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 ^{gij Q, =(hij Q, )*}

(

^{hij Q, 2+σn2 2L}

)

^{, 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

0

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

μ

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

1

ˆ b

1

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

1

ˆ

Q

b ˆ

Q N

b

Q u

b

Ant #j

Ant #1 HARD DEC

ˆ

Q u

b

Q u

b

,1

c

μ ,uN

c

μ moduuNμ

× × ×

,1j ih j i

r

^{1 i}

r

J i

r

Ant #J

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

Ei

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

nI

1 I i i

M

∑

₌ 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

H

( )i

x

{

^{± ±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.

The convolutional encoder is specified as in Table 5.3. At high , the longer constraint length K has a better BER performance. This because the free distance of a

convolutional code is proportional to the constraint length K. Our simulation result shows that

b/ E N_o

dfree

when K =9, the BER approaches 10⁻⁶ at E_b/N_o =5dB. On the other hand, the encoder

with shorter constraint length outperforms one with the longer constraint length at low . This is because at low SNR, the error probability is no longer dominated by the free distance .

b/ E N_o

dfree

Figure 5.2 shows the BER performance of the MIMO-OFDM system in the UMTS defined six-path channel.

-7 -5 -3 -1 1 3 5 Eb/No

10^-4 10^-3 10^-2 10^-1 10⁰

BER

K=

3 4 6 7 9

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

-7 -5 -3 -1 1 3 5 Eb/No

10^-4 10^-3 10^-2 10^-1 10⁰

BER

K=

3 4 6 7 9

Figure 5.2: BER performance of the MIMO-OFDM system in the UMTS defined six-path channel

5.3 The Performance of MIMO MC-CDMA System

Figure 5.3 shows the BER performance of the MIMO MC-CDMA system in the two-path channel. The number of Walsh codes L is equal to the number of active users N_u =256, so

all the spreading codes are used ,i.e., the system is full-loaded. The BER performance for the

first iteration has an error floor at BER=10⁻¹ because large IAI and MPI are included. For the second iteration, the BER performance is improved by using adaptive MMSE and MPIC. This procedure is iterated several times to obtain more and more reliable data decision results.

After several iterations (the 4th iteration in this case), since the adaptive MMSE cannot further improve the BER performance, MPIC is executed alone to achieve full diversity gains gradually. At which iteration the system should turn to MPIC only processing can be decided by compare the decision results between two iterations. When the MPIC decision results of the former iteration are the same as the MMSE decision results of the latter iteration for more than 90%, MPIC can then be executed only at the next and latter iterations. Our simulation results shows that after 9 iterations, the BER performance at high approaches the

theoretical limit and the degradation is only about 0.3 dB at . This simulation result shows that our iterative multi-layered detection method works well and can obtain the full benefits of both spatial diversity and path diversity.

/ 0

Eb N 10 4

BER= ⁻

Figure 5.4 shows the BER performance of the MIMO MC-CDMA system at all four layers in the UMTS defined six-path channel. We can see that after 9 iterations, the BER performance

of the MIMO MC-CDMA system is degrade by only 0.5dB at BER=10⁻⁴ as compared with the case of the perfect LAIC and MPIC.

Figure 5.5 shows the BER performance of the MIMO MC-CDMA system at all four layers in the two-path channel. Our simulations show that the Qth layered detection has a better BER performance than the (Q−1)th layered detection for the same iteration. This is because the

layered detection is started with the first layer and is done in a round robin fashion. Every layer finally approaches almost the same BER performance, i.e., the iterative multi-layered detection method is not sensitive to the order of the layer processing.

Figure 5.6 shows the BER performance of the full-loaded MIMO MC-CDMA system in the two-path channel for different spreading length L. As shown in the figure, the BER performance degrades as the spreading length L increases. This is because the longer spreading length provides the system more frequency diversity. On the other hand, the complexity also grows with the spreading length, which will be specified in the next paragraph. We can see that at the range , the BER degradation is not severe. Therefore,

is a choice to strike a balance between system complexity and BER performance.

L≥16 L=16

Figure 5.7 shows the BER performance of the half-loaded MIMO MC-CDMA system in the two-path channel for different spreading length L. We can observe that unlike the full-loaded

case which only approaches the theoretical limit of BER performance at high (Figure

5.6), the half-loaded system also approaches the theoretical limit of BER performance at low . The simulation results show that the BER degradation becomes severe after

/ 0

Eb N

/ 0

Eb N L<16,

which also matches to the case for full-loaded system in Figure 5.6.

