reduced complexity of qrd-m detection scheme in mimo-ofdm...

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Corresponding Author

Reduced Complexity of QRD-M Detection

Scheme in MIMO-OFDM Systems

Jong-Kwang Kim1, Jae-Hyun Ro

1 and Hyoung-Kyu Song

1

1 uT Communication Research Institute, Sejong University, Seoul, Korea

[email protected], [email protected], [email protected]

Abstract. In multiple input multiple output-orthogonal frequency division

multiplexing (MIMO-OFDM) systems, several detection schemes have been

developed for high error performance and low complexity. In several detection

schemes, maximum likelihood (ML) and QRD-M have optimal error

performance. However, these detection schemes have very high complexity.

Thus, this paper proposes reduced complexity of QRD-M detection scheme in

MIMO-OFDM systems. The proposed detection scheme has two stages, i.e.

partial zero-forcing (ZF) and conventional QRD-M. The proposed detection

scheme has higher error performance and lower complexity than the decision

feedback equalizer (DFE).

Keywords: MIMO-OFDM, partial ZF, QRD-M

1 Introduction

In wireless communication systems, multiple input multiple output-orthogonal

frequency division multiplexing (MIMO-OFDM) system offers high data rate without

additional bandwidth. However, because all transmission signals are simultaneously

sent to the receiver, the received signals are combination of multiple distorted

transmission signals. So, MIMO-OFDM system has always difficulty in accurate

detection of each transmission signal. For accurate detection in MIMO-OFDM

systems, several detection schemes have been developed. Maximum likelihood (ML)

detection has optimal error performance. However, the complexity of ML detection

increases exponentially when the number of transmission antennas and modulation set

increase. And QR decomposition-M algorithm (QRD-M) has optimal error

performance with lower complexity than the ML detection [1]. However, the

complexity of the QRD-M also increases exponentially when the number of

candidates M, transmission antennas and modulation set increase due to tree structure.

Also, zero-forcing (ZF) is attractive for simple linear implementation. However, the

error performance of the ZF is often not acceptable for other systems [2].

The performance indicators of detection schemes in MIMO-OFDM systems are

error performance and complexity. However, in general, these two indicators have

trade-off relationship. Thus, for seeking a compromise between the error performance

and the complexity, this paper proposes very low complex QRD-M detection scheme

which is inferior to conventional QRD-M in terms of the error performance.

Advanced Science and Technology Letters Vol.122 (ASP 2016), pp.214-221

http://dx.doi.org/10.14257/astl.2016.122.42

ISSN: 2287-1233 ASTL Copyright © 2016 SERSC

mailto:[email protected]

mailto:[email protected]

2 System Model

The MIMO-OFDM system model which has 2LM transmission antennas and

receive antennas is considered where L is integer which is larger than 1. As shown

in Fig. 1, input data is demultiplexed into N data substreams [3]. So, M OFDM

symbols which have cyclic prefix (CP) are denoted as 1 2 T

MX X XX where

T

means transpose operator. For simple notation, subcarrier index k is dropped.

And all OFDM symbols from M transmission antennas are sent through rich

scattering complex Rayleigh fading channel as follows,

11 12 1

21 22 2

1 2

,

M

M

M M MM

H H H

H H H

H H H

H

(1)

where , , 1,2, ,ijH i j M means channel coefficient from the j -th transmission

antenna to the i -th receive antenna. Then, at the receiver, M received symbols

1 2 T

MY Y YY after the process of fast Fourier transform (FFT) are denoted as

, Y HX N (2)

where 1 2 T

MN N NN is a complex additive white Gaussian noise (AWGN)

vector which has zero mean and covariance matrix 2HE NN I where H

means transpose operator and I is identity matrix.

Fig. 1. The block diagram of MIMO-OFDM system.

Advanced Science and Technology Letters Vol.122 (ASP 2016)

Copyright © 2016 SERSC 215

3 Conventional Detection Schemes

3.1 ZF

The ZF nulls other transmission signals perfectly regarding as interference by simply

multiplying the pseudo-inverse of channel matrix ZFG by received signals in (2).

1

ZF .H H

G H H H (3)

So, the transmission symbol ZFX̂ is estimated as follows,

ZF ZFˆ , X G Y X N (4)

where ZFN G N is a new noise component vector.

The ZF may have low error performance due to the amplified noise component N .

However, the ZF has low complexity because the ZF only has to multiply the pseudo-

inverse matrix by received signals.

