An Ordered Successive Interference Cancellation Scheme in UWB

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An Ordered Successive Interference Cancellation Scheme in UWB MIMO Systems Jinyoung An and Sangchoon Kim ABSTRACT⎯In this letter, an ordered successive…
An Ordered Successive Interference Cancellation Scheme in UWB MIMO Systems Jinyoung An and Sangchoon Kim ABSTRACT⎯In this letter, an ordered successive Performance of the ZF detector is known to be similar to that interference cancellation (OSIC) scheme is applied for of the MMSE receiver at high signal-to-noise ratios (SNRs). multiple-input multiple-output (MIMO) detection in ultra- This work focuses on the analysis of a ZF related scheme. In wideband (UWB) communication systems. The error rate this letter, we present the error performance of a ZF scheme expression of an OSIC receiver on a log-normal multipath fading channel is theoretically derived in a closed form with an ordered successive interference cancellation (OSIC) for solution. Its bit error rate performance is analytically UWB SM MIMO detection in a log-normal fading channel. compared with that of a zero forcing receiver in the UWB We analytically investigate the theoretic bit error rate (BER) MIMO detection scheme followed by RAKE combining. performance of the ZF-OSIC architecture followed by RAKE combining, called a ZF-OSIC-RAKE, in an UWB SM MIMO Keywords⎯Ultra-wideband (UWB), MIMO, zero forcing receiver. The diversity order that the ZF-OSIC-RAKE offers (ZF), ordered successive interference cancellation (OSIC). for detecting the n-th transmitted data stream is obtained for UWB MIMO systems. It is also seen that the ZF-OSIC-RAKE I. Introduction scheme outperforms the ZF-RAKE. Ultra-wideband (UWB) radio transmission technology has attracted enormous interests for applications requiring high II. System Model data rates over short ranges. To increase the transmission data rate through spatial multiplexing (SM) and extend system RF A multiple antenna UWB communication system with NT coverage, multiple-input multiple-output (MIMO) techniques transmit and NR receive antennas ( N R ≥ N T ) is considered. can be employed in UWB systems for certain applications Independent NT data streams modulated with the pulse- such as high-definition video transmission [1]. In [1], the error amplitude of a short-duration UWB pulse are sent on different performance of UWB MIMO systems over indoor wireless transmit antennas. To avoid severe intersymbol interference, multipath channels was analyzed. A zero forcing (ZF) receiver we assume that the pulse repetition interval is sufficiently large is applied to separate the spatially multiplexed data on a path- compared with the channel delay spread. We also assume that by-path basis. The zero-forced resolvable paths are then the signals put through the multipath channel, and only L combined by a RAKE. This detection structure is called a ZF- resolvable paths for the symbol-by-symbol detection are RAKE. Also, the minimum mean square error (MMSE) exploited by the receiver at each receive antenna. The received detector for MIMO systems on flat Rayleigh channels was signal of the l-th propagation path at the m-th receive antenna considered in [2] and [3]. denoted by xm(l), l = 0,1, , L − 1 , can be obtained by passing Manuscript received April 5, 2009; revised April 29, 2009; accepted May 11, 2009. through a UWB pulse matched filter. The discrete-time T This work was supported by Korea Research