proposal of receive antenna selection methods for mimo

IEICE TRANS. COMMUN., VOL.E91–B, NO.2 FEBRUARY 2008505

PAPER

Proposal of Receive Antenna Selection Methods for MIMO-OFDMSystem

Quoc Tuan TRAN†a), Student Member, Shinsuke HARA††, Member,Kriangsak SIVASONDHIVAT†††, Nonmember, Jun-ichi TAKADA††††, Atsushi HONDA†††††,

Yuuta NAKAYA†††††, Kaoru YOKOO†††††, Ichirou IDA†††††, and Yasuyuki OISHI†††††, Members

SUMMARY The combination of Multiple-Input Multiple-Output(MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) tech-nologies gives wireless communications systems the advantages of lowerbit error rate (BER) and higher data rate in frequency-selective fading en-vironments. However, the main drawbacks of MIMO systems are theirhigh complexity and high cost. Therefore, antenna selection in MIMOsystems has been shown to be an effective way to overcome the draw-backs. In this paper, we propose two receive antenna selection methodsfor a MIMO-OFDM system with radio frequency (RF) switches and polar-ization antenna elements at the receiver side, taking into consideration lowcomputational complexity. The first method selects a set of polarization an-tenna elements which gives lower correlation between received signals andlarger received signal power, thus achieves a lower BER with low compu-tational complexity. The second method first selects a set of polarizationantenna elements based on the criterion of the first method and anotherset of polarization antenna elements based on the criterion of minimizingthe correlation between the received signals; it then calculates the signal-to-interference-plus-noise power ratio (SINR) of the two sets and selectsa set with larger SINR. As a result, the second method achieves a betterBER than the first one but it also requires higher computational complexitythan the first one. We use the measured channel data to evaluate the per-formance of the two methods and show that they work effectively for therealistic channel.key words: MIMO-OFDM, MMSE, RF switch, polarization, antenna se-lection, IEEE 802.11n

1. Introduction

Multiple-Input Multiple-Output (MIMO) wireless systemsare those having multiple antennas at both transmitter andreceiver [1], where the parallel data streams from the trans-mitter are combined at the receiver in such a way that the biterror rate (BER) or the data rate can be improved. In MIMOsystems, the fading characteristic over the channel betweeneach pair of transmit and receive antennas should be fre-quency non-selective, therefore, Orthogonal Frequency Di-vision Multiplexing (OFDM) is employed to this end.

Manuscript received March 28, 2007.Manuscript revised August 19, 2007.†The author is with the Graduate School of Engineering, Osaka

University, Suita-shi, 565-0871 Japan.††The author is with the Graduate School of Engineering, Osaka

City University, Osaka-shi, 558-8585 Japan.†††The author is with Agilent Technologies Japan, Kobe-shi,

651-2241 Japan.††††The author is with the Graduate School of Engineering, Tokyo

Institute of Technology, Tokyo, 152-8550 Japan.†††††The authors are with YRP Research & Development Center,

Fujitsu Limited, Yokosuka-shi, 239-0847 Japan.a) E-mail: [email protected]

DOI: 10.1093/ietcom/e91–b.2.505

MIMO-OFDM systems have the advantages of bothMIMO systems and OFDM, namely, they can achieve lowerBER and higher data rate even in scattering-rich environ-ments. For instance, the IEEE 802.11n standard ensuresover-100 Mbps data transmission under a mandatory 2 × 2MIMO-OFDM mode [2]. However, their main drawback isthe increase of complexity and thus cost. While additionalantenna elements such as patch antennas or dipole antennasare usually inexpensive, radio frequency (RF) devices in-cluding up/down-converters, low-noise amplifiers, digital-to-analog/analog-to-digital converters, etc. are still expen-sive. Hence, the need for decreasing the number of antennaswhile maintaining the good quality of transmission becomesmore important and has gained much attention over the pastfew years. In order to overcome the drawback, several an-tenna selection techniques in MIMO systems have been pro-posed and they proved to be effective [3]–[7].

On the other hand, among RF switches, Micro Elec-tro Mechanical Systems (MEMS) switches have recentlydrawn much attention. As compared with semiconductorRF switches, MEMS switches have lower insertion loss andhigher linearity. For instance, a MEMS switch with an in-sertion loss of around 0.1 dB and an isolation of more than30 dB over a 5 GHz frequency band is available now andit offers the promise of low price [8]. In addition, polar-ization antenna elements at the receiver side of the MIMOsystems have the advantage of diversity and small size [9].Therefore, MIMO systems with RF switches and polariza-tion antenna elements at mobile user terminal side promisegood performance as well as small size, low cost and lowpower consumption. However, suitable antenna selectionmethods need to be considered to reduce the computationaland hardware complexity while keeping good transmissionperformance.

In this paper, we propose two receive antenna selectionmethods for a MIMO-OFDM receiver with RF-switched po-larization antenna elements, which can be applied to futurewireless local area network (WLAN) standards such as theIEEE 802.11n standard. The first method selects a set ofpolarization antenna elements which gives lower correlationbetween received signals and larger received signal power,thus achieves a lower BER with low computational com-plexity. The second method first selects a set of polarizationantenna elements based on the criterion of the first methodand another set of polarization antenna elements based onthe criterion of minimizing the correlation between the re-

Copyright c© 2008 The Institute of Electronics, Information and Communication Engineers

506IEICE TRANS. COMMUN., VOL.E91–B, NO.2 FEBRUARY 2008

ceived signals; it then calculates the signal-to-interference-plus-noise power ratio (SINR) of the two sets and selects aset with larger SINR. Therefore, the second method achievesa better BER than the first one but it also requires highercomputational complexity than the first one. We conducteda channel measurement campaign and used the measuredchannel impulse responses to evaluate the performance ofthe system with the proposed methods by computer simula-tion.

The rest of the paper is organized as follows. Section 2describes the considered MIMO-OFDM system with RF-switched polarization antenna elements. Section 3 presentsthe two proposed receive antenna selection methods. Nu-merical results based on measured data and detailed discus-sions are related in Sect. 4. Finally, Sect. 5 draws the con-clusions of the paper.

