**5. Simulation results**

Performance of DAN SC-FDAAA system will be investigated in this section, as a reference for comparison, the performance of CAN SC-FDAAA will also be evaluated. Cellular structures using FRF =1, 3, 4, 7, 9 and 12 will be considered. The parameters used to generate the results are listed in Tab. I. No channel coding is used for simplicity, and we assume that the transmit signal to noise ratio (SNR) is 10dB. The distributed antennas are located in a cell as shown in Fig. 4. In this study, scheduling among the distributed antennas is not considered. The scheduling algorithm and more complicated situation remain as the topics of our future work.

BER performance is investigated at first. In order to find out behaviors of both average BER and outage BER, the cumulative distribution functions (C.D.Fs) of BER performance are calculated and shown in Figs. 5-8 where the FRF equals to 1, 3, 4 and 7, respectively. For the cases of FRF 9 and FRF 12, the results are similar to the case of FRF 7, therefore those results are not shown for brevity. Fig. 5 shows a comparison between the C.D.Fs of BER in DAN system and CAN system when FRF=1. The x axis is the BER abscissa and y axis is the probability that BER<abscissa. It can be observed that DAN SC-FDAAA outperforms CAN SC-FDAAA by having better BER performance. It can also be observed that when the number of users increases, the BER performance of SC-FDAAA will degrade in both DAN and CAN systems, which can be intuitionally expected due to the reduction of degree of freedom. From the results shown in Figs. 6-8, it can be further observed that when FRF increases, the C.D.F. curves of BER performance "shift" right-side, which means that the BER performance improves due to the reduction of CCI power. In addition, DAN SC-FDAAA always achieves better BER performance than CAN SC-FDAAA no matter how FRF varies. The results of BER performance have shown that the distributed nature of DAN system can significantly improve the BER performance of SC-FDAAA over CAN system.

**Figure 4.** Antenna distribution in DAN system.

( ) <sup>1</sup> <sup>1</sup> . - - \* \* **Z T TP Q P TP P T** =- + (13)

(*k*) and *Q* = *I* , then the inverse ma‐

(14)

Let *Z* =*Crr*

trix *Crr*

(*k*) , *T* = *RNI*

100 Recent Trends in Multi-user MIMO Communications

'

*k*

**R I**


*N*

**5. Simulation results**

<sup>−</sup>1(*k*) , *<sup>P</sup>* <sup>=</sup> *<sup>A</sup>*<sup>0</sup>

<sup>∗</sup>(*k*) where *A*<sup>0</sup>

( ) ( )

*k k*

*N*

*kk k*

1 0 0

'


'

*k*

The SC-FDAAA weight is then obtained by substituting (9) and (13) into (7), given by

( ) ( ) ( ) ' ( ) ( ) ( ) '

Finally, the SINR after the weight control can be expressed, by substituting (14) into (9), as

Performance of DAN SC-FDAAA system will be investigated in this section, as a reference for comparison, the performance of CAN SC-FDAAA will also be evaluated. Cellular structures using FRF =1, 3, 4, 7, 9 and 12 will be considered. The parameters used to generate the results are listed in Tab. I. No channel coding is used for simplicity, and we assume that the transmit signal to noise ratio (SNR) is 10dB. The distributed antennas are located in a cell as shown in Fig. 4. In this study, scheduling among the distributed antennas is not considered. The scheduling algorithm and more complicated situation remain as the topics of our future work.

BER performance is investigated at first. In order to find out behaviors of both average BER and outage BER, the cumulative distribution functions (C.D.Fs) of BER performance are calculated and shown in Figs. 5-8 where the FRF equals to 1, 3, 4 and 7, respectively. For the cases of FRF 9 and FRF 12, the results are similar to the case of FRF 7, therefore those results are not shown for brevity. Fig. 5 shows a comparison between the C.D.Fs of BER in DAN system

( ) ( ) ' ( ) ( ) <sup>1</sup>

*k k kS k k k* **W R A**


<sup>1</sup> . <sup>1</sup> -

1 1 0 0

**A RA** (15)

0 0 . - \* G = *<sup>N</sup> k k kk* **AR A** (16)

