IEICE Communications Express, Vol.3, No.3, 104–109

Fast MIMO channel
calculation technique formulti-antenna system using
spread spectrum techniquefor FDTD methodKazuma Ouchidaa) , Naoki Honma, and Yoshitaka Tsunekawa
Graduate School of Engineering, Iwate University
4–3–5 Ueda, Morioka, 020–8551, Japana) t2313004@iwate-u.ac.jp

Abstract: In this letter, we present a new method that combines
the spectrum spreading technique and FDTD (Finite-Diﬀerence TimeDomain) simulation for reducing the computation time in multipleantenna analysis. In this method, signals for the multiple antennas aregenerated by multiplying non-identical spreading codes, and multiple
antennas are excited at the same time. This approach means that onlya single FDTD simulation is needed whereas the conventional methodneeds as many simulations as there are transmitting antennas. A 2×2
multiple-antenna is simulated by way of a demonstration and it is foundthat the results of the proposed method agree well with those of theconventional method even though its computation time is shorter thanthat of the conventional method.
Keywords: FDTD, MIMO, array antenna, channel capacity, spread
spectrum techniqueClassification: Antennas and Propagation
ReferencescIEICE 2014

DOI: 10.1587/comex.3.104
Received January 11, 2014
Accepted February 13, 2014
Published March 12, 2014[1] J. H. Winters, J. Salz, and R. D. Gitlin, “The impact of antenna diversity on the capacity of wireless communication systems,” IEEE Trans.
Commun., vol. 42, pp. 1740–1751, Feb. 1994.
[2] G. J. Foschini and M. J. Gans, “Capacity when using diversity at transmit and receive sites and the Rayleigh-faded matrix channel is unknownat the transmitter,” Proc. WINLAB Workshop on Wireless Information
Network, March 1996.
[3] J. W. Wallace and M. A. Jensen, “Mutual coupling in MIMO wirelesssystems: a rigorous network theory analysis,” IEEE Trans. Commun.,vol. 3, pp. 1317–1325, July 2004.
[4] J. W. Mcjown and R. L. Hamilton, Jr., “Ray tracing as a design tool forradio networks,” IEEE Network Magazine, vol. 5, no. 6, pp. 27–30, Nov.
1991.
[5] G. Lampard, “The eﬀect of terrain on radio propagation in urban microcells,” IEEE Trans. Veh. Tech., vol. 42, pp. 314–317, Aug. 1993.

104IEICE Communications Express, Vol.3, No.3, 104–109[6] T. Imai and T. Fujii, “Propagation loss in multiple diﬀraction using raytracing,” 1997 Antennas and Propagation Society International Symposium (APS 1997), Proc. APS’97, pp. 2572–2575, July 1997
[7] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas
Propag., vol. AP-14, pp. 302–307, May 1966.
[8] T. Hikage, T. Nojima, S. Watanabe, and T. Shinozuka, “Electric-ﬁeld
distribution estimation in a train carriage due to cellular radios in orderto access the implantable cardiac pacemaker EMI in semi-echoic environments,” IEEE Trans. Commun., vol. E88-B, no. 8, pp. 3281–3286, Aug.
2005.
[9] T. Namiki, “Investigation of numerical errors of the two-dimensional
ADI-FDTD method,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 11,
pp. 1950–1956, Nov. 2000.
[10] J. J. Boonzaaier and C. W. I. Pistorius, “Thin wire dipoles a ﬁnitediﬀerence time-domain approach,” Electronics Letters, vol. 26, no. 22,
pp. 1891–1892, 1990.
[11] M. Obara, N. Honma, and Y. Suzuki, “Fast S-parameter calculation technique for multi-antenna system using temporal-spectral orthogonality for
FDTD method,” IEICE Trans. Commun., vol. E95-B, no. 4, pp. 1338–1344, April 2012.
[12] K. Ouchida, N. Honma, and Y. Tsunekawa, “Fast FDTD analysis ofMIMO channel using spread spectrum technique,” 2013 Asia-Pacific Microwave Conference (APMC 2013), Electric Proc. of APMC 2013, T3D1, Nov. 2013.