2. System Description and Signal Seperation

2.1 Considered MIMO-OFDM System

Figures 1 and 2 show the block diagrams of the trans-mitter and receiver of the considered spatially multiplex-ing MIMO-OFDM system, respectively. The data streamoriginating at the data source is convolutionally encoded,bit-interleaved and Quadrature Phase Shift Keying (QPSK)-mapped. The QPSK mapped data are then converted intoparallel, and frequency-division multiplexed by N-point In-verse Fast Fourier Transform (IFFT). The outputs of IFFT

Fig. 1 Transmitter.

Fig. 2 Receiver.

are converted back to serial sequence and a cyclic prefix(CP) is inserted in each OFDM symbol. The OFDM sig-nals are then forwarded to the Mt antenna elements. Thesignals are upconverted to passband, amplified by a poweramplifier and filtered. In our model, we omit these stages aswell as their equivalents at the receiver, which allows us totreat the system in equivalent baseband expression.

The receiver has Mr antenna branches, and each an-tenna branch connects to only one out of L polarization an-tenna elements through an RF switch. We define the indexof antenna element as l (l = 1, . . . , L), where the l-th an-tenna element has the same polarization and directivity forall the antenna branches. Furthermore, defining the indexof the selected antenna element at the i-th receive antennabranch as li (li = 1, . . . , L; i = 1, . . . ,Mr), we have LMr setsof {l1, . . . , lMr }. It should be noted here that the antenna el-ements at each receive antenna branch have different polar-izations and directional patterns, so selection of a suitableset out of LMr sets of {l1, . . . , lMr } depends on both the polar-ization and directivity.

The received OFDM signals from the selected po-larization antenna elements are first CP removed, and N-point Fast Fourier Transform (FFT) is performed to con-vert the signals back to the frequency domain. The fre-quency domain-converted signals are then detected withthe minimum mean square error (MMSE) filter. Finally,de-mapping, de-interleaving, and Viterbi decoding are per-formed and the resulting data are re-arranged to obtain theoriginal binary sequence.

2.2 Channel Estimation

In the IEEE 802.11n standard, antenna selection for trans-mitter and/or receiver can be optionally done based on in-stantaneous or averaged channel state information [10]. Fig-ure 3 shows the signal burst format enabling receive antennaselection, where the same Preamble j is transmitted L timesfrom the j-th transmit antenna ( j = 1, . . . ,Mt). The Pream-ble j is orthogonal to each other for the transmit antennas( j = 1, . . . ,Mt) because the training sequence for channelestimation in the Preamble j is inserted in a time divisionmanner. At the receiver, when receiving the l-th set of thePreambles, the l-th polarization antenna element is selectedat all the antenna branches (i = 1, . . . ,Mr). This meansthat when the receiver has finished receiving the L-th set

Fig. 3 Signal burst format enabling receive antenna selection.

TRAN et al.: PROPOSAL OF RECEIVE ANTENNA SELECTION METHODS FOR MIMO-OFDM SYSTEM507

of the Preambles, it can have the received data to estimateMt × L × Mr CIRs required for selecting a suitable set ofreceive antenna elements.

2.3 MMSE Signal Separation

Paying attention only to information transmitted over Nsubcarriers, we write the received signal at the n-th (n =1, . . . ,N) subcarrier after the CP removal and N-point FFTas

Y(n) = H(n)X(n) + Z(n) (1)

where the transmitted signal vector X(n), received signalvector Y(n), noise vector Z(n), and channel matrix H(n) arerespectively defined as

X(n) = [X1(n), . . . , XMt (n)]T (2)

Y(n) = [Y1(n), . . . , YMr (n)]T (3)

Z(n) = [Z1(n), . . . , ZMr (n)]T (4)

H(n) = {Hi j(n)}(i = 1, . . . ,Mr; j = 1, . . . ,Mt) (5)

where T is the transpose operation.An (Mr × Mt) weight matrix W of the MMSE filter is

then applied to the received signal Y(n) to obtain an estimateof the transmitted signal as follows

X(n) = WH(n)Y(n) (6)

= [X1(n), . . . , XMt (n)]T (7)

where superscript H denotes the Hermitian transpose. Theweight matrix W is obtained from the mean square error(MSE) criterion

minimize MSE(W(n)) = E[|X(n) − X(n)|2] (8)

where E[(·)] denotes the ensemble average of (·). The solu-tion is given by [11]

W(n) = R−1(n)P(n) (9)

R(n) = E[Y(n)Y(n)H] = H(n)HH(n) +1

S NRIMr (10)

P(n) = E[Y(n)XH(n)] = H(n) (11)

where IMr is the (Mr × Mr) identity matrix and S NR is thesignal-to-noise power ratio per subcarrier per receive an-tenna element.

3. Receive Antenna Selection Criteria

In this section, we review some conventional antenna selec-tion methods and describe the two proposed antenna selec-tion methods. We select one out of L polarization antennaelements for each of Mr receive antenna branches, therefore,the number of possible sets for the receive antenna selectionis LMr . In the following, we call the antenna element “an-tenna” in short and we assume that one out of L polarizationantenna elements has been selected at each antenna branch.

3.1 Capacity Selection Method

In MIMO systems, the Shannon capacity has been consid-ered as a criterion to evaluate the performance of the system[12]. As a result, a lot of papers have discussed the maxi-mization of the capacity in antenna selection for MIMO sys-tems [5], [6]. In this subsection, we consider capacity as acriterion to select the suitable antennas at the receiver sideof the considered MIMO-OFDM system.