1


**R**

0 0

é ù = ê ú <sup>+</sup> ë û *<sup>N</sup> N*

*N*

<sup>−</sup>1(*k*) can be calculated by submitting *Z* , *T* , *P* and *I* into

( ) ( ) ( ) ( )

**AAR**

é ù = - ê ú

\* -

<sup>+</sup> ë û

**I A RA**

=- + é ù

( ) ( ) ( )

'


1 0 0 <sup>1</sup> . <sup>1</sup>

*k k*

*N*

1 0 0

é ù = ê ú <sup>+</sup> ë û

**A RA**

(*k*)=*H*<sup>0</sup>

( ) ( ) ( ) ( ) ( ) ( ) ( )

*k kk k k k k*

0 0 00

ë û

' ' ' '

'

1

*N*

<sup>1</sup> 11 1 <sup>1</sup> <sup>1</sup>


**C R R A IA RA A R**

*rr N N N N*

(*k*)*S*<sup>0</sup>


**Table 1.** Simulation Parameter

Figure 5 C.D.F. of BER performance, FRF=1.

19

Probability%[BER>Abscissa]

65

**Figure 7.** C.D.F. of BER performance, FRF=4.

70

75

80

85

90

95

100

20

55

**Figure 6.** C.D.F. of BER performance, FRF=3.

60

65

70

75

Probability%[BER>Abscissa]

80

85

90

95

100

<sup>10</sup>-3 <sup>10</sup>-2 <sup>10</sup>-1 <sup>10</sup><sup>0</sup> <sup>50</sup>

DAN,U=2 DAN,U=3 DAN,U=4 DAN,U=5 DAN,U=6 CAN,U=2 CAN,U=3 CAN,U=4 CAN,U=5 CAN,U=6

http://dx.doi.org/10.5772/57132

103

DAN,U=2 DAN,U=3 DAN,U=4 DAN,U=5 DAN,U=6 CAN,U=2 CAN,U=3 CAN,U=4 CAN,U=5 CAN,U=6

=6,SNR=10dB

N r

FRF=4

=6,SNR=10dB

N r

Multi-User Interference Suppression by Using Frequency Domain Adaptive Antenna Array

FRF=3

BER

Figure 6 C.D.F. of BER performance, FRF=3.

<sup>10</sup>-3 <sup>10</sup>-2 <sup>10</sup>-1 <sup>10</sup><sup>0</sup> <sup>60</sup>

BER

Figure 7 C.D.F. of BER performance, FRF=4.

**Figure 5.** C.D.F. of BER performance, FRF=1.

18

Figure 6 C.D.F. of BER performance, FRF=3.

**Figure 6.** C.D.F. of BER performance, FRF=3.

**Modulation QPSK** Channel Channel Model Frequency selective block Rayleigh fading

> Number of co-channel cells *B* =6 Number of antennas of mobile user 1

Number of users per cell *U* =2~6 User location distribution Random Number of antennas *Nr* =6 FFT (IFFT) points *Nc*= 256

10-3 10-2 10-1 <sup>100</sup> <sup>20</sup>

FRF=1

N r

=6,SNR=10dB

DAN,U=2 DAN,U=3 DAN,U=4 DAN,U=5 DAN,U=6 CAN,U=2 CAN,U=3 CAN,U=4 CAN,U=5 CAN,U=6

BER

Figure 5 C.D.F. of BER performance, FRF=1.

**Table 1.** Simulation Parameter

30

**Figure 5.** C.D.F. of BER performance, FRF=1.

40

50

60

Probability%[BER>Abscissa]

70

80

90

100

102 Recent Trends in Multi-user MIMO Communications

18

Number of paths *L* =16 Power delay profile Uniform Path loss α =3.5 SNR 10dB

Figure 7 C.D.F. of BER performance, FRF=4.

