Space-Frequency Block Code for MIMO-OFDM Communication Systems with Reconfigurable. antennas.

Transcription

1 Space-Frequency Block Code for MIMO-OFDM Counication Systes with Reconfigurable Antennas arxiv: v1 csit 13 Aug 2015 Vida Vakilian Jean-François Frigon and Sébastien Roy École Polytechnique de Montréal Dept of Electrical Engineering Montréal QC H3T 1J4 Canada {vidavakilian Dept of Elec and Cop Engineering Université Sherbrooke Sherbrooke QC Canada Abstract We propose a space-frequency (SF) block coding schee for a ultiple-input ultiple-output (MIMO) orthogonal frequency-division ultiplexing (OFDM) syste using antennas with reconfigurable radiation patterns In this syste each eleent of the antenna array at the transitter side is assued to be reconfigurable so that it can independently change the physical characteristics of its radiation pattern The proposed block code is full rate and benefits fro spatial frequency and reconfigurable radiation pattern state diversity over frequency-selective fading channels We provide siulation results to deonstrate the perforance of the proposed block coding technique and ake coparisons with that of the previous SF coding schees in MIMO-OFDM systes The results indicate that the proposed code achieves higher diversity and coding gain copared to other available SF codes Index Ters Frequency-selective fading channels ultipleinput ultiple-output-orthogonal frequency-division ultiplexing (MIMO-OFDM) systes space-frequency (SF) coding reconfigurable antennas I INTRODUCTION Reconfigurable antennas can be used in ultiple-input ultiple-output (MIMO) counication systes to increase the capacity and reliability of wireless links 1 5 In a reconfigurable MIMO syste the characteristics of each antenna radiation pattern can be changed by placing switching devices such as Microelectroechanical Systes (MEMS) varactor diodes or field-effect transistor (FET) within the antenna structure 6 8 As a result a syste eploying reconfigurable antennas is able to alter the propagation characteristics of the wireless channel into a for that leads to a better signal quality at the receiver In fact by using reconfigurable antennas and designing a proper code we can achieve an additional diversity gain that can further iprove the perforance of wireless counication systes There are several works in the literature on designing efficient codes for reconfigurable MIMO systes in order to take advantage of the antenna reconfigurability In 5 authors have proposed a MIMO syste equipped with reconfigurable antennas at the receiver that can achieve a diversity order that equals to the product of the nuber of transit antennas the nuber of receive antennas and the nuber of reconfigurable states of the receive antennas They have shown that this diversity gain is achievable only under certain channel propagation conditions and using an appropriate coding technique Later on in 9 authors extended the concept by using reconfigurable eleents at both transitter and receiver sides In their work they have introduced a state-switching transission schee called space-tie-state block coding (STS-BC) to further utilize the available diversity in the syste over flat fading wireless channels However their coding schee does not exploit the frequency diversity offered by the ultipath propagation channels between each transit and receive antenna pair To obtain frequency diversity in ultipath environent a space-frequency (SF) block code was first proposed by authors in 10 where they used the existing space-tie (ST) coding concept and constructed the code in frequency doain Later works also used siilar strategies to develop SF codes for MIMO-OFDM systes However the resulting SF codes achieved only spatial diversity and they were not able to obtain both spatial and frequency diversities To address this proble a subcarrier grouping ethod has been proposed in 1 to further enhance the diversity gain while reducing the receiver coplexity In 18 a repetition apping technique has been proposed