Chapter 4 Multi-cell Environment
4.3 Cellular Interference Modeling
4.3.1 Gaussian Approximation
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 interferingsignal 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( )tdenotes 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 Nu active users, the system load will be Nu 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 No
dfree
when K =9, the BER approaches 10−6 at Eb/No =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 No
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 Nu =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 Nu 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=Nu =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 Eb/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 Eb/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 integer) directional antennas are used at a base station to illuminate S different sectors in a cell, the interference can be reduced by a factor of S. This reduction can be defined as sectored antenna gain G . Another approach for interference reduction is the relatively low speech s
activity factor, which is about 40% during two-way conversations [21]. This can be defined as voice activity gain Gv.
By Gaussian approximation, the interference signal can be modeled as Gaussian noise;
hence the discussion of the system performance in multi-cell environment can be simplified.
It should be noticed that in our MIMO systems, the interference signal power received at each receive antenna is proportional to the number of transmit antenna M. For example, in our simulations M =4 , a -5 dB SIR is equivalent to a -11dB by Gaussian simulation results of the SIR distributions in paragraph 4.2, we can obtain the simulated distribution of user’s average error probability at two tiers’ multi-cell environment (ignoring the effect of noise) in Figure 5.12. We can see that MIMO MC-CDMA systems outperform MIMO-OFDM systems in both downlink and uplink channels.
Figure 5.12: Simulated distribution of user’s average error probability at two tiers’ multi-cell environment
Chapter 6
Conclusions
High data rate and spectral efficiency is a major demand for the future generation of wireless communication systems. Many attractive candidates of transmission schemes are based on OFDM. In this paper, we conduct a comparison of the MIMO-OFDM and MIMO MC-CDMA systems. For MIMO-OFDM system, we adopt the V-BLAST detection and convolutional coding technique; for MIMO MC-CDMA system, we use an iterative multi-layered detection method combined with a MPIC technique to suppress the interference induced by multi-layered transmission and multipath environment. We observe that MIMO MC-CDMA significantly surpasses MIMO-OFDM at low SNR region. At high SNR region, MIMO-OFDM slightly outperforms MIMO MC-CDMA. In Chapter 4, a multi-cell environment is introduced hence we can extend our investigations to more realistic scenario, i.e., cellular structures. Simulations show a good match by replacing the interfering signals with the Gaussian approximation. From computer simulations of the SIR distributions we can obtain the user’s average error probability in a multi-cell environment for both MIMO-OFDM
and MIMO MC-CDMA systems. Simulation results show that MIMO MC-CDMA has a better performance in a multi-cell environment.
APPENDIX A
The Modified MMSE V-BLAST Equalizer
Our goal is to design the equalization matrix G to minimize the mean square error, namely
{
2}
E x Gz− where x is the transmitted signal vector and z is the received signal vector after matching in frequency domain as described in subsection 3.1. Each component of x has zero mean and unit variance, i.e., E
{ }
xxH =I. Moreover, the vector n is the noise with zero meanand variance σ , i.e., n2 E
{ }
nnH =σn2I. By the principle of orthogonality, we have:( )
{
H}
0E x Gz z− = (A-1)
Expand the equation, the first term becomes:
{ } { } { }
The second term becomes:
{ } { ( )( ) }
(
H H σn2 H)
−1 H= +
G H HH H H H H H (A-4)
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