The capacity for each set of {l1, . . . , lMr } is given as

Cl1...lMr =1N

N∑n=1

Cn. (12)

where Cn is the capacity of the MIMO-OFDM system cal-culated at the n-th subcarrier and is defined as in [13]

Cn = log2

⎡⎢⎢⎢⎢⎣det

⎛⎜⎜⎜⎜⎝IMr +EX

Mtσ2Z

H(n)HH(n)

⎞⎟⎟⎟⎟⎠⎤⎥⎥⎥⎥⎦ (13)

where EX and σ2Z denote the total transmit power per sub-

carrier and the noise power per receive antenna per subcar-rier, respectively. The capacity selection method thus can begiven by

Find a set o f {l1, . . . , lMr }which maximizes Cl1...lMr . (14)

The capacity selection method requires matrix mul-tiplication and determinant calculation with the order ofO(M3

r ). As a result, the implementation of the capacity se-lection method in real systems requires heavy computation,namely, high complexity and cost.

3.2 SINR Selection Method

The SINR has been considered as an effective criterion toevaluate the performance of Single-Input Multiple-Output(SIMO) systems [14] as well as MIMO systems [15], [16].Therefore, we consider the SINR selection in selecting aproper set of the antennas at the receiver side for the con-sidered MIMO-OFDM system.

The SINR for the received signal of the n-th subcarrierat the j-th MMSE filter output is written as

S INRjn =EX |U j j(n)|2

Nz + EX∑

j′� j |U j j′ (n)|2 (15)

U j j′ (n) =WHj(n)H j′ (n) (16)

NZ = Mtσ2Z |WH

j (n)|2 (17)

where WHj (n) ( j = 1, . . . ,Mt) and H j′ (n) ( j′ = 1, . . . ,Mt)

denote the j-th row vector of the matrix WH(n) and the j′-thcolumn vector of the channel matrix H(n), respectively.

Defining the S INR for each set of {l1, . . . , lMr } as

S INRl1 ...lMr =1

MtN

Mt∑j=1

N∑n=1

S INRjn (18)


the SINR selection method can be given by

Find a set o f {l1, . . . , lMr }which maximizes S INRl1 ...lMr . (19)

The SINR selection method promises to approach the per-formance of the lower bound, however, the problem is that itrequires high computational complexity to calculate matrixmultiplication and matrix inversion with the order of O(M3

r ).

3.3 Proposed Receive Antenna Selection Methods

3.3.1 MAPMIC Selection Method

As a solution to the high computational complexity prob-lem, we propose a receive antenna selection method whichpromises good performance and requires low computationalcomplexity. The method proposes a cost function whichmaximizes the received signal power and minimizes the cor-relation between the received signals for a selected set ofantennas.

Assume that a signal from the j-th (also j′-th) trans-mit antenna arrives at the i-th receive antenna. For a bettertransmission performance, the received signal power shouldbe larger. In addition, the correlation between the receivedsignals from the j-th and j′-th transmit antennas should belower in order that the receiver can separate the received sig-nals well.

Defining H j(n) ( j = 1, . . . ,Mt) as the j-th column vec-tor of the matrix H(n), we can calculate the power σ2

j of thesignal from the j-th transmit antenna to all the receive anten-nas as well as the correlation r j j′ between the signals fromthe j-th and the j′-th transmit antennas at all the receive an-tennas as follows

σ2j =

1N

N∑n=1

∣∣∣HHj (n)H j(n)

∣∣∣ (20)

r j j′ =1N

N∑n=1

∣∣∣HHj (n)H j′ (n)

∣∣∣ . (21)

Note that the received signal power in (20) and the correla-tion between received signals in (21) are averaged over theN subcarriers. The received signal power should be largerwhereas the correlation should be smaller, so we introducethe following cost function:

COS Tα =Mt−1∑j=1

Mt∑j′= j+1

r j j′√σ2

jσ2j′

· 1√σ2

jσ2j′

. (22)

Equation (22) is not a simple sum of the normalizedcorrelations over all the subcarriers. Each term in (22) is thenormalized correlation further divided by the square root ofthe received signal powers from the j-th and j′-th transmitantennas. Dealing with (22) as a function of {l1, . . . , lMr },we perform the max− power/min−correlation (MAPMIC)selection method as follows

Find a set o f {l1, . . . , lMr }which minimizes COS T l1...lMr

α . (23)

The advantage of the MAPMIC selection method isthat it reduces the computational complexity because it doesnot calculate the determinant, matrix inversion and matrixmultiplication.

3.3.2 Hybrid Selection Method

The advantage of the MAPMIC selection method is that itreduces the computational complexity. However, in someenvironments where the MIMO channels are strongly cor-related, the performance of the MIMO system is not de-termined by the received signal power but is mainly de-termined by the correlation between the arriving signals.Therefore, in such environments, the performance of thesystem with the MAPMIC selection method often becomesworse. Therefore, another criterion based on minimizing thenormalized correlation between the arriving signals, namely,the min − correlation (MIC) criterion should also be takeninto consideration. Defining the normalized correlation be-tween the arriving signals as

COSTβ =Mt−1∑j=1

Mt∑j′= j+1

r j j′√σ2

jσ2j′

(24)

where COSTβ is averaged over all the N subcarriers,the MIC selection method searches through LMr sets of{l1, . . . , lMr } to find a set which minimizes the cost functionCOSTl1...lMr

β .The proposed hybrid selection method is the combi-

nation of the MAPMIC selection method and the MIC se-lection method. It decides either of an antenna set ob-tained from the MAPMIC criterion or the one obtained fromthe MIC criterion by comparing their calculated SINRs.Namely, for LMr sets of {l1, . . . , lMr }, it first searches for aset α which minimizes the cost function COSTl1...lMr

α and aset β which minimizes the cost function COSTl1...lMr

β ; it thencalculates the SINRs for sets α and β and selects a set withlarger SINR. Figure 4 shows the block diagram of the pro-posed hybrid selection method.

The hybrid selection method can be summarized as

Fig. 4 Hybrid selection.


Find a set o f {l1, . . . , lMr }f rom sets α and β

which gives larger S INRl1 ...lMr . (25)

The hybrid selection method promises a better perfor-mance than the MAPMIC selection method but it requiresmore computational complexity because it combines the cri-teria of the MAPMIC selection method and the MIC selec-tion method and needs the calculation of the SINR values.However, as the hybrid selection method calculates SINRvalues only for two sets, it requires less computational com-plexity than the SINR selection method which requires LMr

values of SINR.