that obtains full-diversity in frequencyselective fading channels Although their proposed technique achieves full-diversity order it does not guarantee full coding rate Subsequently a block coding technique that offers fulldiversity and full coding rate was derived However the SF codes proposed in the above studies and other siilar works on the topic are not able to exploit the state diversity available in reconfigurable ultiple antenna systes In this paper we propose a coding schee for reconfigurable MIMO-OFDM systes that achieves ultiple diversity gains including space frequency and state Basically the proposed schee consists of a code that is sent over transit antennas OFDM tones and radiation states In order to obtain state diversity we configure each transit antenna eleent to independently switch its radiation pattern to a direction that can be selected according to different optiization criteria eg to iniize the correlation aong different radiation

2 states We construct our proposed code based on the fundaental concept of rotated quasi-orthogonal space-tie block codes (QOSTBC) By using the rotated QOSTBC the proposed coding structure provides rate-one transission (ie one sybol per frequency subcarrier per radiation state) and leads to a sipler Maxiu Likelihood (ML) decoder As the siulation results indicate our proposed code outperfors the existing space-frequency codes substantially The rest of this paper is organized as follows In Section II we introduce the channel and syste odel for a reconfigurable MIMO-OFDM syste In Section III we briefly discuss the code design for reconfigurable ultiple antenna systes Siulation results are presented in Section IV and finally conclusions are drawn in Section V Notation: Throughout this paper we use capital boldface letters for atrices and lowercase boldface letters for vectors ( ) T denotes transpose of a vector C stands for the set of coplex valued nubers Operator diag(a 1 a 2 a n ) represents a diagonal n n atrix whose diagonal entries are a 1 a 2 a n stands for the floor operation and I N represents the N N identity atrix Operator col{ } stacks up the atrices on top of each other II CHANNEL AND SYSTEM MODELS FOR RECONFIGURABLE MIMO-OFDM SYSTEMS Consider a MIMO-OFDM syste with M t reconfigurable eleents at the transitter where each of these eleents is capable of electronically changing its radiation pattern and creating P different radiation states as shown in Fig 1 In this syste we assue the receiver antenna array consist of M r oni-directional eleents with fixed radiation patterns Moreover we consider an N c -tone OFDM odulation and frequency-selective fading channels with L independent propagation paths between each pair of transit and receiver antenna in each radiation state The channel gains are quasistatic over one OFDM sybol interval The channel ipulse response between transit antenna i and receive antenna j in the p-th radiation state can be odelled as L 1 h ij p (τ) = α ij p (l)δ(τ τ lp ) (1) l=0 where τ lp is the l-th path delay in the p-th radiation state and α ij p (l) is the coplex aplitude of the l-th path between the i-th reconfigurable transit antenna and the j-th receive antenna in the p-th radiation state The average total received power is noralized to one The frequency response of the channel at the n-th subcarrier between transit antenna i and receive antenna j in the p-th radiation state is given by L 1 p (n) = α ij p (l)e j2πn fτ lp (2) H ij l=0 where f = 1/T s is the subcarrier frequency spacing and T s is the OFDM sybol duration The space-frequency codeword transitted during the p-th radiation state C p C Mt Nc can be expressed as C p = c 1 p(0) c 1 p(1) c 1 p(n c 1) c 2 p (0) c2 p (1) c2 p (N c 1) c Mt p (0) cmt p (1) cmt p (N c 1) (3) where c i p (n) denotes the data sybol transitted by transit antenna i on the n-th subcarrier during the p-th radiation state At the receiver after cyclic prefix reoval and FFT the received frequency doain signal of the n-th subcarrier and p-th radiation