I. J. Communications, Network and System Sciences, 2008, 2, 105-206
Published Online May 2008 in SciRes (http://www.SRPublishing.org/journal/ijcns/).
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
Performance Analysis of an AMC System with an Iterative
V-BLAST Decoding Algorithm
Sangjin RYOO1, Kyunghwan LEE2, Intae HWANG3
1 Department of Electronics Engineering, Chonnam National University, Korea
2 T&M Algorithm Research, Innowireless, Inc., Korea
3 Department of Electronics & Computer Engineering, Chonnam National University, Korea
Abstract
In this paper, the iterative Vertical-Bell-lab Layered Space-Time (V-BLAST) decoding algorithm of an
Adaptive Modulation and Coding (AMC) system is proposed, and the corresponding MIMO scheme is
analyzed. The proposed decoding algorithm adopts iteratively extrinsic information from a Maximum A
Posteriori (MAP) decoder as an a priori probability in the two decoding procedures of the V-BLAST scheme
of ordering and slicing in an AMC system. Furthermore, the performance of the proposed decoding
algorithm is compared with that of a conventional V-BLAST decoding algorithm and a Maximum
Likelihood (ML) decoding algorithm in the combined system of an AMC scheme and a V-BLAST scheme.
In this analysis, each MIMO schemes are assumed to be parts of the system for performance improvement.
Keywords: Iterative V-BLAST Decoding, MAP Decoder, AMC, STD, Turbo Code
1. Introduction
To improve the throughput performance together with
the development of the MIMO scheme, the AMC
scheme has attracted considerable attention as the
forerunner of next-generation mobile communication
systems [1]. The AMC scheme adapts a coding rate and
modulation scheme to the channel condition [2],
resulting in improved throughput performance.
Consequently, the combination of a MIMO scheme and
an AMC scheme can potentially improve the throughput
performance. V-BLAST [3,4] was selected as the MIMO
multiplexing scheme [5] and the turbo-coding [6] was
chosen as the channel coding scheme of the AMC due to
the complexity of the aforementioned combined system.
The turbo-coding scheme with iterative decoding implies
the use of parallel concatenated recursive systematic
convolutional codes. Such a scheme is iteratively
decoded with a Posteriori Probabilities (APP) algorithms
for the constituent codes [7,8]. In addition, the turbo
decoding algorithms used with MIMO is currently an
area that is actively researched [9,10].
A performance analysis is offered here of AMC
systems with several V-BLAST decoding algorithms
including the turbo decoding algorithm used with MIMO.
For greater performance improvement, the proposed
system utilizes a 2×2 MIMO channel using two
transmitter antennas and two receiver antennas, a 4-2×2
MIMO channel applying a Selection Transmit Diversity
(STD) scheme [11] that selects two antennas from four
transmitter antennas, a 4×4 MIMO channel using four
transmitter antennas and four receiver antennas, and a
8×8 MIMO channel using eight transmitter antennas and
eight receiver antennas.
2. The AMC System with the Proposed
Iterative V-BLAST Decoding Algorithm
Figure 1 shows the structure of the AMC system used
with the proposed iterative V-BLAST decoding
algorithm. An AMC system that uses a conventional V-
BLAST decoding algorithm combines a V-BLAST
scheme with a turbo-coded AMC system. The proposed
decoding algorithm of an AMC system differs from the
conventional V-BLAST decoding algorithm insofar as
the extrinsic information from a MAP decoder is used as
an a priori probability in the ordering and slicing
decoding procedures of the V-BLAST scheme [12].