3.3.3 Further Reduction of Computational Complexity inthe Proposed Selection Methods

In the IEEE 802.11a standard [17], the lengths of the FFTwindow and cyclic prefix are 64 and 16, respectively, andmultipaths spread within the cyclic prefix. This implies thatsuccessive subcarriers are correlated [18], so we do not haveto average the received signal power in (20) and the correla-tion between received signals in (21) as well as the SINR in(18) over the N subcarriers. Namely, in calculating σ2

j , r j j′

and S INR, we can replace averaging over all the N subcar-riers by equi-distant Nave subcarriers (Nave ≤ N), thus canreduce the computational complexity in the proposed MAP-MIC selection method and hybrid selection method.

4. Experimentation and Performance Evaluation

4.1 Wireless Channel Measurement

Figure 5 shows the layout of a room (1205 cm × 662 cm×250 cm) and a corridor where we conducted the channelmeasurement campaign. The room provided a typical officewhere several desks and chairs were set up. A transmitter(Tx) had 2 × 4 uniform rectangular antenna array of dual-polarized patch antenna elements (see Fig. 6(a)), however,as we considered a 2 × 2 MIMO system with transmit an-tennas having horizontal polarization, we used only 2 hor-izontally polarized patch antennas (Mt = 2) with adjacentspacing of 0.5λ. On the other hand, a receiver (Rx) had twoantenna branches (Mr = 2), and each branch had three po-larization antenna elements (L = 3) (D1 and D2 directionsin horizontal polarization, and D3 direction in vertical po-larization; D1 direction, D2 direction and D3 direction wereorthogonal to each other) (see Fig. 6(b)). The adjacent an-tenna branch spacing was 0.5λ.

The channel measurements were performed during thetime when there were no people and moving objects ex-cept those who took part in the experiment. There weretotal 45 positions used for CIR measurement and we triedto keep unmoved during a measurement at a position. Dur-ing the channel measurement campaign, the calibration wasdone to remove the system response of the measuring equip-ments. We placed the transmitter on a stand in the corridor.

Fig. 5 Layout of the experimental room.

(a) Transmitter. (b) Receiver.

Fig. 6 Picture of the transmitter and receiver.

The transmitter sent a periodic multi-tone signal (period of0.8 μsec) with a center frequency of 4.5 GHz and a band-width of 120 MHz, which was captured by the receiver. Thereceiver estimated the CIRs and saved them in the frequencydomain, which were later re-sampled to be changed fromthe data of 120 MHz bandwidth to the data of 20 MHz band-width. The receiver was placed on a hand cart and movedfrom position 1 to 45 (pointed by black arrows). At eachposition, we slightly moved the receiver to make the fadingand measured the snapshots of CIRs (‘snapshot of CIRs’was defined as the CIRs from all the transmit antennas to allthe polarization antenna elements while ‘vector snapshot ofCIR’ was defined as a CIR from a transmit antenna to a po-larization antenna element). There were 12 vector snapshotsof CIR for each snapshot of CIRs, where a vector snapshotof CIR was taken by the receiver through switching controlcircuits. The measurement time for a snapshot of CIRs inthe experiment was 32 μsec, which was well within the co-herence time of the experimental indoor environment. Wemeasured ten snapshots of CIRs in total at each position andused them in the simulation of evaluating the performanceof the antenna selections at each position.

4.2 Simulation Conditions

We evaluate the performance of the system by computersimulation with the measured CIRs. Table 1 summarizesthe main parameters used for the computer simulation. Thetransmitter sends data through two antennas with horizontal


Table 1 System parameters.

Transmit antennas 2

Receive antennas 2

Polarization antennas 3

Modulation/Detection QPSK/coherent detection

Payload length 10 OFDM symbols

Data subcarriers 52

FFT/Cyclic prefix length 64/16 samples

Interleave size 12×8

Coding/Decoding Convolutional coding/

Soft Viterbi decoding

Code rate 1/2

Constraint length 7

Table 2 Set index γ and corresponding polarization antenna element.

γ Antenna set Antenna polarization

0 3, 3 Vertical-vertical (D3,D3)

1 3, 1 Vertical-horizontal (D3,D1)

2 3, 2 Vertical-horizontal (D3,D2)

3 1, 3 Horizontal-vertical (D1,D3)

4 1, 1 Horizontal-horizontal (D1,D1)


6 2, 3 Horizontal-vertical (D2,D3)



polarization. On the other hand, the receiver has two an-tenna branches and selects one of three polarization antennaelements at each of the two antenna branches. We assumea coherent QPSK and a half-rate convolutional coding/SoftViterbi decoding with a constraint length of 7, and set thedepth length of interleaving to (12 × 8). The subcarrier ar-rangement in this paper is based on that of the IEEE 802.11astandard. A payload contains data symbols and is 10 OFDMsymbols long. One OFDM symbol is composed of 80 sam-ples, where the cyclic prefix length is 16 samples and theuseful symbol length is 64 samples. Here, the OFDM sym-bol is generated with the 64-point IFFT, where only 48 sub-carriers convey information, 4 subcarriers are known pilotsignals and the other 12 subcarriers are virtual subcarriers.In the following figures, the noise power is set to −100 dBm.

Furthermore, as the number of receive antennabranches and the number of polarization antenna elements ateach branch are 2 and 3, respectively, there are 9 (LMr = 32)sets of polarization antenna elements. The receiver selectsa suitable set out of these 9 sets to achieve a better perfor-mance. Table 2 shows the relationship between the antennaset index γ of {l1, l2} and the polarization antenna element l1at the receive branch 1 and the polarization antenna elementl2 at the receive branch 2, where l1 and l2 can take the value

Fig. 7 Received power versus position for each polarization antennaelement at antenna branch 1 (for one snapshot of CIRs).