**Figure 7.** C.D.F. of BER performance, FRF=4.

20

**Figure 8.** C.D.F. of BER performance, FRF=7.

System capacity given by bits/s/Hz can be calculated by Shannon capacity definition [15-16] using the SINR given in (15). However, the number of users that can be accommodated is a practical criterion to be considered as system capacity. Therefore, the following results will focus on the number of simultaneous users instead of the value given by bits/s/Hz. The average BER performance of DAN SC-FDAAA as a function of FRF is shown in Fig. 9. Since un-coded system is assumed, average BER=10-2 is used as a criterion to see how many users can be accommodated by using DAN SC-FDAAA. In the next, link capacity (maximum number of users/cell) and cellular link capacity (link capacity/FRF) of DAN SC-FDAAA are evaluated and the results are shown in Fig. 10 and Fig. 11.

Figure 8 C.D.F. of BER performance, FRF=7.

21 Fig. 10 shows the link capacity of DAN SC-FDAAA and CAN SC-FDAAA. It is shown that 4 users can be accommodated by DAN SC-FDAAA when FRF 1 is used while 2 users can be accommodated by CAN SC-FDAAA, therefore, the link capacity can be doubled by using DAN SC-FDAAA. As the FRF increases, link capacities increase as the CCI power decreases. And when FRF is larger than 4, 6 users can be accommodated. Since *Nr* =6 and the AAA receiver can deal with up to *Nr* −1 interference, it can be concluded that the maximum number of users/ cell of the DAN SC-FDAAA can approach its maximum value when FRF is larger than 4.

22

2.5

Figure 10 Link capacity. **Figure 10.** Link capacity.

3

3.5

4

4.5

LInk Capacity

5

5.5

6

6.5

7

23

10-6

Figure 9 Average BER. **Figure 9.** Average BER.

10-5

10-4

Average BER

10-3

10-2

10-1

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>11</sup> <sup>12</sup> <sup>10</sup>-7

DAN

CAN

N r

=6,SNR=10dB

Multi-User Interference Suppression by Using Frequency Domain Adaptive Antenna Array

FRF

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>11</sup> <sup>12</sup> <sup>2</sup>

Link Capacity=Maximum number of users/cell

FRF

DAN,U=2 DAN,U=3 DAN,U=4 DAN,U=5 DAN,U=6 CAN,U=2 CAN,U=3 CAN,U=4 CAN,U=5 CAN,U=6

http://dx.doi.org/10.5772/57132

105

DAN CAN

Figure 9 Average BER. **Figure 9.** Average BER.

Figure 10 Link capacity. **Figure 10.** Link capacity.

22

23

21

75

**Figure 8.** C.D.F. of BER performance, FRF=7.

the results are shown in Fig. 10 and Fig. 11.

80

85

Probability%[BER>Abscissa]

90

95

100

104 Recent Trends in Multi-user MIMO Communications

<sup>10</sup>-3 <sup>10</sup>-2 <sup>10</sup>-1 <sup>10</sup><sup>0</sup> <sup>70</sup>

DAN,U=2 DAN,U=3 DAN,U=4 DAN,U=5 DAN,U=6 CAN,U=2 CAN,U=3 CAN,U=4 CAN,U=5 CAN,U=6

=6,SNR=10dB

N r

FRF=7

BER

Figure 8 C.D.F. of BER performance, FRF=7.

System capacity given by bits/s/Hz can be calculated by Shannon capacity definition [15-16] using the SINR given in (15). However, the number of users that can be accommodated is a practical criterion to be considered as system capacity. Therefore, the following results will focus on the number of simultaneous users instead of the value given by bits/s/Hz. The average BER performance of DAN SC-FDAAA as a function of FRF is shown in Fig. 9. Since un-coded system is assumed, average BER=10-2 is used as a criterion to see how many users can be accommodated by using DAN SC-FDAAA. In the next, link capacity (maximum number of users/cell) and cellular link capacity (link capacity/FRF) of DAN SC-FDAAA are evaluated and

Fig. 10 shows the link capacity of DAN SC-FDAAA and CAN SC-FDAAA. It is shown that 4 users can be accommodated by DAN SC-FDAAA when FRF 1 is used while 2 users can be accommodated by CAN SC-FDAAA, therefore, the link capacity can be doubled by using DAN SC-FDAAA. As the FRF increases, link capacities increase as the CCI power decreases. And when FRF is larger than 4, 6 users can be accommodated. Since *Nr* =6 and the AAA receiver can deal with up to *Nr* −1 interference, it can be concluded that the maximum number of users/ cell of the DAN SC-FDAAA can approach its maximum value when FRF is larger than 4.