Figure 5.8 shows the BER performance of the MIMO MC-CDMA system for different number of users N_u with fixed spreading length L=16, i.e., the system load is ranging from 1 to 1/4. We can see that the BER decreases with the value of . This is

because if more Walsh codes are used, more LAI and ICI will occur to received signals, hence degrade the system performance.

u/ N L

Nu

Figure 5.3: BER performance of the MIMO MC-CDMA system in the two-path channel with , i.e., a full-loaded system

u 256 L=N =

Figure 5.4: BER performance of the MIMO MC-CDMA system in the UMTS defined six-path channel with L=N_u =256, i.e., a full-loaded system

Figure 5.5: BER performance of the MIMO MC-CDMA system at all four layers in the two-path channel

-7 -5 -3 -1 1 3 5

Eb/No

10^-4 10^-3 10^-2 10^-1

BER

Nu=L=

4 8 16 32 64 128 256

Perfect LAIC and MPIC

Figure 5.6: BER performance of the full-loaded MIMO MC-CDMA system in the two-path channel for different spreading length L

-7 -5 -3 -1 1 3 5 Eb/No

10^-4 10^-3 10^-2 10^-1

BER

L = 2Nu = 4 8 16 32 64 128 256

Perfect LAIC and MPIC

Figure 5.7: BER performance of the half-loaded MIMO MC-CDMA system in the two-path channel for different spreading length L

-7 -5 -3 -1 1 3 5

Eb/No

10^-4 10^-3 10^-2 10^-1

BER

Nu=

16 14 12 10 8 6

Perfect LAIC and MPIC

Figure 5.8: BER performance of the MIMO MC-CDMA system for different number of users with fixed spreading length

Nu L=16

5.4 Comparison of the MIMO-OFDM and MIMO MC-CDMA systems

We compare the system performance of the MIMO-OFDM and MIMO MC-CDMA systems in this paragraph. For MIMO-OFDM systems, the convolutional encoders in Table 5.3 with rate are used; and for MIMO MC-CDMA systems, we consider the case with system load . Table 5.5 compares the complexity of the two systems. Most

complexity of the MIMO-OFDM system is for decoding process. For the MIMO MC-CDMA system, spreading and despreading process are the dominant factor of the total complexity.

1/ 2

/ 1/ 2 Nu L=

Figure 5.9 shows the BER performance of the two types of systems. We observe that MIMO MC-CDMA systems significantly outperform MIMO-OFDM systems in the low

region. This is because the MPIC method for MIMO MC-CDMA systems can fully achieve diversity gains including both spatial diversity and multipath diversity. On the other hand, MIMO-OFDM systems slightly outperform MIMO MC-CDMA systems in the high

region. This is because the coding gain for MIMO-OFDM systems can be fully achieved when is high.

System

Process MIMO-OFDM MIMO MC-CDMA

Each layer: at all receivers at each receiver

8N 2MN 2

MMSE 4 (4N M J² +2M³) + +

4MNJ 2LMN+6MN

LAIC

MPIC 0 ^{8NP+4 (N L+1)}

Decoding MN2 /^K R 0

Total 1392640 1032224 Table 5.5: The complexity comparison of MIMO-OFDM and MIMO MC-CDMA system

(measured by the number of the real multiplier, K = , 9 L=16, P=2)

Figure 5.9: BER performance of MIMO-OFDM systems with 1/2-rate convolutional coding and half-loaded MIMO MC-CDMA systems

5.5 Multi-cell Environment

5.5.1 Gaussian Approximation

In this paragraph we discuss the BER performance of the MIMO-OFDM and MIMO MC-CDMA systems in the multi-cell environment. The model of the cellular system is as described in Figure 4.8. A simplified multi-cell environment is assumed, i.e., all interfering cells have the same and constant weighting factor . In order to verify the Gaussian

approximation in Eq. (4.3),

/ 0

E Ei

Figure 5.10 and Figure 5.11 show the simulation results of the MIMO-OFDM system with code rate R=1/ 2 and the half-loaded MIMO MC-CDMA system respectively, in a simplified multi-cell environment. The BER is plotted as a function of the difference in received power between each interfering base station and the desired base station with the number of interfering cells as a parameter. The dashed curves represent the Gaussian approximation. We can see that for both MIMO-OFDM and MIMO MC-CDMA systems the Gaussian approximation model accurately.

Figure 5.10: BER performance of the MIMO-OFDM system in a multi-cell environment with code rate R=1/ 2, constraint length K = , and 9 E_b/N₀ =8dB

Figure 5.11: BER performance of the half-loaded MIMO MC-CDMA system in a multi-cell environment with Walsh codes length L=16 and E_b/N₀ = B8d

5.5.2 Analyses of System Performance in Multi-cell Environment

In order to reduce interferences, directional antenna can be used [15]. When S (a small

In order to reduce interferences, directional antenna can be used [15]. When S (a small

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 26-0)