A Real-Time Wireless Channel Emulator For MIMO Systems

Transcription

1 A eal-time Wirele Channel Emulator For MIMO Sytem Hamid Elami, Ahmed M. Eltawil Abtract: The improvement in channel capacity hailed by MIMO ytem i directly related to intricate detail of the wirele channel uch a the degree of correlation between the multiple channel etablihed due to a MIMO configuration. Capturing thee detail in real time emulation ytem become abolutely eential to validate theoretical reult in a controlled etting. Thi paper preent method to achieve ignificant improvement in peed and complexity for real time channel emulation maintaining high reolution in time and frequency. In particular, thi paper preent a frequency domain emulation technique that reduce add/multiply operation by 54% compared to conventional FI emulation. A comprehenive complexity analyi i performed to compare the complexity of different technique. implementing thee platform tem from the fact that the complexity of multi-channel emulator grow quadratically with the number of channel involved. For example, for a 4x4 MIMO ytem, 16 wirele channel need to be emulated in real time to fully characterize the interaction between all tranmit and receive antenna. Furthermore, in highly diperive environment, each wirele channel by itelf can have an extended temporal repone which lead to further complexity of the ytem [2]. Keyword: MIMO n, channel emulation, operation per output ample, complex convolution, Fourier tranformation. I. INTODUCTION Wirele communication ytem deign and implementation are governed mainly by channel model and ignal recontruction algorithm. The time varying nature of the channel leave the efficiency of uch ytem highly dependant on the current channel tate under which the ytem i functioning. While tatitical model of the wirele channel are ufficient for firt order theoretical tudie, imulation and experimentation are eential to validate both the theoretical aumption and reult, thu leading to a true cientific procedure. Furthermore, the ability to accurately emulate the wirele channel under repeatable, controlled laboratory etting allow cro layer validation, wherea algorithm deigner can tet and validate their repective algorithm under realitic fading wirele channel condition. Digital bae-band deigner can then architect the bet hardware configuration that map algorithm to phyical ytem and ue the ame tet mechanim to etablih functionality. Thi methodology allow for a portable and complete tet platform that lead to an improved a well a accelerated deign cycle. An example of uch a ytem i preented in Fig. (1). Traditional emulation platform are deigned primarily for ingle input ingle output ytem, where a ingle wirele channel i aumed to exit between tranmit and receive terminal. An example of uch a ytem wa preented in [1] where a wide-band, real-time mobile channel emulator wa deigned and implemented for temporal correlative channel baed on FI filter repreenting the channel impule repone. However with the advent of MIMO-baed tandard uch a n, the need for multi-channel real-time emulator i becoming an immediate reality. The challenge in Figure 1: configuration of a portable tet platform In thi paper, we invetigate performing the emulation procedure in the frequency domain with the target of improving the efficiency of the proce and reducing the computational load of the real-time ection of the entire ytem. IEEE n tandard i choen to be a cae tudy in our work. Thi tandard deploy an M element tranmitter and an N element receiver to upport high data rate tranmiion [3]. Our reult indicate that for the ame level of accuracy, a frequency baed approach require 54% le add/multiply operation a compared to a typical FI baed approach, with the added feature of being highly calable to upport any number of tranmit/receive pair. The paper i organized a follow: Section II ummarize wirele channel iue and behavior. In ection III, the ytem block diagram i introduced and each block decription i provided. Section IV preent multiple algorithm to implement the emulator a well a a complexity analyi of the different approache. Finally, the paper i concluded in ection V. II. CHANNEL DESCIPTION Due to multipath propagation in a radio channel, everal replica of the tranmitted ignal are received at the receiver end. For an M*N MIMO wirele network, the received ignal can be expreed a: L ( t) = H l ( ϕ l ). U( t τ l ) + N ( t) (1) l= 1 U.S. Government work not protected by U.S. Copyright