Foundation Grant funded by the Korean received signal vector, x(l ) = ⎡⎣ x1 (l ) x2 (l ) xN R (l ) ⎤⎦ , at Government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-331-D00382). Jinyoung An (phone: +82 51 200 5589, email: and Sangchoon Kim the matched filter output for the l-th path can be written as (phone: +82 51 200 7795, email: are with the Department of Electronics Engineering, Dong-A University, Busan, Rep. of Korea. x(l ) = Es H (l ) a + w (l ), (1) doi:10.4218/etrij.09.0209.0140 472 Jinyoung An et al. © 2009 ETRI Journal, Volume 31, Number 4, August 2009 where Es is the average symbol energy. Here, the information for i = 1, 2, , N T symbol vector over NT transmit antennas is denoted by FZF,i (l ) = H i (l ) + 2 ki (l ) = arg min fi( j ) (l ) a = [a1 a2 aNT ] T , where an is an information symbol from the j n-th transmit antenna. The received noise vector is represented yki (l ) (l ) = fi ( ki ( l )) (l ) xi (l ) T xi+1 (l ) = xi (l ) − h ki (l ) (l ) ⋅ Quan ⎡⎣ yki (l ) (l ) ⎤⎦ by w (l ) = ⎡⎣ w1 (l ) w2 (l ) wN R (l ) ⎤⎦ , where wm(l) is a real H i+1 (l ) = H iki ( l ) (l ) end zero-mean white Gaussian noise of variance N0/2. For the l-th ⎛ T ⎞ delayed path, an NR×NT discrete-time channel matrix H(l) can Permutate the elements of y (l ) ⎜ = ⎡ yk1 (l ) (l ) yk2 (l ) (l ) ykN (l ) (l ) ⎤ ⎟ ⎝ ⎣ R ⎦ ⎠ be expressed as H (l ) = ⎡⎣h1 (l ) h 2 (l ) h NT (l ) ⎤⎦ where the column according to the original sequence ( 1, 2, , N T ) . T Fig. 1. ZF-OSIC algorithm for each path in ZF-OSIC-RAKE. vector hn(l) is given as h n (l ) = ⎡⎣ h1n (l ) h2 n (l ) hN R n (l ) ⎤⎦ . Here, hmn(l), m =1, 2, , N R , n = 1, 2, , N T , is the channel coefficient of the l-th path for the signal from the n-th transmit antenna to ( Hi (l ), FZF,i (l ), xi (l ) ) denotes the specific variables in the i-th detection step. Initial values are set to be H1 (l ) = H (l ), the m-th receive antenna. It is given by hmn (l ) = ζ mn (l ) g mn (l ) FZF,1 (l ) = FZF (l ), x1 (l ) = x(l ); fi( j ) (l ) and Quan [ i ] indicate [4], where ζ mn (l ) ∈ { ± 1 } with equal probability is a discrete random variable (RV) representing pulse-phase inversion, and the row j of FZF,i (l )(= H i (l ) + ) and quantization operation, gmn(l) is the fading magnitude term with a log-normal respectively; and H i +1 (l ) = H iki (l ) (l ) depicts the nulling of distribution. column ki(l) of the channel matrix Hi(l). To obtain the single zero-forced signal of the l-th path signal in OSIC step i, the row of FZF, i(l) with the minimal norm is III. Ordered Successive Interference Cancellation chosen. After getting the zero-forced signal vector associated with each multipath component, we reorder the elements of the In the ZF-RAKE examined in [1], ZF detection is zero-forced vector according to the original sequence of the performed by the filter matrix F ZF(l)=H(l)+, where transmitted data streams. Then, RAKE combining of the zero- ( ⋅) denotes the pseudoinverse. The output signal vector, forced signals is accomplished to detect each data stream and + T y (l ) = ⎡⎣ y1 (l ) y2 (l ) y NR (l ) ⎤⎦ , for the l-th path of a leads to obtaining a DV for each transmitted data stream. The particular bit is given by y(l)=FZF(l)x(l). The decision variable DV of the RAKE combiner output for a particular bit of the (DV) of the MRC output for a particular bit of the n-th n-th transmitted data stream can be written as (2). transmitted data stream can be written as The instantaneous SNR γ n of the DV of the RAKE