Fig. 8 Received power versus position for each polarization antennaelement at antenna branch 2 (for one snapshot of CIRs).

of 1, 2 or 3 which corresponds to the D1, D2 or D3 direction,respectively.

4.3 Performance Evaluation

We use 10 snapshots of CIRs at each of 45 positions to eval-uate the performance of the system with seven antenna se-lections: the MAPMIC selection, the hybrid selection, thecapacity selection, the selective diversity (SELDIV) selec-tion (see Appendix), the random selection (the one whichrandomly selects a polarization antenna element at each re-ceive antenna branch), the SINR selection and the lowestBER selection (the one which selects a set of polarizationantenna elements with the lowest BER).

4.3.1 Received Power Performance

Figures 7 and 8 show the received power for a snapshot ofCIRs for the polarization antenna elements 1, 2 and 3 (di-rections D1, D2 and D3) at antenna branches 1 and 2, re-spectively. The received power of each polarization antennaelement varies for all the receive antenna positions. Fur-thermore, there is no polarization antenna element whosethe received power is always smaller than the received pow-ers of the other polarization antenna elements at all the re-


Fig. 9 Received power versus transmit power at position 18 (for onesnapshot of CIRs).

Fig. 10 Received power versus transmit power at position 34 (for onesnapshot of CIRs).

ceive antenna positions. It means that all the polarizationantenna elements used in the channel measurement cam-paign received the signal well and the data processing forall the polarization antenna elements in the measurementcampaign worked effectively too. Therefore, the channelmeasurement campaign was valid. In addition, although thetransmitter sent signals through the antennas with horizon-tal polarization, the received power of the antenna elementswith vertical polarization (polarization antenna element 3)at the two branches are not always smaller than the receivedpowers of the antenna elements with horizontal polarization(polarization antenna elements 1 and 2). It proves that theuse of polarization antenna elements at the receiver side iseffective.

From Figs. 7 and 8, it can be seen that the receivedpowers at different polarization antenna elements are dif-ferent, which leads to different received powers for differentselected sets of polarization antenna elements. Figures 9 and10 show the received power per receive antenna versus thetransmit power for selected sets of polarization antenna ele-ments for a snapshot of CIRs at positions 18 and 34, respec-tively. Note that the transmit power is measured at the trans-mit antennas as shown in Fig. 1 while the received powerper receive antenna is measured at the selected polarization

Fig. 11 Set index versus position (for one snapshot of CIRs).

antenna elements as shown in Fig. 2. The random selec-tion randomly selects a set of polarization antenna elementsout of 9 sets during 10000 loops of the simulation for eachof 10 snapshots of CIRs, it thus gives the received powerequivalent to the average of those obtained from selecting9 sets of polarization antenna elements. The SELDIV se-lection selects a polarization antenna element which givesthe largest received signal power at each antenna branch,therefore, it gives the largest received power. In Fig. 9, thereceived powers for the SELDIV selection, MAPMIC se-lection, hybrid selection, capacity selection, SINR selectionand lowest BER selection are the same and larger than thatfor the random selection. In Fig. 10, the received powersfor the MAPMIC selection, hybrid selection, capacity selec-tion, SINR selection and lowest BER selection are the sameand larger than that for the random selection but is smallerthan that for the SELDIV selection. However, it should benoted that the lowest BER selection promises to find a set ofpolarization antenna elements which gives the lowest BER.Therefore, in Fig. 10, the SELDIV selection does not selectthe same set of polarization antenna elements as the lowestBER selection, and its performance gets worse. It is be-cause the performance of the MIMO systems depends onthe received signal power and the correlation of the arrivingsignals, and selecting a set of polarization antenna elementswhich maximizes the received power does not always helpto achieve a lower BER.

4.3.2 Antenna Selection and BER Performance

As shown in Sect. 4.3.1, we defined the received power atthe RF switch outputs, so even for the same transmit power,different antenna selections gave different received powers.Therefore, in the following, we show the BER versus thetransmit power instead of the received power.

Figure 11 shows the antenna set index γ versus the re-ceive antenna position for a snapshot of CIRs selected forthe lowest BER selection, proposed MAPMIC selection andhybrid selection, respectively. The set index γ varies from0 to 8, which shows that the use of polarization antenna el-ements is effective. In addition, the set index obtained with


Fig. 12 BER performance at position 1.


the hybrid selection matches the one obtained with the low-est BER selection at 28 points while the set index obtainedwith the MAPMIC selection matches the one with the low-est BER selection at only 20 points. Therefore, the hybridselection promises to be more effective than the MAPMICselection.

We calculate the BER at 45 positions for the sevenantenna selections. The BER at each position is the aver-age of those calculated with 10 snapshots of CIRs, wherethe chanel temporal variation is ignored for each snapshot(in other word, block fading is assumed). Note that foreach snapshot of CIRs, we run the simulation 10000 times.Therefore, the number of samples used for calculating theBER for each receive antenna position is 96000000 (theresult comes from the multiplication of 2, 10, 48, 10000and 10 which correspond to the number of transmit an-tennas, OFDM symbols in the payload, data subcarriers inone OFDM symbols, loops for simulation and snapshots ofCIRs, respectively) and it is enough for calculating the BERdown to 10−6.

Figures 12–16 show the BER versus the transmit powerat positions 1, 18, 32, 34 and 44, respectively. In addition,Tables 3 and 4 show the received signal power P1, P2 and P(P1, P2 are the received signal powers averaged for antennabranch 1 and 2, respectively; P is the received signal power




averaged for two antenna branches), the correlation COSTβand the SINR for a snapshot of CIRs selected for the MAP-MIC selection, hybrid selection and SELDIV selection atpositions 1 and 34, respectively. The data in Tables 3 and 4are calculated at the transmit power of −5 dBm with all thesubcarriers, and they are used as examples for explaining theperformance of the considered selections at positions 1 and34.

The random selection randomly selects a set of polar-


Table 3 Power, correlation and SINR at position 1 (for one snapshot ofCIRs, at transmit power of −5 dBm).