3.2 QRD-M

In the QRD-M, the channel matrix H is decomposed as H QR where Q is

M M unitary quadrature matrix which is satisfied with H Q Q I and R is

M M upper triangle matrix by using QR decomposition for low complexity.

11 12 1

22 2

1 2

0,

0 0

M

M

M

MM

R R R

R R

R

H QR q q q

(5)

where , 1,2, ,i i Mq is the i -th column of Q .

To remove the influence of Q , the left side of the Y is multiplied by H

Q and

resultant vector 1 2 T

MW W WW is denoted as

,H W Q Y RX N (6)

where HN Q N is a new noise vector which has same statistical property with

existing noise vector N .

After the QR decomposition, squared Euclidean distances are calculated in (6) with

tree structure. At the first stage, the l -th squared Euclidean distance between the

received signal and all modulated symbols at the bottom layer in (7) is calculated as

follows,


216 Copyright © 2016 SERSC

2

1 ,M MM le l W R C (7)

where 1 2

T

SC C C

C is modulated candidates vector in constellation S

and l is index number of C . Then, M candidates with the smallest squared

Euclidean distances are retained and transferred to next layer as survival paths. At the

second stage, M S squared Euclidean distances between the received symbol and

modulated symbol are calculated like first stage. However, from the second stage to

final stage, accumulated squared Euclidean distance at previous layers has to be

calculated as follows,

2

2 1 1 1 1 1ˆ, M M M l M M Me d l W R R X d E d C

(8)

where ˆNX d is the d d M -th survival candidate and 1E d is accumulated

squared Euclidean distance at the first layer. This process is repeated until the last

layer. And at the last layer, a path with the minimum accumulated squared Euclidean

distance is selected as transmission symbol. Fig. 2 shows the tree structure of QRD-M

in 4 4 MIMO-OFDM system. In Fig. 2, X̂ is estimated transmission symbol

which has minimum accumulated Euclidean distance.

Fig. 2. The tree structure of QRD-M in 4 4 MIMO-OFDM system.

4 Proposed Detection Scheme

The proposed detection scheme has two stages. At first, partial ZF (slightly different

to conventional ZF) stage is used to divide large matrix into multiple small matrix for

low complexity. Then, conventional QRD-M (full M) is used to each small matrix for



high error performance. For easy understanding, the proposed detection scheme is

described in 4 4 MIMO-OFDM system without noise components. So, the received

signals in 4 4 MIMO-OFDM system can be denoted as follows,

11 12 13 141 1

21 22 23 242 2

31 32 33 343 3

41 42 43 444 4

.

H H H HY X

H H H HY X

H H H HY X

H H H RY X

(9)

4.1 Partial ZF

Unlike the conventional ZF, partial ZF nulls not all interference signals. So, the partial

ZF does not have to calculate the pseudo-inverse of channel matrix. The purpose of

the partial ZF is to simply divide the 4 4 MIMO-OFDM system into two 2 2

MIMO-OFDM system for low complexity. So, one matrix contains 1X and

2X .

And another matrix contains 3X and

4X . For the partial ZF, cancelling is used as

follows,

1, 1 3

2, 2 4

,c

c

Y Y Y

Y Y Y

K (10)

where 31 41

32 42

k k

k k

K is a weight matrix for cancelling which is satisfied with

equation as follows,

33 34 31 32 13 23

43 44 41 42 14 24

.

T TH H k k H H

H H k k H H

(11)

So, after the cancelling, the received signals 1 1, 2,

T

c c cY Y Y in (10) are as follows,

1, 111 12

1

2, 221 22

,c

c

c

Y XH H

Y XH H

Y

(12)

where ijH , , 1,2i j is a new channel component. For clarity, the new channel

components are denoted as follows,

11 12 31 3211 12

21 22 41 4221 22

.H H H HH H

H H H HH H

K (13)

In the result of (12), the modified received signals contain only 1X and

2X .

Likewise, the same cancelling process is applied to the 3 4

TY Y and existing 4 4



MIMO-OFDM system is divided into two 2 2 MIMO-OFDM systems. Another

2 2 MIMO-OFDM system 2 3, 4,

T

c c cY Y Y is as follows,

3, 333 34

2

4, 443 44

.c

c

c

Y XH H

Y XH H

Y

(14)

4.2 QRD-M in 2 2 MIMO-OFDM

After the partial ZF, two 2 2 MIMO-OFDM systems are generated in (12) and

(14). And then, all transmission symbols 1 2 4ˆ ˆ ˆ, , ,X X X are estimated by applying

conventional QRD-M with M S to the (12) and (14). The complexity of the

proposed detection scheme is very lower than the conventional QRD-M which is

applied to original MIMO-OFDM system in (2) because the QRD-M in the proposed

detection scheme is applied to only 2 2 MIMO-OFDM system. In Table 1, the

complexity of the proposed detection scheme is explained. In the calculation of the

complexity, only complex multiplication is considered assuming the multiplication of

two complex numbers require four multiplications.