120 S.J. RYOO ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
Figure 1. Transmitter-receiver structure of an AMC
system with the proposed iterative V-BLAST decoding
algorithm
This scheme operates iteratively and is defined as the
main MAP iteration. Furthermore, whenever the scheme
operates internally, iterative decoding of the MAP
decoder is performed. This method is defined as sub
MAP iteration. For the proposed system, a system
equipped with M transmitter antennas and N receiver
antennas is considered. It is assumed that each
transmission channel is modeled as a flat Rayleigh
fading channel. The received signal in the V-BLAST
receiver is denoted by
X = Hs + n (1)
where X=[x1,…,xN]T is the received signal vector,
s=[s1,…,sM]T is the transmitted symbol vector, H is the
N×M channel matrix, n=[n1,…,nN]T is the noise vector.
The superscript T signifies the transpose matrix, and the
noise vector, n, is modeled as a complex Gaussian
random process. In addition, sm is the 2Q-ary modulated
symbol; that is sm=f(d1
m,…,dQ m)∈Φ={φ1,…,φ2Q}, where
Q denotes the bit number per symbol, f(·) denotes the
symbol modulation function, {dq
m}q=1,…,Q represents the
q-th information bits that correspond to s
m, and
{φi}i=1,…,2Q represents the i-th symbol. The proposed
slicing algorithm does not make a hard decision with the
received signal but makes a decision with the extrinsic
information from the MAP decoder [13]. This extrinsic
information from the MAP decoder is the log-likelihood
function, which can be described as
(
)
()
,
1
log
0
m
q
mq m
q
pd
L
pd
=
=
=
(2)
where Lm,q is the extrinsic information that corresponds
to dq
m [14]. Specifically, {dq m}q=1,…,Q is determined by
{Lm,q}q=1,…,Q, respectively. (e.g., if Lm,q is greater than 0,
dq
m is determined to be 1. Otherwise, dq m is determined
to be 0.) The proposed slicing algorithm then performs
the quantization operation appropriate to the
constellation in use corresponding to {dq
m}q=1,…,Q. In a
conventional V-BLAST ordering procedure, the
decoding order is determined by the SNR of the
corresponding layer. The conventional V-BLAST
ordering is described as
lk = arg
m
min ||(Hk
†)m||2 (3)
where k denotes the decoding stage and the superscript †
represents the pseudo-inverse matrix. The SNR is a
function of the channel power, and the layer with the
largest channel power is the first layer that is decoded. A
high SNR signifies a low symbol error rate. From this
fact, it follows that the maximum SNR criterion can be
considered to be a specific version of the minimum
symbol error criterion. The proposed ordering algorithm
is a function not only of the SNR but also of the
extrinsic information. It can be modified accordingly to
lk = arg
m
min Pm(e|Xk, Hk, Lm
(i)) (4)
where Pm (e|Xk, Hk, Lm
(i)) is the symbol error probability
of the m-th layer and Lm
(i)=[Lm,1 (i),···,Lm,Q (i)]T is the
extrinsic information vector of the lk-th layer at the i-th
main MAP iteration. The symbol error probability, Pm,
can be calculated from
Pm(e|Xk, Hk, Lm(i))
=
22
11,
1
2
QQ
Q
qppq==≠
∑
∑P(φq| Lm
(i))P(φq→ φp|Xk, Hk, Lm (i)) (5)
where φq is the original transmitted symbol, φp is the
possible symbol excluding the original transmitted
symbol (φq), and P(φq→ φp|Xk, Hk, Lm
(i)) is the pair-wise
symbol error probability, which can be obtained from
P (φq→ φp |Xk, Hk, Lm
(i))
= P [ p(φq|ym) < p(φp|ym) ]
= P [ log p(φq|ym) < log p(φp|ym)] (6)
where y
m
is the desired symbol that deletes the
interference of other symbols after the nulling process
of the V-BLAST decoding in the received symbol of
the
m -th layer, x
m
. With the assumption that the
variance of noise corresponding to the
m -th layer is
σ
m
2
/2, in Eq. (6), the log posteriori function of φ
p
is
described by
log p(φp|ym) (7)
= log [ p(φp|Lm
(i)) p(ym|φp)/p(ym) ]
=log p(φp|Lm
(i)) + [Re(φ
p －φq)(2ym－(φp+φq))*]/2σm
2
where the superscript * signifies a complex conjugate.