Selection MAPMIC Hybrid SELDIV

P1 4.62×10−7 4.61×10−7 4.62×10−7

Power P2 6.88×10−7 3.08×10−7 6.88×10−7

P 5.75×10−7 3.85×10−7 5.75×10−7

Correlation 0.85 0.64 0.85

SINR 0.73 0.95 0.73

Table 4 Power, correlation and SINR at position 34 (for one snapshot ofCIRs, at transmit power of −5 dBm).

Selection MAPMIC Hybrid SELDIV

P1 2.64×10−6 2.64×10−6 2.67×10−6

Power P2 3.36×10−6 3.36×10−6 3.90×10−6

P 3.00×10−6 3.00×10−6 3.29×10−6

Correlation 0.78 0.78 0.96

SINR 1.08 1.08 0.13

ization antenna elements. Therefore, there is no guaranteethat it always selects a proper set of polarization antenna el-ements out of 9 sets of polarization antenna elements during10000 loops of the simulation for each of 10 snapshots ofCIRs. As a result, the BER obtained from the random se-lection is equivalent to the average BER obtained from theselection of 9 sets of polarization antenna elements. In addi-tion, the average BER depends much on the worst BERs ob-tained from the wrong selections of antennas. Therefore, theBER performance of the random selection is usually worsethan those of the other selections, except for the case thatthose selections happen to select the wrong sets of polariza-tion antenna elements (see Fig. 15). The lowest BER selec-tion selects the set of polarization antenna elements whichgives the lowest BER. However, it requires a kind of com-puter simulation to calculate the BERs for 9 sets of polar-ization antenna elements for each measured CIR, therefore,its performance means the lower bound but is difficult to bereached in real systems. The SINR selection performs thebest as its performance reaches that of the lower bound inFigs. 12, 13, 15 and 16, and its BER curve is the closest tothat of the lower bound in Fig. 14. The SELDIV tries tomaximize the received signal power and it performs betterthan the random selection in Figs. 12, 13, 14 and 16 but itsperformance is worse in Fig. 15. It should be noted that theperformance of the MIMO systems depends on the receivedsignal power and the correlation of the MIMO channels. InFig. 15, the correlation obtained with the SELDIV selectionis very high and the obtained SINR is low, which means thatthe SELDIV selection selects a wrong set of polarization an-tenna elements when it only tries to maximize the receivedsignal power (see Table 4). Therefore, it can be concludedthat only maximizing the received signal power is not a goodchoice in MIMO systems.

The MAPMIC selection proves to be effective as its

Fig. 17 CDF of BER.

performance is equivalent to (see Figs. 12, 13, 14 and 15) oreven better than that of the capacity selection (see Fig. 16).It should be noted that the capacity selection is a general se-lection and not specialized to a specific receiver. Therefore,it is expected that for certain channels, optimal selection interms of capacity may yield supoptimal performance par-ticularly for suboptimal receivers [7]. The hybrid selectionshows to be more effective than the MAPMIC selection asits performance is the same as that of the MAPMIC selec-tion (see Figs. 13, 15 and 16) or even better (see Figs. 12 and14). The superior performance of the hybrid selection overthe MAPMIC selection in Fig. 12 can be explained with theaid of Table 3 (the explanation for Fig. 14 can be done inthe similar way). The hybrid selection calculates the SINRsfor the set of polarization antenna elements obtained fromthe criterion of the MAPMIC selection and another set ob-tained from the criterion of minimizing the correlation. Inthis case, it finds that the SINR for the set of polarizationantenna elements obtained by minimizing the correlation ishigher and it selects this set. Higher SINR means betterperformance, therefore, the performance of the hybrid se-lection is better than that of the MAPMIC selection, whichalso means that the combination of COSTα and COSTβ iseffective.

Figure 17 shows the cummulative distribution func-tion (CDF) of the BERs of the seven antenna selectionsat the transmit power of −5 dBm. At the point of 0.5 ofthe CDF curves, the BERs of the MAPMIC selection, hy-brid selection, capacity selection, SELDIV selection, ran-dom selection, SINR selection and lowest BER selection are8.5×10−4, 5.5×10−5, 2×10−3, 4×10−3, 4.5×10−2, 1.5×10−5

and 2.5 × 10−6, respectively. It should be noted again thatthe lowest BER selection requires a kind of computer sim-ulation to calculate the BER for each measured CIR and itsperformance is the lower bound of the system but is diffi-cult to be reached. The performance of the random selec-tion is the worst while that of the SINR selection is the bestas it outperforms the other selections and its CDF curve isthe closest to that of the lower bound. The proposed MAP-MIC selection and hybrid selection show to be effective asthey outperform the capacity selection, SELDIV selection


Fig. 18 CDF of BER for MAPMIC selection.

Fig. 19 CDF of BER for hybrid selection.

and random selection. Furthermore, the performance of thehybrid selection is superior to that of the MAPMIC selectionand its CDF curve is the second closest to that of the lowerbound.

Figures 18 and 19 show the CDF of the BERs ofthe MAPMIC selection and hybrid selection at the trans-mit power of −5 dBm, where the number of subcarriers arechanged from 52 to 1, respectively. The CDF curves of bothselections do not change when the number of subcarriersare 52, 32 and 16, respectively, which shows that the num-ber of subcarriers used in both selections can be reduced to16 without performance degradation (see Sect. 3.3.3). Theperformance of the hybrid selection and MAPMIC selec-tion begin to degrade when the number of subcarriers usedfor averaging are smaller than 16 and 8, respectively. There-fore, the computational complexity can be reduced more butthere is a trade-off between the computational complexityand the performance of the system.