1c

IEICE 2014

DOI: 10.1587/comex.3.104
Received January 11, 2014
Accepted February 13, 2014
Published March 12, 2014

Introduction

Technologies for enhancing the data-rate in wireless communication are being actively pursued, and diversity antenna [1] and Multiple-Input MultipleOutput (MIMO) systems [2] are among the key technologies. The characteristics of the multiple antennas greatly impact the diversity gain and/orchannel capacity. The eﬀect of antenna characteristics on MIMO channel
has been generalized by Wallace et al. [3], but the performance of a MIMO
system strongly depends on the interaction between the antennas and thepropagation characteristics. Therefore, evaluations of multiple antenna systems still need full simulations including the antennas and propagation environment. Unfortunately, this still incurs great computation cost even withrecent progress in computers. Hence, a method that oﬀers eﬃcient MIMO
channel simulations is needed.
The ray-tracing method [4, 5, 6] and the FDTD (Finite-Diﬀerence TimeDomain) method [7, 8] have been used for evaluating the propagation characteristics. Since the ray-tracing method is based on geometric optics theory,
structures with a lot of detail cause an excessive increase in computation
time or inadequate analysis accuracy. The FDTD method divides the analysis region into small cells, and Maxwell’s equations are applied to explain
the electromagnetic interactions among the cells. The FDTD method is convenient for analyzing detailed structures including antennas and propagation

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environments. For this reason, large scale analyses performed in recent years
have used the FDTD method [8]. However, calculation time and memory
increases in proportion to the total volume of analysis space.
A fast analysis method for multiple-antenna systems using OFDM (Orthogonal Frequency Division Multiplexing) pulse has been proposed [11].
This method enables the simultaneous analysis of multiple antennas since theexcitation signals are spectrally orthogonalized (a beneﬁt of OFDM modulation). However, this method cannot analyze two channels with the same
frequency and which results in intermittent frequency response.
To resolve this drawback, this letter introduces the idea of the spread
spectrum technique into FDTD analysis. The spectrum spreading codes for
multiple transmitting antennas are made orthogonal to each other, and thisenables the signals to be separated with high isolation at the receiving antennas [12]. That is, the multiple transmitting antennas are excited simultaneously and the MIMO channel can be calculated with just one single
simulation. This letter describes in detail the proposed scheme and its mechanism. Numerical analysis results are also described; show that the proposed
method oﬀers much faster analysis than the FDTD method with conventional
Gaussian pulse.

2

FDTD Analysis Using Spread Spectrum TechniqueFig. 1. The concept of the proposed methodcIEICE 2014

DOI: 10.1587/comex.3.104
Received January 11, 2014
Accepted February 13, 2014
Published March 12, 2014

Fig. 1 shows the concept of the proposed FDTD analysis method. In theconventional method, m transmitting antennas are excited independently,
so m simulations are needed. In the proposed method, the signals for themultiple transmitting antennas are generated using non-identical spreading
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codes, and the multiple transmitting antennas are excited at the same time.
At each receiving antenna, the mixed signals are multiplied by their respective
spreading codes, and a band-pass ﬁlter extracts the desired signal. This isbecause the band-pass ﬁlter can remove the interference components. Finally,a spreading code is multiplied to this signal again because input signals arespread spectrum signal. These processes yield the input-output responses of
all antennas, aj , bij (i = 1...n, j = 1...m). The MIMO channel is given by
hij = bij /aj .