state at the j-th receive antenna can be written as yp j (n) = M t Hp ij M (n)ci p (n)+zj p (n) (4) t i=1 where Hp ij (n) is the frequency response of the channel at the n-th subcarrier between transit antenna i and receive antenna j in the p-th radiation state as defined in (2) zp j (n) is the additive coplex Gaussian noise with zero ean and unit variance at the n-th subcarrier and γ is the received signal-to noise ratio (SNR) The received signal during the p-th radiation state y p = yp(0) T yp(1) T yp(n T c 1) T with y p (n) = yp 1(n) y2 p (n) ymr p (n) T can be written as where y p = M t H p c p +z p (5) H p = diag{h p (0) H p (1) H p (N c 1)} (6) is the channel atrix c p = vec(c p ) is the transitted codeword and z p C NcMr 1 is the noise vector during the p-th radiation state In (6) H p (n) is an M r M t channel atrix with entries defined in (2) The SF codeword over all P radiation states can be represented as C = C 1 C 2 C P () where C p is given in (3) The received signals over all radiation states is defined by y = y T 1 y T 2 y T P T C PNcMr 1 and can be represented by y = M t Hc+z (8) where c = vec(c) H = diag{h 1 H 2 H P } C PNcMr PNcMt is the overall channel atrix and z = z T 1 zt 2 zt P T C PNcMr 1 is the noise vector

3 Reconfigurable Antenna Array Oni-directional Antenna Array Input Bits Mapping Space-Frequency Encoder OFDM Modulation OFDM DeModulation Space-Frequency Decoder DeMapping Output Bits Radiation Pattern Control Signal Fig 1 Block diagra of a Reconfigurable MIMO-OFDM syste eploying reconfigurable antennas at the transitter III SPACE-FREQUENCY CODE DESIGN FOR RECONFIGURABLE MIMO-OFDM SYSTEMS In this section we present our proposed coding schee for a reconfigurable antenna syste where each antenna eleents can independently change its radiation pattern direction In particular we construct the code based on the principle of a quasi-orthogonal coding structure for an arbitrary nuber of transit antennas and radiation pattern states In each radiation state we consider a coding strategy where the SF codeword is a concatenation of G T p as follows: C p = G 1T p G 2T p G MT p 0 T N c MLM t (9) where M = Nc LM t and 0 N is the all-zeros N N atrix In this expression 0 N will disappear if N c is an integer ultiple of LM t In this work for siplicity we assue N c = LM t q for soe integer q Each G p atrix {12 M} takes the following for: G p = col{x 1 X 2 X L } (10) where X l is the M t M t block coding atrix which is equivalent to an Alaouti code structure for M t = 2 To aintain siplicity in our presentation we design the code for M t = 2 transit antennas however extension to M t > 2 is possible by following the siilar procedure In the case of having two transit antennas X l = A ( x 1 x 2 ) where A ( x 1 x 2 ) = x1 x 2 x 2 x 1 (11) and therefore G p can be expressed as A(S2(p 1)L+1 S 2(p 1)L+2 ) A(S G 2(p 1)L+3 S 2(p 1)L+4 ) p = (12) A(S2pL 1 S 2pL ) In (12) Si is a set of cobined sybols coputed as S S S T 1 3 2PL 1 = Θ s s s T 1 3 2PL 1 S 2 S 4 S 2PL T = Θ s 2 s 4 s 2PL T (13) where {s 1 s 2PL} is a block of sybols belonging to a constellation A Θ = U diag{1e jθ1 e jθpl 1 } and U is a PL PL Hadaard atrix The θ i s are the rotation angles Different optiization strategies can be used to find the optial values of rotation angles θ i s such that they axiize the coding gain The objective function in this optiization is defined as the iniu Euclidean distance between constellation points As an exaple consider a reconfigurable MIMO-OFDM syste with M t = 2 transit antennas P = 2 radiation states and L = 2 ultipaths In this scenario the transitted codewordsc 1 and C 2 given in (14) are constructed according C 1 = 1 4 C 2 = 1 4 S 1 1 S2 1 S3 1 S4 1 S1 M S2 S3 M S4 S2 1 S1 1 S4 1 S3 1 S2 M S1 S4 M S3 S 1 5 S6 1 S 1 S8 1 S5 M S6 S M S8 S6 1 S5 1 S8 1 S 1 S6 M S5 S8 M S (14)