Figure 20 shows the BER versus the number of subcar-riers for averaging the received signal power, the correlationbetween received signals, the SINR and the capacity at thetransmit power of −5 dBm (see (20), (21), (18) and (12)).The BERs of random selection and lowest BER selection donot depend on the number of subcarriers and are equal to4.5 × 10−2 and 2.5 × 10−6, respectively (see Fig. 17). TheBER of the SELDIV selection is obtained in the case when

Fig. 20 BER versus the number of subcarriers for averaging the receivedsignal power, the correlation between received signals, the SINR and thecapacity.

the number of subcarriers used for calculating the receivedsignal power is 52 and it is equal to 4 × 10−3 (see Fig. 17).For each of the remaining selections, we first calculate theCDF of the BERs at the transmit power of −5 dBm with thenumber of subcarriers as a parameter (refer Figs. 18 and 19);we secondly calculate the BERs at the point of 0.5 of theCDF curves; and finally we have the BER versus the num-ber of subcarriers. It can be seen that the BERs of the fourselections do not change when the number of subcarriersdecreases from 52 to 16, and begin to get worse when thenumber of subcarriers is smaller than 16. This means thatthe number of subcarriers used for calculation in the fourselections can be reduced to 16 without performance degra-dation. Though the SELDIV selection uses 52 subcarriersfor averaging the power, its performance is still worse thanthat of the capacity selection when the number of subcarri-ers used for averaging the capacity is equal to or larger than4. The BER performance of the MAPMIC selection is bet-ter than those of the capacity selection and random selectionwhen the number of subcarriers is not smaller than 2. How-ever, there is still a large gap between the performance ofthe MAPMIC selection and that of the SINR selection. TheBER performance of the hybrid selection is better than thatof the MAPMIC selection when the number of subcarriers isnot smaller than 4. Furthermore, the gap between the BERperformance of the hybrid selection and that of the SINRselection is considerably smaller than the gap between theBER performance of the MAPMIC selection and that of theSINR selection. When the number of subcarriers is equalto 1, there is no difference in the BER performance of thehybrid selection, MAPMIC selection and capacity selection.Their BERs then are slightly worse than that of the SINR se-lection but are still better than that of the random selection,which implies that the use of antenna selection is useful evenwhen the number of subcarriers used for calculation is 1.

4.4 Computational Complexity

Here, we discuss the computational complexity of the MAP-MIC selection, hybrid selection, capacity selection and


Table 5 Computational complexity.

SINR LMr [( Mr(Mr+1)(2Mr+1)3 + 2Mt M2

r + M2r

selection +Mt Mr + Mr + Mt + 5)MtNave + Mt + 1]

Capacity LMr [( Mr(Mr+1)(2Mr+1)6 + M2

r Mt + M2r

selection +2Mr + 1)Nave + 1]

MAPMIC LMr [ Mt2 (NaveMr(Mt + 1) + 3Mt − 1)]

selection

Hybrid LMr [ Mt2 (NaveMr(Mt + 1) + 5Mt − 3)]

selection +2[( Mr(Mr+1)(2Mr+1)3 + 2Mt M2

r + M2r

+Mt Mr + Mr + Mt + 5)MtNave + Mt + 1]

Table 6 Computational complexity (Mt = Mr = 2; L = 3).

Nave 52 32 16

SINR selection 40275 24795 12411

Capacity selection 10305 6345 3177

MAPMIC selection 2853 1773 909

Hybrid selection 11821 7301 3685

SINR selection only in terms of complex multiplicationsto see how much the computational complexity can be re-duced.

Table 5 shows the computational complexity for calcu-lating LMr values of the cost functions used in the MAPMICselection, hybrid selection, capacity selection and SINR se-lection, respectively. Note that Nave may take the values of52, 32, 16, . . ., as mentioned in Sect. 3.3.3.

Table 6 shows the computational complexity for thefour selections, where Mt and Mr are set to 2, L is set to 3,and the number of subcarriers Nave is set to 52, 32 and 16, re-spectively. Note again that we can reduce the number of sub-carriers for averaging the received signal power, the correla-tion between received signals, the SINR and the capacity to16 without any performance degradation (see Fig. 20). FromTable 6, we can see that the computational complexity ofthe MAPMIC selection, hybrid selection and capacity selec-tion is around 7.1%, 29.4% and 25.6% of that of the SINRselection when Nave = 52 and is around 7.3%, 29.7% and25.6% of that of the SINR selection when Nave = 16. Thecomplexity of the MAPMIC selection thus is the smallest.The complexity of the hybrid selection is higher than thatof the MAPMIC selection and capacity selection, but it islower than that of the SINR selection. It should be noted thecomputational complexity needs LMr values of SINR for theSINR selection while it only needs 2 values of SINR for thehybrid selection. Furthermore, LMr values of capacity needsLMr calculations of the determinant and matrix multiplica-tion. Therefore, the computational complexity of the SINRselection and capacity selection becomes huge quickly whenL and Mr get large while it does not happen for the hybridselection. For instance, when Mt = Mr = 4, L = 3 andNave = 52, the computational complexity of the hybrid se-lection, capacity selection and SINR selection is 268172,

501309 and 3925989, respectively. The computational com-plexity of the hybrid selection and capacity selection thus is6.8% and 12.8%, respectively, which shows that the compu-tational complexity of the hybrid selection is lower than thatof the capacity selection and SINR selection.

5. Conclusions

In this paper, we have proposed two antenna selection meth-ods for a MIMO-OFDM system with RF-switched polariza-tion antenna elements at receiver side, taking into low com-putational complexity. To evaluate the performance of thesystem in a real environment, we have conducted a chan-nel measurement campaign to obtain the channel impulseresponses and used them as parameters when evaluating theperformance.

The proposed MAPMIC selection method works effec-tively in the real environment and promises to decrease agreat deal of computational complexity. The hybrid selec-tion performs better than the MAPMIC selection but it alsorequires more computational complexity. There is a trade-off between the performance and the computational com-plexity, therefore, the choice of the MAPMIC selection orhybrid selection depends on the requirement for better per-formance or lower computational complexity.

Acknowledgments

The authors gratefully acknowledge the financial supportof the National Institute of Information and Communica-tions Technology of Japan. Furthermore, the authors wouldlike to show their sincere gratitude to Mr. Hiroya Tanaka ofTokyo Institute of Technology for his helpful suggestions.

