系統之電腦模擬與效能鑑定 (頁 14-0)