4 to (9) The entries of C p are coputed using (13) As a result we obtain C T 1 as s s 1 3 +ŝ 1 5 +š 1 s s 1 4 +ŝ 1 6 +š s 1 4 ŝ 1 6 š s 1 3 +ŝ 1 5 +š 1 s 1 1 s 1 3 +ŝ 1 5 š 1 s 1 2 s 1 4 +ŝ 1 6 š s 1 4 ŝ 1 6 +š 1 1 s 1 3 +ŝ 1 5 š 1 s M 1 + s M 3 +ŝ M 5 +š M s M 2 + s M 4 +ŝ M 6 +š M 8 2 s 4 ŝ 6 š 8 s 1 + s 3 +ŝ 5 +š s M 1 s M 3 +ŝ M 5 š M s M 2 s M 4 +ŝ M 6 š M s 4 ŝ 6 +š 8 s 1 s 3 +ŝ 5 š (15) and C T 2 as s s 1 3 ŝ 1 5 š 1 s s 1 4 ŝ 1 6 š s 1 4 +ŝ 1 6 +š s 1 3 ŝ 1 5 š 1 s 1 1 s 1 3 ŝ 1 5 +š 1 s 1 2 s 1 4 ŝ 1 6 +š s 1 4 +ŝ 1 6 š 1 1 s 1 3 ŝ 1 5 +š 1 s M 1 + s M 3 ŝ M 5 š M s M 2 + s M 4 ŝ M 6 š M 8 2 s 4 +ŝ6 +š 8 s 1 + s 3 ŝ5 š s M 1 s M 3 ŝ M 5 +š M s M 2 s M 4 ŝ M 6 +š M s 4 +ŝ 6 š 8 s 1 s 3 ŝ5 +š (16) where s i = e jθ1 s i ŝ i = e jθ2 s i and š i = e jθ3 s i Note that the above codeword provides rate-one transission (ie one sybol per OFDM tone per radiation state) IV SIMULATION RESULTS In this section we present siulation results for both conventional and reconfigurable MIMO-OFDM systes The reconfigurable ultiple antenna syste eploys antenna eleents capable of dynaically changing their radiation pattern directions at the transitter where in this work we consider that each eleent hasp = 2 radiation states The conventional MIMO-OFDM syste uses oni-directional antenna eleents with fixed radiation pattern at both transitter and receiver ends For both systes we consider M t = 2 antennas at the transitter and M r = 1 antenna at the receiver and an OFDM odulation technique with N c = 128 subcarriers as well as a cyclic prefix equal to or longer than the axiu channel delay spread In our siulations we consider that the receiver has perfect channel state inforation We also assue that the sybols are chosen fro a BPSK constellation leading to a spectral efficiency of 1 bit/sec/hz if the cyclic prefix overhead is ignored The average sybol power per transit antenna is set to be E s = 1/M t and the noise variance is σn 2 = 1/γ We carry out the siulations for a 2-ray equal power channel odel for two different delay spreads Furtherore for a reconfigurable antenna syste we assue the sae delay spread for both radiation states Bit Error Rate SF Code Proposed in 19 QOSF Code Proposed in 20 Our Proposed QOSF Code SNR Fig 2 BER vs SNR for a reconfigurable ulti-antenna syste withm t = 2 P = 2 M r = 1 in a 2-ray channel with a delay spread of 5µs (ie τ l1 = τ l2 ) The channel coefficients α ij p (l) are zeroean identically-distributed Gaussian rando variables with a variance of σlp 2 We assued that they are independent for each ultipath transit antenna and radiation pattern state The powers of all paths in each radiation state are noralized such that L 1 l=0 σ2 lp = 1 For our proposed QOSF schee the rotation angles are chosen as θ 1 = π 4 θ 2 = π 2 and θ 3 = 3π 4 Fig 2 shows the bit error rate (BER) perforance of the proposed code in ultipath propagation channels with a delay spread of τ = 5µs As shown in this figure the proposed code outperfors those of 19 and 20 In particular at a bit error rate of 10 5 the perforance iproveent copared to 19 and 20 is nearly and 6 db respectively This perforance iproveent deonstrates the superiority of our proposed schee which is due to the extra diversity gain offered by the use of reconfigurable antenna eleents Fig 3 depicts the BER perforance of the proposed code for a delay spread of τ = 20µs It is evident fro the figure that at a BER of 10 5 our proposed coding schee outperfors the codes presented in 19 and 20 by about 6 and4db respectively Copared to the results in Fig 2 it can be seen that as delay spread increases the BER perforance iproves This is due to benefiting fro lower correlation between subcarriers and therefore higher frequency diversity in ultipath propagation channels V CONCLUSIONS We proposed a space-frequency coding technique for MIMO-OFDM systes using antennas with reconfigurable radiation patterns The proposed code is constructed based on the principle of quasi-orthogonal coding schee and consists of a block of transitted sybols expanding over space frequency and radiation state diensions We provided siulation results to deonstrate the perforance of the proposed

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