SIMULINK Simulation of a Stationary Indoor MIMO Wireless System.

Transcription

1 ISSC 2005, Dubin. September 1 2nd. SIMULINK Simuation of a Stationary Indoor MIMO Wireess System. Pat Cambers φ Conor Downing* Hussein Baer Scoo of Eectronic and Communications Engineering, Dubin Institute of Tecnoogy, Kevin Street, Dubin 8, IRELAND E-mai: φ pcambers@dit.ie E-mai: * cdowning@dit.ie E-mai: baer@eircom.net Abstract A SIMULINK simuation of a mutipeinput/mutipe-output (MIMO) Communications system mode is described wit reference to actua radio canne measurements from a microwave network anayser. Resuts are presented wic indicate te effect of a canging surrounding environment wit respect to a stationary MIMO communications system. Te approac taken is to assume tat canges in te surrounding pysica environment give rise to measurement errors wit respect to te quantities tat were originay measured. Keywords capacity, antenna, MEA, MIMO, SIMULINK, measurement error. I INTRODUCTION Te use of mutipe antenna arrays (MEAs) as recenty been demonstrated as a means of increasing te spectra efficiency in wireess inks. [1] [2]. Anderson [3] [4] as suggested a metod wereby a transmit weigt factor is appied to eac eement in te transmitter array as we as a receive weigt factor at eac receiver eement. In teory tese weigt factors form a mutipe-input/mutipe-output (MIMO) communications system wit an improved capacity in bits/sec/hz by comparison to a singe antenna system. Te signa to noise ratio (SNR) of tis MIMO communications system becomes caracterised by te eigenvaues of te canne transfer function matrix of te MEA. Tis matrix is derived from measurements of te canne transfer functions tat exist between eac of te transmit and receive eements. Eac of tese canne transfer functions is made up of a number of measurabe components, wic are based on te pysica signa pats between eac eement described. In tis work a simuation was deveoped to first demonstrate te MIMO communications system principe and ten to examine te effect of a canging pysica environment on a stationary MIMO communications system. Te approac taken was to assume tat a measurement error woud arise as tis surrounding environment canged. II THE MEA AND THE MIMO CHANNEL MODEL Measurements of te radio canne transfer functions were made for an MEA antenna system in a speciay buit encosure. Tis encosure is described in more detai beow. Te encosure provides a radio environment wic contains a receive and transmit antenna being moved at moved at af waveengt increments to simuate a MEA and to minimise te effect of mutua couping [10]. Mutua couping is not considered in tis work and furter detais of te measurements and te environment in wic tey were made are given in section IV.

2 It can be assumed at tis stage tat measurements were made in an environment, wic contained easiy identifiabe muti-pat signa components. Tese woud give rise to an eco signature [5] or series of identifiabe peaks at eac receiver antenna due to different pysica signa pats. Te canne t transfer functions between te i transmitter and t te j receiver eement,, may be cacuated i, j from measurements of S 21 due to te ine of sigt (LOS) and non-los signa pats between te transmitter and receiver array. Equation (1) beow sows ow cacuation of, may be made wit i j respect to te measurements described. i,j j2πτ p a exp 1 f = = exp { jφ } t a is te ampitude of te τ is te time of arriva of te (1) muti-pat component. t muti-pat component and f is te frequency of te carrier wit φ referring to a measurement of pase of te t muti-pat component. Four muti-pat components coud be identified, tus te variabe refers to te pat number from 1-4. Eac of tese components was ceary due to a different pysica pat between te transmitter and receiver. Measurements were made on an Anritsu 37369A microwave network anayser and based on te dimensions of te pysica environment in wic tese measurements were made it coud be surmised tat pat 1 was te LOS signa pat, pats 2 and 3 were bot two first-order signa pats and pat 4 was a second-order signa pat. For te case considered ere were tere are N eements at te transmitter array and N eements at te receiver array, an N x N matrix may be constructed for eac eement as beow 1,1 2,1 = N,1 1,2 1, N 2. N N, N (2) i, j Te eements of tis matrix represent te canne t transfer functions between te i transmitter and t te j receiver. Eac eement, arising from te i j couping between eac system of transmit and receive antenna systems described previousy. In te context of MEAs, te receive signa vector, y, may be written in terms of as we as te transmit signa vector, x, and te measure of power of added Gaussian wite noise (AWGN), γ, as beow in equation (3): y = x + γ (3) Tis matrix,, may ten be mutipied by its compex conjugate,, to form a matrix of a measure of power gains. Normaising tis matrix wit respect to its trace effectivey puts a constraint on te transmit power of te MEA. Equation (4) beow gives an expression for te matrix, H, mentioned earier.. tr(. H = (4) ) By definition H is a symmetric matrix and so performing a singuar vaue decomposition (SVD) on H wi produce its eigenvaues. From tis tere now exist tree new matrices, U, S and V suc tat U HV = diag, λ, λ ) = S In equation (5) ( 1 2 k λ (5) U, V compex and are bot unitary matrices, and S is a rea, diagona matrix containing te eigenvaues of H wic, in tis case, are equivaent to te singuar vaues of H due to H being symmetric [7]. Te subscript k refers to te rank of H. H is a square matrix and it can be assumed tat its rows are not ineary reated due to te pysica significance of eac of te terms in te matrix, tus k = N. It can be assumed tat tere is a reationsip between, te matrices U and V, and, te transmit and receive weigt factors, respectivey, wic were mentioned earier in te context of a MIMO communications system. Tus te SNR of te MIMO communications system, assuming tat H as been measured correcty, woud be caracterised by te matrix product in equation (5). As a resut of tis tere is no couping between eac canne or system of transmit and receive antennas in te MEA of a MIMO communications system since te matrix S, contains no off-diagona terms. Equation (6) beow is te now we-known equation for te potentia capacity of a MIMO communications system, C in bits/sec/hz. [11] [1]