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Appendix: SELDIV Selection Method

Selecting an antenna with larger received signal power outof several antennas at the receiver side is a simple andpractical way to improve the performance of the system[19]. Therefore, the selective diversity (SELDIV) selectionmethod is employed by selecting the antennas with largerreceived signal power.

In this paper, for simplicity, we suppose that the re-ceived signal power Pli at polarization antenna element l(l = 1, . . . , L) of antenna branch i (i = 1, . . . ,Mr) is averagedover all the subcarriers and can be monitored at the receiver.The SELDIV selection method can be done as follows.

Step 1. Calculate the received signal power Pli for MrL po-larization antenna elements.

Step 2. For each antenna branch, among L polarization an-tenna elements, select the one which gives the largestreceived signal power.

The SELDIV selection method promises low compu-tational complexity as it only calculates the received signalpower. However, as it does not consider the correlation be-tween the received signals, the performance obtained withthe SELDIV selection method may be poor in the environ-ments where the MIMO channels are highly correlated.

Quoc Tuan Tran received the B.Eng., andM.Eng. degrees in communications engineeringfrom Osaka University in Osaka, Japan in 2003,and 2005, respectively. He is currently pursuingthe Ph.D. course at Osaka University, engagingin the research on digital signal processing tech-niques for wireless communications systems.

Shinsuke Hara received the B.Eng., M.Eng.and Ph.D. degrees in communications engineer-ing from Osaka University, Osaka, Japan, in1985, 1987, and 1990, respectively. He was anAssistant Professor from April 1990 to Septem-ber 1997 and an Associate Professor from Oc-tober 1997 to September 2005 in Osaka Uni-versity. Since October 2005, he has been withthe Graduate School of Engineering, Osaka CityUniversity as a Professor. From April 1995 toMarch 1996, he was also a visiting scientist at

Telecommunications and Traffic Control Systems Group, Delft Universityof Technology, Delft, The Netherlands. His research interests include mo-bile and indoor wireless communications and digital signal processing.

Kriangsak Sivasondhivat received the B.S.degree (First Class Honors) from ChulalongkornUniversity, Bangkok, Thailand, in 1997 and theM.S. degree from Tokyo Institute of Technol-ogy, Japan, in 2000, respectively, all in electri-cal engineering. Since 2003, he has been work-ing towards the Ph.D. degree at Tokyo Instituteof Technology. From 2000 to 2006, he waswith Telecommunications Research and De-velopment Division, National Electronics andComputer Technology Center (NECTEC), Thai-

land, where he worked on smart antenna development. Since 2007, he hasbeen a research and development engineer at Agilent Technologies, Japan.His research interests are parameter estimation, radio propagation measure-ment and modeling, array signal processing and multiple-input multiple-output systems.

Jun-ichi Takada received B.E. and D.E.degrees from Tokyo Institute of Technology,Japan, in 1987 and 1992, respectively. From1992 to 1994, he has been a Research Associateat Chiba University, Chiba, Japan. From 1994to 2006, he has been an Associate Professor atTokyo Institute of Technology, Tokyo, Japan.Since 2006, he has been a Professor at Tokyo In-stitute of Technology. His current research inter-ests are wireless propagation and channel mod-eling, antennas and antenna systems for wireless

applications, and cognitive radio technology. He is a member of IEEE,ACES, and ECTI Association Thailand.


Atsushi Honda was born in Chiba, Japan,in 1977. He received the B.E. degree in electri-cal and electronic engineering from Tokyo In-stitute of Technology, Tokyo, Japan, in 2003.He joined Fujitsu Laboratories Ltd., Yokosuka,Japan, in 2003. His current research interestsinclude antenna and RF technologies for futurewireless communications.

Yuuta Nakaya was born in Ishikawa, Japan,on October 7, 1977. He received the B.E de-gree in information and systems engineeringfrom Kanazawa University, Japan in 2000, andthe M.E. degree in electrical and electronics en-gineering from Tokyo Institute of Technology,Tokyo in 2002. In 2002, he joined Fujitsu Lab-oratories Ltd., Yokosuka, Japan. He is currentlywith Fujitsu Ltd., Yokosuka, Japan. He receivedthe Young Engineer Awards from IEICE Japanin 2004. His current research interests include

MIMO communication systems.

Kaoru Yokoo was born in Chiba, Japan, in1977. He received the M.E. degree in electronicengineering from Tokyo Institute of Technol-ogy, Tokyo, Japan, in 2002. In 2002, he joinedFujitsu Laboratories Ltd., Kanagawa, Japan.

Ichirou Ida was born in Asahikawa, Japanon February 15, 1968. He received the B.E.degree from Shibaura Institute of Technology,Tokyo, Japan, in 1991 and the M.E. and D.E.degrees from Chiba University, Chiba, Japan, in1993 and 2001, respectively, all in electronic en-gineering. From 1993 to 1998, he was an engi-neer with Tokyo Aircraft Instrument Company,Tokyo, Japan, where he worked on electromag-netic compatibility design of electrical circuits.From 2001 to 2003, he was with the Fraunhofer

Institute for Microelectronic Circuits and Systems, Duisburg, Germany.From 2003 to 2004, he was a Post-doctoral Research Fellow at TokyoInstitute of Technology, Tokyo, Japan. He is currently with Fujitsu Ltd.,Yokohama, Japan, working on the new-generation mobile antenna systems.His research interests include analysis and measurement of small antennasas well as design of adaptive RF and antenna systems for mobile commu-nications.

Yasuyuki Oishi received the B.S. degreein applied physics from University of Tsukuba,Tsukuba, Japan in 1984. He joined FujitsuLtd., Kawasaki, Japan in 1984 and has been en-gaged in the research and development for mo-bile communication systems. He is a member ofthe Institute of Electrical and Electronics Engi-neers (IEEE).

proposal of receive antenna selection methods for mimo

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