3. Simulation Results
3.1. MCS Level and Parameters for Simulation
Table 1 shows the Modulation and Coding Scheme

PERFORMANCE ANALYSIS OF AN AMC SYSTEM WITH AN ITERATIVE 121
V-BLAST DECODING ALGORITHM
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
(MCS) level selection thresholds, and Table 2 shows the
simulation parameters. The detailed parameters in Table
1 are established on the basis of the 1X EV-DO
standards [15]. There are many references in the
selection of the MCS level selection threshold. For
example, the threshold can be selected to satisfy the
required Bit Error Rate (BER) and the required Frame
Error Rate (FER). As more emphasis is placed here on
the data transmission rate, the threshold that maximizes
the throughput performance was selected. That is, the
threshold of the selected MCS level is derived from the
MCS level transmission rate performance intersection in
each system. One frame is set up with one transmission
slot with a frame length of 2,048 symbols. If one bit
error occurs in one frame, it is assumed to be a frame
error. When a frame error does not occur, the
transmission rate is calculated in accordance with the V-
BLAST technique in the order of (bit length × data rate
× number of transmit antenna). The performance of the
transmission rate closely corresponds to the capacity of
the FER. Thus, in accordance with the transmission rate,
a performance analysis is obtained by the error
probability.
Table 1. MCS levels
MCS
level
Data rate
(Kbps)
Number of bits
per frame
Code
rate Modulation
1 614.4 1,024 1/3 QPSK
2 1,228.8 2,048 2/3 QPSK
3 1,843.2 3,072 2/3 8PSK
4 2,457.6 2,096 2/3 16QAM
Table 2. Simulation parameters
Parameter Value
Turbo-coding scheme PCCC
MAP iteration of the AMC system
with a conventional V-BLAST technique 4
Main MAP iteration of the AMC system
with the proposed V-BLAST technique 4
Sub MAP iteration of the AMC system
with the proposed V-BLAST technique 2
Channel Flat fading
3.2. Complexity of Each Decoding Algorithm
This section outlines the complexity of the proposed
decoding algorithm, the conventional V-BLAST
decoding algorithm, and the ML decoding algorithm in
the combined system of an AMC scheme and a V-
BLAST scheme. The multiplication operation
contributes to the complexity of implementing the
system. Except for the procedures of a channel
deinterleaver and the MAP decoder in the receiver, each
decoding algorithm was compared to the number of
multiplication operations, as shown in Table 3 [16]. In
this table, C is the number of symbols, S is the number
of sub MAP iterations, L is the number of main MAP
iterations, and B is the number of bits per symbol. Some
examples of the table show that the proposed decoding
algorithm is more complex than a conventional V-
BLAST decoding algorithm but less complex than an
ML decoding algorithm. In particular, when used with a
higher-order modulation, the proposed decoding
algorithm is less complex than the ML decoding
algorithm. According to the table, as the modulation
changes from QPSK to 16QAM in the case of M=N=4,
the computational complexity of the proposed decoding
algorithm ranges from approximately 24% to 0.1% of
the complexity of the ML decoding algorithm.
Furthermore, comparing with the complexity of the
proposed scheme in [16], the complexity of the proposed
scheme is relatively less complex for M=N=4, QPSK,
and L=3 or 4.