3 N C = og k = 1 Te expression P 1 + λk ϕ 2 (6) P. ϕ is te SNR of te MIMO λ k communications system. Te quantity, P, is te avaiabe transmit power wic can be assumed at tis stage to be uniformy aocated to eac transmit eement since equation (3) ods and is a scaar quantity and ϕ, is te noise component in eac of te signa pats. As suc it is now cear from equation (6) tat te MIMO communications system mode wi ave a iger potentia capacity in bits/sec/hz tan te traditiona set-up of one receiver and one transmitter. III SIMULINK SIMULATION In order to demonstrate te MIMO communications system principe, a SIMULINK [8] simuation was deveoped. In doing tis, a number of conditions and assumptions were made. 1) A coding sceme for a MIMO communications system was not considered in te simuation. Simpe binary, two-stage data transmission was used. It was assumed tat te MIMO principe coud be adequatey demonstrated witout any eaborate coding provided te effect of AWGN was not considered. 2) Te simuation was based on measured quantities, wic were ten normaised wit respect to te constraint mentioned in equation (4). 3) Te measure of power in te signa was considered and so te matrices, U and V coud be used as te weigting factors previousy described. 4) Te number of sampes transmitted by te system remained fixed as te effect of increasing te eement dimension, N, was considered. Tus te 5 x 5 system transmitted no more information ten te 2 x 2 MIMO communications system. As indicated by equation (3) te receive signa vector is formed from a matrix mutipication of te matrix of canne transfer functions and te transmit signa vector. In te case of tis SIMULINK simuation, te receive signa vector wi be defined by a matrix mutipication of te normaised matrix, H. In a simiar manner te transmit signa weigting described wi be defined by a matrix mutipication of U and te receive signa weigting wi be defined by a matrix mutipication of V. Figure (1) beow sows ow sampes from a seria transmission source, i.e. Bernoui random number generator (BRG) were adapted for parae transmission on a MEA. Figure 1: A parae transmission sceme in SIMULINK for a 3 x 3 MIMO communications system. Te buffer bock aong wit te demux bock convert seria data to parae data suitabe for te MEA. Te unbuffer bocks are merey a formaity witin te simuation. Te to workspace bock aows te transmit data to be stored as an array in MATLAB. Te BRG as its output set suc tat it transmits a two-eve (binary) code. Te buffer bock takes te seria data and converts it into a set of frames. Te demux bock can ten transmit eac of te eements from te frame of data separatey, wic is suitabe for te MEA. As mentioned previousy te canne transfer functions effectivey perform a matrix mutipication on te transmit data. Figure (2) beow sows ow te effect of te normaised matrix of canne transfer functions, H, was impemented in SIMULINK. Figure 2: A matrix mutipication in SIMULINK for a 3 x 3 MIMO communications system. Te exampe above refers to te matrix H. Te matrix mutipications of and V are performed in SIMULINK in a simiar manner. Te symbos U and V, in te mode above, refer to SIMULINK notation. Te case sown is for a 3 x 3 system of transmitters and receivers ( N = 3 ) but is naturay simiar to a cases of eement dimension, N. Te matrix mutipications invoving impemented witin te simuation in a simiar fasion. Ports 1 3 on te LHS and te RHS of figure (2) above refer to te inputs and outputs, respectivey, of te sub-system for te matrix mutipication of H. Tree SIMULINK sub-systems U U and V are

