PAPER An Iterative MIMO Receiver Employing Virtual Channels with a Turbo Decoder for OFDM Wireless Systems

878 IEICE TRANS. COMMUN., VOL.E98 B, NO.5 MAY 015 PAPER An Iterative MIMO Receiver Empoying Virtua Channes with a Turbo Decoder for OFDM Wireess Systems Akihito TAYA, Member, Satoshi DENNO a), Koji YAMAMOTO, Senior Members, Masahiro MORIKURA, Feow, Daisuke UMEHARA, Hidekazu MURATA, Senior Members, and Susumu YOSHIDA, Feow SUMMARY This paper proposes a nove iterative mutipe-input mutipe-output MIMO) receiver for orthogona frequency division mutipexing OFDM) systems, named as an iterative MIMO receiver empoying virtua channes with a Turbo decoder. The proposed MIMO receiver comprises a MIMO detector with virtua channe detection and a Turbo decoder, between which signas are exchanged iterativey. This paper proposes a semi hard input soft output SHISO) iterative decoding for the iterative MIMO receiver that achieves better performance than a soft input soft output SISO) iterative decoding. Moreover, this paper proposes a new criterion for the MIMO detector to seect the most ikey virtua channe. The performance of the proposed receiver is verified in a 6 MIMO-OFDM system by computer simuation. The proposed receiver achieves better performance than the SISO MAP iterative receiver by 1.5 db at the bit error rate BER) of 10 4, by optimizing the number of the Turbo iteration per the SHISO iteration. Moreover, the proposed detection criterion enabes the proposed receiver to achieve a gain of 3.0dBattheBERof10 5,compared with the SISO MAP iterative receiver with the Turbo decoder. key words: mutipe-input mutipe-output, virtua channe, soft-input softoutput, og ikeihood ratio, iterative scheme 1. Introduction Since a ot of onine appications are avaiabe even on mobie or wireess devices, high-speed wireess access networks are demanded for the appications. As a resut, broad band wireess communication systems such as the ong term evoution LTE) and the IEEE 80.11ac have been deveoped where orthogona frequency division mutipexing OFDM) [1] is appied to combat with severe mutipath fading, and mutipe-input mutipe-output MIMO) [], [3] is empoyed to increase the transmission speed. In principe, transmission speed can be increased in MIMO systems by increasing spatiay mutipexed streams. The MIMO spatia mutipexing has been intensivey investigated for downinks of wireess communications where signas are transmitted from base stations or access points to terminas, because higher speed data transmission is required in downinks than in upinks. As a resut, many receiver configurations have been proposed, e.g., minimum mean square error MMSE) fiters, ordered successive de- Manuscript received August, 014. Manuscript revised November 18, 014. The authors are with the Graduate Schoo of Informatics, Kyoto University, Kyoto-shi, 606-8501 Japan. The author is with the Graduate Schoo of Natura Science and Technoogy, Okayama University, Okayama-shi, 700-8530 Japan. The author is with the Graduate Schoo of Science and Technoogy, Kyoto Institute of Technoogy, Kyoto-shi, 606-8585 Japan. a) E-mai: denno@cne.okayama-u.ac.jp DOI: 10.1587/transcom.E98.B.878 tectors OSDs), eigenbeam-space division mutipexing E- SDM), and the maximum ikeihood detection MLD) with QR decomposition and M-agorithm QRM-MLD) [4]. Basicay, if these inear MIMO detectors are appied in MIMO systems, the maximum number of the spatiay mutipexed streams is equa to the number of degrees of freedom that is minn T, N R )wheren T and N R denote the number of transmit antennas and that of receive antennas, and min) is a function of outputting the smaest vaue in the input vaues. When these schemes are used in downinks, the transmission speed is imited by the number of receive antennas, because terminas do not have enough room to insta many antennas whie base stations or access points do. In other words, base station antennas are not fuy expoited to increase the transmission speed for a user. In order to increase the transmission speed for a user, some receivers have been proposed that can be appied in MIMO systems where the number of the spatiay mutipexed streams is more than that of receive antennas [5], [6]. These receivers assume that the number of the streams is by about one more than that of the receive antennas. Those receivers are cassified into inear detectors. In contrast with inear detectors, non-inear detectors achieve superior performance in MIMO systems where