combiner output for a particular bit of the n-th data stream is zn = ∑ l = 0 α n2 (l ) yn (l ), L −1 (2) given by γ n = 2λ ∑ l = 0 α n2 (l ) with λ = Es N 0 . By L −1 −1 where α n2 (l ) = 1 υn (l ) and υn (l ) = ⎡⎣ H(l ) H H(l ) ⎤⎦ . Here, following an analysis similar to that in [1], we obtain the nn (⋅) is the conjugate transpose. The diversity order of an quadratic form, α n2 (l ) = h n (l ) H S n (l ) h n (l ) , where Sn(l) is a H (NR, NT, L) MIMO system based on the ZF-RAKE scheme is NR×NR non-negative Hermitian matrix constructed from given by the parameter DZF=L(NR–NT+1). h n +1 (l ), h n + 2 (l ), , h NT (l ) . Then, γ n can be expressed as In a ZF-RAKE, a bank of separate filters has been γ = 2λ ∑ L NR λ ( n ) q ( n ) 2 = 2λ γ ′ , where q ( n ) and λ ( n ) , n i =1 i i n i i considered to estimate the NT data substreams. However, the respectively, are the zero-mean unit-variance Gaussian RV and output of one of the filters can be exploited to help the eigenvalue of the matrix S = diag S (0) S (1) S ( L −1) . n [ n n n ] operation of the others. In the OSIC technique [5], the signal Thus, the eigenvalues of Sn(l) with N R − N T + n are equal with the highest post-detection SNR is first chosen for to 1, and the others with NT–n eigenvalues are 0. Hence, the processing and then cancelled from the overall received signal matrix Sn has LNR eigenvalues, among which the L(NR–NT+n) vector. This reduces the burden of inter-channel interference on the receivers of the remaining data substreams. To apply OSIC eigenvalues are equal to 1, and the other L(NT–n) eigenvalues to the ZF-RAKE architecture for multipath channels, the OSIC are equal to 0; therefore, γ n′ = ∑ L ( N R − NT + n ) qi( n ) . The 2 i =0 procedure for each path is performed prior to RAKE variable γ n′ is a central chi-square distributed RV with combining. The zero-forced signal is first obtained in the detection step of each propagation path signal. Then, the zero- DZF-OSIC = L ( N R − N T + n) degrees of freedom, which has a (n) forced signals are combined to detect each substream. This probability density function (PDF) of detection scheme is called a ZF-OSIC-RAKE. The OSIC algorithm for the l-th path signal is shown in Fig. 1. Here, ( fγ n′ (t ) = 0.5κ Γ(κ ) t κ −1e− t 2 , (3) ) ETRI Journal, Volume 31, Number 4, August 2009 Jinyoung An et al. 473 where κ = 0.5 D (ZF-OSIC n) , and Γ(⋅) is the gamma function ZF (4, 3, 2) ZF-OSIC (4, 3, 4) ZF (4, 4, 4) ZF-OSIC (5, 4, 4) ∞ ZF-OSIC (4, 3, 2) ZF (4, 3, 8) ZF-OSIC (4, 4, 4) ZF (6, 4, 4) defined as Γ(b) = ∫ τ b −1 −τ e dτ , b 0 . Thus, by averaging ZF (4, 3, 4) ZF-OSIC (4, 3, 8) ZF (5, 4, 4) ZF-OSIC (6, 4, 4) 0 ( ) 100 100 the conditional BER P (t ) = Q r ( n) 2λ t over the PDF -1 10 10-1 fγ n′ (t ) , the average BER for a particular bit of the n-th 10 -2 10-2 BER BER transmitted data stream over log-normal fading channels can be 10-3 10-3 calculated as 10-4 10-4 ∞ Pb(,ZF-OSIC n) = ∫ Pr( n ) (t ) fγ n′ (t ) dt . (4) 0 0 2 4 6 8 10 12 0 2 4 6 8 10 12 SNR per bit (dB) SNR per bit (dB) To derive the average BER in a closed form, a tightly (a) (b) approximated expression of Q-function such as Q( β ) Fig. 2. BER vs. SNR for different values of (a) L and (b) NR. 2 2 (1 12)e − β 2 + (1 6)e − 2 β 3 [2] is employed. Then, the conditional BER, given λ = Es N 0 , can be approximated as power gain due to the increase of diversity order in each r (n) P (t ) (1 12 ) e −λt + (1 6 ) e − 4λ t 3 . (5) increasing cancellation step. Also, multipath