**Author details**

**References**

Wei Peng and Fumiyuki Adachi

Tohoku University, Japan

\*Address all correspondence to: peng@mobile.ecei.tohoku.ac.jp

Proc. IRE, vol. 46, pp. 555-570, March 1958.

cation Magazine, vol. 40, pp. 58-66, April 2002.

tech House Publishers, UK, 1999.

IEEE ICICS 2009, pp.1-5, March 2009.

E94-B, no. 7, pp. 2003-2012, July. 2011.

vol. 42, pp. 377–384, Nov. 1993.

pp. 207-209, March 2005.

[1] J. G. Proakis, Digital Communications, fourth edition, New York: McGraw Hill, 2001.

Multi-User Interference Suppression by Using Frequency Domain Adaptive Antenna Array

http://dx.doi.org/10.5772/57132

107

[2] R. Price and P. E. Green, "A Communication Technique for Multipath Channels,"

[3] D. Falconer, S. L. Ariyavistakul, A. Benyamin-Seeyar and B. Edison, "Frequency Do‐ main Equalization for Single-carrier Broadband Wireless Systems," IEEE Communi‐

[4] R. Van Nee and R. Prasad, OFDM for Wireless Multimedia Communications, Arc‐

[5] F. Adachi, K. Takeda, T. Obara, T. Yamamoto and H. Matsuda, "Recent advances in single-carrier frequency-domain equalization and distributed antenna network,"

[6] K. Sivanesan and N. C. Beaulieu, "Outage and BER of MRC Diversity in Band-limit‐ ed Micro-cellular Systems with CCI," IEEE Communications Letters, vol. 9, Issue. 3,

[7] J. Zhang and J. Andrews, J, "Distributed Antenna Systems with Randomness", IEEE Transactions on Wireless Communications, vol. 7, no. 9, pp. 3636 - 3646,Sept. 2008.

[8] W. Peng and F. Adachi, "Frequency Domain Adaptive Antenna Array for Broadband Single-Carrier Uplink Transmission," IEICE Transactions on Communications, vol.

[9] W. Peng and F. Adachi, "Single-Carrier Frequency Domain Adaptive Antenna Array

[12] J. H. Winters, "Signal Acquisition and Tracking with Adaptive Arrays in the Digital Mobile Radio System IS-36 with Flat Fading," IEEE Trans. Vehicular Technology,

[10] Ahmed EI Zooghby, Smart Antenn Engineering, Arctech House Publisher, 2005.

for Distributed Antenna Network," IEEE ICCS, pp. 1-5, Dec. 2010.

[11] Simon Haykin, Adaptive Filter Theory, New York: Prentice Hall, 2002.

Figure 11 Cellular link capacity. **Figure 11.** Cellular link capacity.

Larger FRF means more bandwidth will be consumed. In order to measure the spectrum efficiency, cellular link capacity is calculated and the results are shown in Fig. 11. It is shown that cellular link capacity of DAN SC-FDAAA can achieve its' maximum value when FRF =1 and decreases when FRF increases. Note that in our previous work on the cellular link capacity for conventional cellular system [17], it has been pointed out that the cellular link capacity can be maximized by using FRF=1 in the area near cell center and FRF = 3 in the area near the cell edge. Therefore, by using the DAN SC-FDAAA, a smaller FRF can be used and the spectrum efficiency can be greatly improved as a result. In addition, taking FRF=1 as an example, DAN SC-FDAAA achieves twice of the cellular link capacity as CAN SC-FDAAA does.