3
3.1

Numerical results
Analysis condition

Fig. 2. Analysis modelc


IEICE 2014

DOI: 10.1587/comex.3.104
Received January 11, 2014
Accepted February 13, 2014
Published March 12, 2014

The numerical analysis model of this study uses dipole arrays. The results
obtained by the proposed method are compared to those of the conventional
method. Fig. 2 shows the analysis model. The distance between the transmitting and receiving antennas is D1 [m], and element spacing is D2 [m].
Transmitting antennas are Tx1 ∼ Tx2, and receiving antennas are Rx1 ∼Rx2. Element lengths are 0.1125 m for Tx1 and Rx1, and 0.0875 m for Tx2
and Rx2. Since we verify the analysis accuracy of the proposed method inthis simulation, various Tx1 and Tx2 values are examined because we want
to change the values of h11 and h22 . The distance between each element
and the PML boundary condition is 0.3125 m. The cell size is 12.5 mm, andthe delta gap model is used as the feeding model. PML boundary condition is employed for this calculation, and the number of PML layers is 8.
The analysis frequency is 1.5 GHz, and the time step, Δt, is 24.07×10−12 s.
Spread code is PN (Pseudorandom Noise) series, spreading code period isTc = 6.162×10−9 s, and spreading code length is T = 4.930×10−8 s. Numberof necessary time steps is Ntotal . When using Gaussian pulse, two individual
analyses for two antennas are performed. In order to equalize the total calculation time, the number of time steps for Gaussian pulse is set to Ntotal /2.
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Fig. 3. Analysis results

3.2 Analysis results
Fig. 3 (a) plots channel error versus propagation distance. The channel error
is deﬁned as,
J=||H ref − H||2F,||H ref ||2F

(1)

where, H is the propagation channel being evaluated and H ref is the propagation channel created by the Gaussian pulse with suﬃciently long timeanalysis (50000 time steps). Nt needs to be set so that the excitation signal
reaches the receiving antenna, i.e.,
Nt =D1,vc Δt(2)

where vc is the wave velocity in a vacuum; Δt is the time step. In theproposed method, a sliding correlator is used to detect the transmitted signal.
Therefore, the number of time steps required for the analysis is expressed as,c

IEICE 2014

DOI: 10.1587/comex.3.104
Received January 11, 2014
Accepted February 13, 2014
Published March 12, 2014

Ntotal =D1+ T + α,vc Δt(3)108IEICE Communications Express, Vol.3, No.3, 104–109

where, T is the length of the excitation signal, α is the number of timesteps required for sliding correlation. In this simulation, T = 2048 andα = 100 time steps. Transmission power is 0 dBm, noise power is −80 dBm,and element spacing, D2 , is 2 m. The antenna spacing, D1 , is changed from
10 m to 20 m. The results in Fig. 3 (a) show that the greater the propagation
distance between the antennas becomes, the larger the channel errors becomein the conventional method. The reason is the propagation time between thetransmitting and receiving antennas. Since the transmitted signal from one
antenna cannot reach another antenna, the channel cannot be calculated
correctly. On the other hand, the proposed method can analyze two-elementantennas with a single FDTD simulation, and it is clear that the channel
can be accurately analyzed in Ntotal time steps. This is because the antenna
spacing, D1 , satisﬁes (3).
Fig. 3 (b) plots channel capacity versus propagation distance. ‘Exact’
shows the channel capacity obtained by long calculations (50000 time steps)
with the Gaussian pulse. The channel capacities obtained by the proposed
method agree very well with the exact result. However, a large error occurredin the results for the Gaussian pulse with Ntotal /2 time steps. Therefore, itis found that the proposed method can analyze MIMO channels with lesscomputation time than the conventional method.

4Conclusion

This letter presented a fast FDTD analysis method for multiple-antenna systems that use the spread spectrum technique. Spread spectrum codes maintain orthogonality among the excited signals. Simulations showed that theproposed method yields channel capacities that agree well with those of theconventional method even though the computation time is shorter than thatof the conventional method. The results demonstrated that our analysis
method is eﬀective in reducing the computation time of FDTD analysis ofmultiple-antenna systems. As a ﬁnal remark, the proposed method can beapplied to antenna arrays that have more than 2×2 antennas.

Acknowledgments
This research was partially supported by JSPS KAKENHI (25709030).

c

IEICE 2014

DOI: 10.1587/comex.3.104
Received January 11, 2014
Accepted February 13, 2014
Published March 12, 2014109