Table 1. The complexity of the proposed detection scheme.

Scheme Required complex multiplications

Partial ZF with LU decomposition 3 2

2

28 172 43 log

9 9 3M M M M M

Conventional QRD-M in 2 2 system 212 8 48S S

The whole proposed detection scheme

3 2

2

28 172 43 log

9 9 3M M M M M

+ 212 8 48

2

MS S

Table 2. The used simulation parameters.

Parameter Value or scheme

The number of subcarriers 256

CP length 64

Modulation scheme (BER)

Modulation scheme (Complexity)

BPSK,

BPSK, QPSK and 16-QAM

Channel 7-path Rayleigh fading

5 Simulation Results

In this section, the simulation results for bit error rate (BER) performance and

required complexity are shown. The used simulation parameters are explained in



Table 2. Fig. 3 shows the BER performance of the proposed detection scheme and

ZF-DFE for comparison. At low signal-to-noise ratio (SNR), the BER performance of

the proposed detection scheme is lower than the ZF-DFE because the partial ZF stage

in the proposed detection scheme amplifies the noise components. So, due to these

amplified noise components, the conventional QRD-M stage in the proposed detection

scheme may detect wrong transmission symbol no matter how it has great error

performance. However, at high SNR, the error performance of the proposed detection

scheme is higher than the ZF-DFE because the partial ZF stage amplifies the noise

components with lower scale than that of low SNR. So, the conventional QRD-M

stage detects the transmission symbol well.

Fig. 4 shows the required complexity of the proposed detection scheme and ZF-

DFE for comparison like Fig. 3 according to the number of the transmission antennas

and the used modulation scheme. The used modulation scheme is binary phase shift

keying (BPSK), quadrature phase shift keying (QPSK) and 16-quadrature amplitude

modulation (QAM). When the modulation scheme is BPSK and QPSK, the required

complexity of the proposed detection scheme is lower than the ZF-DFE because the

conventional QRD-M does not require many complex multiplications. However,

when the modulation scheme is 16-QAM, the required complexity of the proposed

detection scheme is higher than the ZF-DFE at low antenna number because the

conventional QRD-M requires many complex multiplications due to highly increased

modulation set. However, when the number of the transmission antennas is high, the

required complexity of the proposed detection scheme is lower than the ZF-DFE.

Fig. 3. The BER performance of the proposed detection scheme in 4 4 MIMO-OFDM

system.



Fig. 4. The required complex multiplications of the proposed detection scheme in 4 4

MIMO-OFDM system.

6 Conclusion

This paper proposes the low complex QRD-M detection scheme in MIMO-OFDM

systems. The proposed detection scheme has higher error performance than the ZF-

DFE at high SNR. And, the required number of the complex multiplications is lower

than the ZF-DFE when the modulation order is not large. Thus, the second stage in

the proposed detection scheme needs low complex QRD-M detection scheme not to

require many complex multiplications regardless of modulation order.

Acknowledgments

This research was supported by Basic Science Research Program through the National

Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and

future Planning (No. 2013R1A2A2A01067708) and was supported by ICT R&D

program of MSIP/IITP. [R0101-14-0189, Development of the next generation

convergence broadcasting and monitoring systems combined with the networks].

References

1. Choi, H.J., Song, H.K.: Advanced QRD-M Detection with Iterative Scheme in the MIMO-

OFDM System. IEICE Trans. Inf. & Syst., vol. E97-D, no. 2, pp. 340--343 (2014)

2. Ahn, J.K, Jang, H.W., Song, H.K.: An Improved Low Complexity Detection Scheme in

MIMO-OFDM Systems. IEICE Trans. Inf. & Syst., vol. E97-D, no. 5, pp. 1336--1339

(2014)

3. Yu, S.J., Ahn, J.K., Song, H.K.: Channel-Adaptive Detection Scheme Based on Threshold

in MIMO-OFDM Systems. IEICE Trans. Inf. & Syst., vol. E97-D, no. 6, pp. 1644--1647

(2014)



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