2 where L i the number of multipath that exit in the channel, (t) = [r 1 (t), r 2 (t),, r N (t)] T i the vector of received ignal at each N element of the receiver, U(t) = [u 1 (t), u 2 (t),, u M (t)] T i the vector of tranmitted ignal from each M element of the tranmitter, N(t) i a vector of N independent complex Gauian random variable modeling the noie in the ytem, ϕl and τ l are the angle of arrival (AoA) and the delay of arrival (DoA) of the l th multipath repectively and finally H l i an M N matrix providing the amplitude and the phae of the M N complex ub-channel between Tx and x for the l th multipath. Impinging ignal to the receiver antenna element, (t), due to patial imilarity and temporal dependency follow patial and temporal correlation pattern. Temporal correlation i captured uing cluter-oriented modeling of the channel and i defined by a double exponential decaying pattern for L multipath in the channel [4]. Thi concept i illutrated in Fig. (2). A complete impule repone of temporal correlative channel with L=18 and it aociated pectrum for an n channel model i illutrated in Fig. (3). Spatial correlation, on the other hand, meaure the reemblance of any two component of the received ignal at the receiver antenna element and i a function of the power azimuthal pectrum (PAS) of both antenna end of the ytem. Power azimuthal pectrum i imply the ditribution of the tranmitted or the received power veru azimuthal angle; for a ytem with line of ight (LoS) component, PAS ha a peak at the LoS direction. A typical urban channel or an indoor channel ha a Laplacian power azimuth ditribution with tandard deviation σ. A more confined PAS, i.e. maller σ, implie higher correlation amongt ignal component at the receiver antenna element [2]. To accommodate the randomne of the channel a well a it correlation pattern, the channel matrix H l could be further expanded a follow [3]: K l 1 H l = P l Hl, LoS + H (2) l, NLoS Kl + 1 Kl + 1 in which P l i the power, K l i the rice K-factor and H l,los and H l,nlos are the channel matrice for LoS and non-los, repectively, all for the l th tap. H l,los for ytem with LoS, repreent the matrix of the magnitude and the phae of the correpondent component for each ub-channel. H l,nlos nonethele, tand for the random behavior of the channel and i to be updated every coherence time in compliance with Channel Impule epone Time x 10 Channel Spectrum Normalized Frequency (a) (b) Figure 3: a ample channel impule repone and it pectrum the channel fading profile. Equation (2) alo carrie the correlation pattern exiting in the ytem a follow: temporal correlation cale the LoS matrice with a erie of L correlated complex coefficient obeying it aociated pattern for each ub-channel. Spatial correlation however applie to each H l,nlos uing the Kronecker product of correlation matrice of both receive and tranmit end derived from their relative PAS and an i.i.d. complex Gauian random variable repreenting the channel [3]. In the other word H l,nlos can be decompoed a: H {[ ] [ ]} 1 2 [ H ] = (3) l, NLoS tx rx. i. i. d. where tx and rx are correlation matrice of tranmit and receive antenna repectively and i the Kronecker product. The emulation proce involve computing the channel for each coherence time according to equation (2) and performing a real-time convolution with the incoming data. III. EMULATION POCESS Channel emulation can not be performed on general purpoe proceor due to their limited and relatively low throughput in real-time application. To increae the peed, i.e. the ytem throughput, and decreae the complexity the entire ytem the emulation proce i partitioned into two complementary tage. The real-time proceing i performed on high peed hardware while the channel coefficient are generated uing a non real-time application on a eparate PC or a tand alone proceor a outlined in Fig. (4). Arrival Time X v TX Figure 2: cluter-oriented modeling and it correlation with the eceived ignal t Figure 4: PC and hard-ware collaboration in channel emulation

3 Channel coefficient are computed on the PC baed on the channel profile provided by the uer. The coefficient matrice (H l ) are then downloaded and tored in the hardware and the emulation on real time data tart accordingly. The emulation proce i performed at baeband, which neceitate a down/up F converion architecture a illutrated in Fig. (5). The received analog ignal at radio frequency (F) i firt proceed by an input F interface that down convert the ignal to a digital bae-band (DBB) ignal. The emulator core then applie the channel artifact to the DBB ignal baed on channel coefficient that are received from the PC. Finally, an output F interface perform the revere converion proce and return the ignal back to the analog F domain. A new et of channel coefficient ha to be downloaded to the emulation core every coherence time and interpolation/decimation factor are downloaded onto F interface according to the channel profile determined by the uer. The extenion of thi baic idea to a 2x2 MIMO ytem with a ingle ended interfering ource i illutrated in Fig. (6). where the oftware running on the PC ha to generate the coefficient et baed on the correlation pattern among the ub-channel. The real-time hardware conit of everal parallel emulation filter. Sub-channel output have to be ynchronou with high accuracy to