4 were ten created out of eac tese matrix mutipications, U, H and V. Te overa SIMULINK mode for a 3 x 3 MIMO ( N = 3 ) communications system can be seen in figure (3) beow. Figure 3: Te 3 x 3 MIMO SIMULINK simuation. Te outputs from te transmitter in figure (1) are connected to ports 1 3 on te LHS above. Data from ports 1 3 on te RHS is written to arrays in MATLAB. U, H and V contains Eac of te bocks marked sub-systems, simiar to te one in figure (2), for te reevant matrix mutipications. Te parae data from te outputs of a transmitter simiar to te one in figure (1) are connected to ports 1 3 on te LHS above. Data from ports 1 3 on te RHS may be compared wit te array of origina seria transmit data as indicated in figure (1). Conversion of te data from te system in figure (3) back to seria form, aong wit te comparison to te origina data, is done outside of te simuation. As discussed previousy te matrices U and V are cacuated by SVD of te matrix H, wic is derived from pysica measurements. Te transfer functions of te MIMO communications system are tus contained aong te diagona of te matrix, S, defined in equation (5). However, if te matrix H were to cange wie U and V remained te same, ten it is ikey tat a of te transfer functions of te MIMO communications system woud not be contained witin te matrix, S. It is aso ikey tat te matrix tat woud represent tis particuar MIMO communications system woud contain off-diagona terms. Tis indicates tat tere woud be some degree of couping between eac system of transmit and receive antennas. Tis woud inevitaby ead to a drop in te potentia capacity of te MIMO communications system since te off diagona or couping terms woud appear in te denominator of equation (6) in addition to te noise component, ϕ. Te goa of te SIMULINK simuation was twofod. Firsty, to demonstrate te MIMO communications system principe, i.e. tat a given set of data coud be transmitted using te same carrier frequency aong mutipe adjacent cannes in a MEA. Secondy, to examine te effects of canges in te surrounding pysica environment wic utimatey ead to canges in te matrix, H. I V RESULTS Te SIMULINK simuation is based on experimenta measurements. Tese were obtained in a speciay constructed encosure, wic consisted of two igy refective surfaces at rigt anges to eac oter. Oter surfaces were covered by microwave absorbing materia. Tis reduced te number of pats to one direct pat, two singy refected or first order pats, and one douby refected or second order pat. Tis aowed four pats to be ceary identified on an MNA in te time domain. Oter sources of refection coud tus be eiminated. Te experimenta set-up is sown beow in figure (4). Two antennas were paced 36cm apart, tis distance was deemed adequate for making measurements in te far-fied regime wit respect to a 5.2 GHz carrier frequency (λ =5.77cm). Figure (4) Te experimenta set-up A 30cm ruer can be seen on te far antenna. It indicates tat te two antennas were 20 cm off te ground. Eac antenna is a printed strip monopoe antenna [9]. Beow eac antenna is a grid wit afwaveengt spacings (2.8cm) wit respect to te carrier frequency. A set of measurements of 21 comprising of ampitude in db, puse arriva time in nanoseconds and pase in degrees were made using an Anritsu 37369A microwave network anayser (MNA). As indicated previousy, eac of tese quantities outined for a given set of measurements is reevant to equation (1). Twenty-five sets of measurements were made. Te approac was simpy to od te first antenna in position wie making measurements every time te second antenna was moved troug te series of five af-waveengt increments. Ten te first antenna was moved by a af-waveengt increment and ten ed in position once more wie second antenna proceeded troug te same five af-waveengt increments again. Tis S