combining yields enhanced performance in both ZF-OSIC-RAKE and ZF- By using (3) and (5) in (4), the average BER for the ZF-OSIC- RAKE. In an (NR, 4, 4) case, Fig. 2(b) shows the analytical and RAKE expressed in a closed form can be obtained as simulated results of BER as a function of SNR per bit for (κ − 1)! (κ − 1)! various NR. The increase in NR increases the diversity order of Pb(,ZF-OSIC n) + . (6) the ZF-OSIC-RAKE receiver as well as that of the ZF-RAKE. 12 ( 2λ + 1) Γ (κ ) 6 ( (8 / 3)λ + 1) Γ (κ ) κ κ Here, (⋅)! is the factorial defined as s ! = s ⋅ ( s − 1) 2 ⋅1 . V. Conclusion The average BER over all NT data streams can be given by BERZF-OSIC = (1 N T ) ∑ n =T1 Pb(,ZF-OSIC Nn) . Note that to obtain the The error performance of a UWB MIMO system over indoor log-normal fading channels has been analyzed. The UWB theoretical performance of the ZF-RAKE, the same formula as MIMO receiver employs ZF-OSIC detectors and then a RAKE that of ZF-OSIC-RAKE can be used except κ = 0.5 DZF . temporal combiner. It has been shown that the ZF-OSIC for detecting the n-th transmitted data stream in an (NR, NT, L) IV. Simulation Results MIMO system achieves a diversity order of L(NR–NT+n). The ZF-OSIC offers better performance than the ZF receiver. Consider the binary PAM scheme (Es=Eb). In the simulations, the SNR per bit in decibels is defined as ηb = 2λ (dB) + 10 log10 L ( N R − N T + 1) for (NR, NT, L) systems. References The log-normal fading amplitude g(l) can be expressed as [1] H. Liu, R.C. Qiu, and Z. Tian, “Error Performance of Pulse-Based g (l ) = eψ (l ) , where ψ (l ) is a Gaussian RV with mean μψ (l ) Ultra-Wideband MIMO Systems over Indoor Wireless and variance σψ2 . We assume that the standard deviation of Channels,” IEEE Trans. Wireless Commun., vol. 4, no. 6, Nov. 20 log10 g (l ) = ψ (l ) ( 20 log10 e ) is 5 dB. To satisfy 2005, pp. 2939-2944. E[ g (l ) 2 ] = e− ρ l representing the average power of path l, [2] N. Kim, Y. Lee, and H. Park, “Performance Analysis of MIMO μψ (l ) = −σψ2 − ρ l 2 is required, where σψ is obtained as System with Linear MMSE Receiver,” IEEE Trans. Wireless σψ = 5 ( 20 log10 e ) . Here, the power decay factor ρ = 0 is Commun., vol. 7, no. 11, Nov. 2008, pp. 4474-4478. used. The receiver is assumed to have perfect knowledge of the [3] A. Zanella, M. Chiani, and M.Z. Win, “MMSE Reception and channel fading coefficients of L resolvable paths. In the figures, Successive Interference Cancellation for MIMO Systems with theoretic and simulated BER curves of the UWB MIMO High Spectral Efficiency,” IEEE Trans. Wireless Commun., vol. 4, system are shown with lines and markers, respectively. no. 3, May 2005, pp. 1244-1253 For a (4, 3, L) MIMO system, Fig. 2(a) shows the analytical [4] A.F. Molish, J.R. Foerster, and M. Pendergrass, “Channel Models and simulated BERs of the ZF-RAKE and ZF-OSIC-RAKE for Ultra-Wideband Personal Area Network,” IEEE Wireless as a function of SNR per bit in decibels. The analytical results Commun., vol. 10, no. 6, Dec. 2003, pp. 14-21. are similar to the simulated BER performance and demonstrate [5] P.W. Wolniansky et al., “V-BLAST: An Architecture for the performance boost in using the ZF-OSIC-RAKE over the Realizing Very High Data Rates Over the Rich-Scattering ZF-RAKE. This boost in BER performance comes from a Wireless Channel,” Proc. IEEE ISSSE, Sept. 1998, pp. 295-300. 474 Jinyoung An et al. ETRI Journal, Volume 31, Number 4, August 2009
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