avoid timing jitter in the combiner that create the final compoite ignal. IV. IMPLEMENTATION ALTENATIVES Generally peaking, there are two method to perform real-time convolution of two ignal, either in the time domain or in the frequency domain. Initially we will dicu the conventional time domain technique, followed by a full dicuion of the frequency domain approach. A. Time Domain Emulation Time domain emulation i the mot traight forward approach for convolution and ha been purued by deigner thu far to implement emulator. Multiply-accumulator (MAC) FI filter are ued to convolve channel repone with the incoming data a illutrated in Fig. (7). Figure 6: MIMO multiple acce extenion of the channel emulator A it name ugget, multiplication, toring and accumulation are the three main function in MAC FI filter that are performed by multiplier, hift regiter and adder. The configuration in Fig. (7) i an efficient implementation of uch filter with only one multiplier and one adder. The imple tructure and it component have made thi implementation a popular choice for channel emulation. However 2L-1 add/multiply operation required to generate an output ample make them an inefficient candidate for emulating channel with long impule repone that could be either a a reult of a highly diperive medium, high reolution requirement or both. At each coherence time moreover, the emulation proce in real-time i interrupted to update the channel coefficient et. Thee drawback have motivated u to earch for fater more efficient emulation algorithm. B. Frequency Domain Emulation Frequency domain preent a powerful alternative to time domain in real-time application. FFT engine followed by multiplier replace FI filter and IFFT engine return the ignal back to time domain where overlap-and-add technique inert the tail effect of each block to the ucceive block. Fig. (8) depict thi architecture. N-point Fourier tranform i performed over vector of N-ample buffered incoming DBB ignal. The reult then i multiplied with the downloaded channel pectrum from the PC and an N-point invere Fourier tranform return the ignal to time domain. The tructure illutrated in Fig. (8) deploy dual memory pace (DMS) technique at the data and the channel + Figure 5: real-time channel emulation on hard-ware Figure 7: channel emulation core uing an efficient implementation of MAC FI

4 f M Figure 8: real-time emulation in frequency domain with DMS technique input interface to eliminate the delay experienced by the ytem to fill up the input buffer and to facilitate the coefficient update procedure at each coherence time repectively. Due to the fat tructure of Fourier tranform and vector-oriented proceing (compared to the ingle-bitproceing in MAC FI filter) a coniderable gain i achievable through frequency domain emulation. C. Sampling in the Frequency Domain Frequency analyi et ome requirement for ytem deign in frequency domain. Deep fat notche reiding in the frequency repone of the channel mainly et thoe requirement. To capture all notche accurately regardle of how deep they get and how fat they drop a minimum ampling rate in frequency ha to be atified. Fig. (9.a) depict the effect of poor ampling on a notch a an example. It can be een that poor ampling doe not reflect the depth of the notch preciely and therefore it reult in erroneou reult. Depending on the deign pecification and the amount of tolerable error in the ytem, a minimum number for frequency ample i determined. For an n MIMO channel and over channel ample the average of maximum pectrum ampling error for N= 2 n veru n i depicted in Fig. (9.b). A hown for thi pecific ytem 11 N = 2 = 2048 could be choen to atify 0.5dB error tolerance. D. Adaptive Frequency Domain Emulation Further increae in efficiency can be achieved by noting that the channel change every coherence time and that the wore cae channel (deep notche) doe not occur 100% of the time. Baed on thi, a full FFT/IFFT i not alway required. Channel Spectrum A channel notch Poor ampling of the notch Normalized Frequency Sampling Offet in db Sampling Error = 0.43 db log2 of Number of FFT point (a) ampling error in (b) optimum FFT length capturing deep fat notch for 0.5% error tolerance Figure 9 A imple offline analyi on each et of channel coefficient performed on the PC will improve the performance of frequency domain by tagging each channel coefficient with the optimum FFT length identifying the required number of frequency ample, N, to meet 0.5dB error requirement. The algorithm running on the hardware perform the frequency tranformation on real-time ignal according to thi value thu adaptively meeting the required computational load. For the purpoe of our cae tudy, channel coefficient et are tagged by four different identifier, 256, 512, 1024 and 2048 to identify the required FFT/IFFT length. It i important to mention that ince longer FFT engine are the cacade of maller engine, only