5 was repeated unti te first antenna ad passed troug five af-waveengt increments and ence 25 sets of measurements were made. Using tese measurements and te SIMULINK mode outined, te MIMO communications system principe for te exampe of a 3 x 3 MEA ( N = 3 ) was demonstrated. Figure (5) beow sows a signa being transmitted by te MEA witout te MIMO communications system mode aving been impemented as we a comparison between two oter signas: te transmit and receive data aong one of te tree adjacent cannes in a 3 x 3 MIMO communications system as we as te originay transmitted signa. Given tat knowedge of te canne aows te matrices U and V matrices to cacuated and tus te matrix, S contains te resutant transfer functions of MIMO communications system as described by equation (5). Any cange in H, say to H + H, U and V remain te same, wi wie te matrices ave an impact on te MIMO communications system since knowedge of te canne transfer function woud become incorrect as a resut. In te context of tis simuation, te diagona eements of te matrix S are used to set te signaing eves expected at te receiver were a toerance of ± 5% deviation from tese expected eves is deemed acceptabe. Using tis as a framework various measured components are individuay removed from H, namey te LOS, te two first order refection signas and te second order refections signa. Meanwie, te matrices U and V are maintained witin te simuation. Tis is tougt to mode canges in te surrounding pysica environment in te sense tat signa pats mentioned may be obstructed. As described, te origina transmit data and te resutant receive data can be ported to MATLAB arrays for comparison. From tis a bit error rate (BER) may be cacuated. In tota tere are 1000 sampes so an average percentage BER is cacuated over ten sets of one undred sampes. Figures (6) and (7) beow sow te effect of removing te signa components previousy described on te BER wit increasing dimension, N, of te MEA. Figure 5: SIMULINK simuation of te MIMO principe. Te upper pot sows a signa being transmitted by a MEA witout te MIMO communications mode system being impemented. Te midde pot sows te same signa being transmitted by te MEA wit te MIMO communications system mode wic may be readiy compared wit te origina transmission in te ower pot. Figure 6: SIMULINK simuations of te MIMO principe. Te upper curve sows te effect of removing te LOS signa, wit te ower curve sowing te effect of removing te second order signa. It is cear tat te signa in te upper pot is severey corrupted due to interference between eac system of transmit and receive antenna and tat te MIMO communications system mode removes tis effect of te interference.

6 VII REFERENCES [1] Foscini, G.F. and Gans, M.J. On Limits of Wireess Communication in a Fading Environment Wen Using Mutipe Antennas. Wireess Persona Communications, Voume 6, no.3 pp , Marc Figure 7: SIMULINK simuations of te MIMO principe. Te upper curve sows te effect of removing te first, first order signa, wit te ower curve sowing te effect of removing te second, first order signa. V CONCLUSIONS Figure (5) sows mutipe cannes using te same carrier frequency transmitting in cose proximity to anoter using te MIMO communications principe witout te consequence of signa deterioration. It is cear tat a MIMO communications system aows for efficient use of te radio spectrum. Figure (6) is consistant wit iterature [6], wic states tat tere is an increase in potentia capacity in bit/sec/hz as te number of antennas, N, is increased. In figure (6) tere is a decrease in te BER as N increases wen bot te LOS signa component and te second order component are removed. However tis is not consistent wit te resuts tat are presented in figure (7). In figure (7) te reationsip between te BER and te first order signa components is examined. In te case of te first, first order signa tere is a decrease in te BER as te amount of antennas is increased but ony after te BER as increased first. For te second, first order signa it is cear tat te opposite is true. Te remova of first order signas wi tus require furter investigation. VI ACKNOWLEGMENTS Tis work was carried out under a Dubin Institute of Tecnoogy (DIT) Scoarsip. Te autors woud ike to tank F.M. Boand of Trinity Coege, Dubin for some very epfu insigts. Te autors are aso indebted to A. Grennan, G. Farre, M. Amman of te DIT for teir ep and comments. [2] Mansoor, S., Gespert D., Siu, D.S., Smit, P., Guest Editoria MIMO Systems and Appications. IEEE Journa on Seected Areas in Communications, Voume 21, no.3 pp , Apri [3] Andersen. J.B., Antenna Arrays in Mobie Communications - Gain, Diversity and Canne Capacity, Radio Science Buetin, No. 290, pp 4 7, September [4] Andersen. J.B., Array Gain and Capacity for Known Random Cannes wit Mutipe Eement Arrays at Bot Ends, IEEE Journa on Seected Areas in Communications, Voume 18, no.11 pp , November [5] Grennan, T., Downing, C., Foey, B., Capacity Variation of Indoor Radio MIMO Systems Using a Deterministic Mode" Iris Signa and Systems Conference, University of Limerick, Juy [6] Poock, T.S., Abayapaa, T.D., C., Kennedy, R., Fundamenta Limits of MIMO Capacity for Spatiay Constrained Arrays" Proceedings 4 t Austraian Communication Teory Worksop, 2003, pgs [7] Peterson, K.B., M.S., Pederson, Te Matrix Cookbook" <ttp://www2.imm.dtu.dk/pubdb/views/edoc_do wnoad.pp/3274/pdf/imm3274.pdf> January 5 t 2005 [8] [9] Amman, M., Contact information: Scoo of Eectronic and Communications Engineering, DIT, Kevin Street, Dubin 8. [10] Svantesson, T, Raneim, A Mutua Couping Effects on te Capacity of Mutieement Antenna Systems" Department of Signas and Systems, Camers University of Tecnoogy, Sweden / , IEEE pgs [11] Sannon, C.E., A Matematica Teory of Communication, Te Be System Tecnica Journa, Vo. 27, pp , , Juy, October 1948.

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