Table 3. Complexity of each decoding algorithm
(L=4, S=2, M=N=4)
ML
decoding
Conventional
decoding
Proposed
decoding
Required
multiplicationsCM(M+1)N
(M+1)N3+
(3/2)M2N+
[(7/2)M-1]N-1
(M+1)N3+
L[M2N(B+1)+
(3M-1)N-1]
QPSK 5,120 467 1,260
8PSK 81,920 467 1,516
16QAM 1,310,720 467 1,772
3.3. Performance of the AMC Systems with
Several V-BLAST Decoding Algorithms
Figure 2 shows the throughputs of the AMC systems
with several V-BLAST decoding algorithms in a 2×2
MIMO scheme. It is clear that the proposed decoding
algorithm achieves a better throughput performance
compared to the conventional V-BLAST decoding
algorithm over the entire SNR range. Additionally, the
proposed decoding algorithm is close to the existing ML
decoding algorithm in terms of the throughput
performance.
Figure 3 shows the throughputs of the AMC systems
with several V-BLAST decoding algorithms in a 2×2
and 4-2×2 MIMO channel. It is demonstrated that the
systems in a 4-2×2 MIMO channel achieve superior
throughput performance relative to the others. The
systems in the 4-2×2 MIMO channel that utilize a STD
scheme show improvements in the SNR through the
selection diversity gain. These improvements lead to a
reduced error rate and an increase in the probability of
selecting the MCS level with a higher data rate. These
systems therefore achieve greater throughput

122 S.J. RYOO ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
performance compared to the other systems. In addition,
the proposed decoding algorithm achieves superior
throughput performance relative to the conventional V-
BLAST decoding algorithm in 4-2×2 MIMO channel
using a STD scheme. It can be inferred that the proposed
decoding algorithm achieves this effect as well in
conjunction with a STD and a MIMO diversity scheme.
Figure 4 shows the throughputs of the AMC systems
with several V- BLAST decoding algorithms in a 2×2, a
4×4, and an 8×8 MIMO scheme. The results show that
the approximate maximum throughput improvement for
these three MIMO schemes is 421 Kbps, 545 Kbps, and
880 Kbps, respectively. Accordingly, it can be inferred
that the effect of the proposed decoding algorithm
increases as the number of system antennas increases.
Moreover, when each MIMO scheme is applied, the
performance is enhanced significantly.
Figure 2. Throughputs of the AMC systems with several V-
BLAST decoding algorithms in a 2×2 MIMO scheme
Figure 3. Throughputs of the AMC systems with several V-
BLAST decoding algorithms in a 2×2 and 4-2×2 MIMO
scheme
Figure 4. Throughputs of the AMC systems with several V-
BLAST decoding algorithms in a 2×2, 4×4, and 8×8 MIMO
scheme
4. Conclusions
In this paper, to improve the throughput performance in
a downlink, AMC systems with several V-BLAST
decoding algorithms were implemented and compared. It
was found that the performance can be improved
through application of the STD as a MIMO diversity
scheme. Through the SNR improvement of the receiver
of the systems that utilized a STD scheme, the error
probability was decreased in the range of a relatively
low SNR and, ultimately, the throughput performance
was improved. The throughput performance can also be
enhanced by increasing the number of antennas in the
MIMO channel.
The proposed decoding algorithm achieves a better
throughput performance than the conventional V-
BLAST decoding algorithm over the entire SNR range.
For the example of M=N=4 and QPSK, it was
demonstrated that the proposed decoding algorithm has
nearly 24% lower complexity than the existing ML
decoding algorithm while it provides an approximate
increase of 8.3% in capacity compared to the
conventional V-BLAST decoding algorithm.
In addition, the simulation results show that the
maximum throughput improvement in each MIMO
channel is nearly 421 kbps (a 17.7% increase in
capacity) for a 2×2 MIMO, 545 kbps (an 8.3% increase
in capacity) for a 4×4 MIMO, and 880 kbps (a 5.5%
increase in capacity) for an 8×8 MIMO. Thus, the effect
of the proposed decoding algorithm increases while the
number of system antennas increases. Accordingly, if
the MIMO schemes or the MIMO channel can be
applied in each case for a higher throughput
performance, the proposed decoding algorithm will then
be a practical candidate for next-generation mobile
communication systems.
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Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences, 2008, 2, 105-206
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