one 2048 engine i required [4]. Through thi adaptive implementation a ignificant improvement in the ytem throughput and add/multiply operation per output ample i achieved. E. Complexity Analyi Complexity analyi ha been performed for all three method decribed above over an n MIMO channel with 18 multipath (L=18) paced 1n apart for a 100MHz over-the-air data rate tranmiion ytem. Metric to meaure the algorithm complexity are real addition and real multiplication operation to generate an output ample. For MAC FI filter there are alway a fixed 2 (2L 1) real addition and 4 L real multiplication per output ample. eal addition and multiplication operation for frequency domain algorithm on the other hand depend on the Fourier tranform implementation methodology and i independent of 2 f N + 2 the length of the channel impule repone. ( ) N real addition and g ( N ) + 4 N 2 real multiplication are performed to generate N output ample, where N i the FFT/IFFT length and f ( N) and g ( N ) are the internal real addition and multiplication to perform N-point FFT/IFFT. Table 1 outline the ummary of implementation and operation information for four different FFT/IFFT engine [5, 6]. Finally, table 2 preent the reult of the complexity analyi averaged over channel coherence time with a Doppler frequency of 250 Hz for an n ytem. Thi applie to an indoor wirele communication channel with a moving object at the peed of m/. A conitent improvement in complexity i achieved in the algorithm baed upon frequency domain implementation. The adaptive frequency domain emulation realize a dratic improvement of up to 54% in cumulative add/multiply operation. adix-2 adix-4 Add Mul. Add Mul. Duration in clock cycle Table 1: FFT/IFFT implementation and operation information

5 Figure 10: general block diagram of the frequency domain channel emulator F. Channel emulator, from Input F to Output F Fig. (8) illutrate the entire ytem block diagram that wa ued to imulate the performance of the channel emulator from input F ignal to output F ignal. Input F ignal i firt down converted to IF and ampled by an analog to digital converter (ADC) running at f = 105MHz. 14-bit wide IF digital ample are then digitally down converted to bae-band with I/Q eparation. A direct digital yntheizer (DDS) i ued to generate the yntheized inuoid. A erie of FI decimator filter are ued to downample the ignal to the required ampling rate. The decimation tage conit of cacaded integrator comb (CIC) filter, followed by a compenation FI filter, followed by a final FI filter that i ued to adjut for the fine remaining down ampling factor. f The rate of the decimated digital ignal i f = where i the cumulative down ampling factor of the three mentioned decimator filter. The channel reolution in time T = 1 (minimum time f pacing between two ucceive multipath) i alway much higher than the rate of the data in bae-band, f >> f. Therefore, rate matching need to be done prior to Fourier tranformation in the emulation core. ate matching could be performed by interpolating the incoming ignal up to the channel reolution; however thi tep i unneceary in mot circumtance. To avoid over ampling, rate matching i performed in two tep in thi architecture. In the firt tep, the analog IF ignal i converted to digital domain with ampling rate of f that meet the Nyquit criterion. eal Addition eal Multiplication MAC FI FFT Adaptive FFT Table 2: Complexity analyi (per ample) reult for 200MHz ampling rate for an n tet cae It i then down converted to bae-band and down ampled to f. The econd tep i to match the rate of the new ignal with the channel reolution. Thi i imply done by adding f ufficient zero ( 1 f zero) between any two data ample. Following the rate-matching, pectrum multiplication and an IFFT apply the channel artifact to the ignal in the digital bae-band domain. The ignal i then up converted back to F through a digital up converter followed by an analog up converion to the carrier frequency. V. CONCLUSION Frequency domain algorithm for wirele channel emulation are preented in thi paper a an efficient alternative for conventional time domain algorithm. Complexity analyi illutrate a ignificant 54% improvement in the add/multiply operation required to generate an output ample. VI. EFEENCES [1] J.J. Olmo et al., Deign and Implementation of a Wide- Band eal-time Channel Emulator in IEEE Tran. on Vehicular Technology, vol. 48, no. 3, May [2] L. Schumacher et al., From Antenna Spacing To Theoretical Capacitie Guideline for Simulating MIMO Sytem IEEE International Sympoium on Peronal, Indoor and Mobile adio Communication, vol. 2, pp Sept [3] IEEE TGn Channel Model, IEEE /940r4. [4] A.A. Saleh and.a. Valenzuela, A Statitical Model for Indoor Multipath Propagation IEEE Journal on Selected Area in Comm., vol SAC-5, no. 2, Feb [5] [6] D. Takahahi, An Extended Split-adix FFT Algorithm IEEE Signal Proceing Letter, vol. 8, no. 5, May 2001.