the number of spatiay mutipexed streams is more than that of the receive antennas. For instance, the detector with virtua channes achieves superior performance with reasonabe compexity even when the number of the streams is twice as many as that of the receive antennas [7] [9]. Moreover, the SISO iterative receiver composed of the MIMO detector with virtua channes and the convoutiona decoder has been proposed for further performance improvement [9]. On the other hand, Turbo codes [10] have been considered to combine with MIMO detectors [11] [14], because Turbo codes are powerfu to improve transmission performance. However, even if Turbo decoders are appied to the SISO iterative receiver with the MIMO detector with the virtua channe detection, the performance is not improved, which is shown in this paper. This paper proposes a nove iterative receiver, caed as a semi hard input soft output SHISO) iterative receiver, that fuy expoits the potentia gain of Turbo decoders to achieve superior performance even when the number of the streams is more than twice as many as that of the receive antennas. The SHISO iterative receiver outperforms a SISO iterative receiver, which is shown in the foowing section. Copyright c 015 The Institute of Eectronics, Information and Communication Engineers

TAYA et a.: AN ITERATIVE MIMO RECEIVER EMPLOYING VIRTUAL CHANNELS WITH A TURBO DECODER FOR OFDM WIRELESS SYSTEMS 879 moduation signa vector, and the number of the subcarriers. The output signa vector is emitted from the transmit antennas, and is traveing mutipath fading channes. Then, the vector is received at the receive antennas, which is expressed as foows. T 1 y n = h t d n t + n n, ) t=0 Fig. 1 System mode. Basicay, the proposed receiver comprises a MIMO detector with virtua channe detection and the Turbo decoder, between which signas are exchanged iterativey. The ordered successive detector OSD) is used to detect the signa in each virtua channe of the MIMO detector. In the proposed receiver, the extrinsic information is fed back from the Turbo decoder to the MIMO detector, and the MIMO detector estimates the phase on the maximum a posteriori probabiity MAP) estimation with the extrinsic information. However, the hard decision signa of the phase is provided to the Turbo decoder, whist the ordered successive detector output signas are fed to the decoder. This SHISO iteration has not been proposed before and is a key idea to improve the performance. Moreover, we propose a new criterion, Extended MAP estimation, for the proposed receiver to seect the most ikey virtua channe for furthermore improving the transmission performance with itte additiona compexity. The rest of this paper is structured as foows. Section introduces a mode of the MIMO system. Section 3 describes a configuration of our proposed receivers with virtua channes, and Sect. 4 shows the performance of the proposed receivers, obtained by computer simuations. Finay, Sect. 5 presents concuding remarks.. System Mode We consider a downink with N T antennas at a transmitter and N R antennas at a receiver. At the transmitter, data bits are encoded using a Turbo code, intereaved, and moduated into Quaternary phase-shift keying QPSK) signas. The QPSK signas are then moduated on the orthogona subcarriers in the system with the OFDM. Let n denote a time index, the output signa vector d n C NT 1 is written as, d n = 1 N 1 N where k, ˆD k k=0 nk jπ ˆD k e N, 1) C N T 1 and N denote a subcarrier index, a The OSD is one of seria interference canceers, which is appied in the proposed iterative receiver. On the other hand, interference is canceed by using repicas of the interference signas that are generated from aprioriinformation fed back from the decoder in Turbo equaizers, which are we known as iterative receivers. Hence, the proposed receiver is competey different from Turbo equaizers [15] [17]. where y n C N R 1, h t C N R N T, n n C N R denote a received signa vector, a channe matrix of tth path, the additive white Gaussian noise AWGN) vector. In addition, T represents the maximum deay of the channe that is assumed not to exceed the cycic prefix ength. The receiver converts the received signa vector in the time domain into the frequency domain with the fast Fourier transform FFT). The frequency domain signa vector in the kth subcarrier, Ŷ k C N R 1, is expressed as Ŷ k = 1 N 1 nk jπ y n e N N n=0 =Ĥ k ˆD k + ˆN k, 3) where Ĥ k = T 1 t=0 h kt jπ N te C N R N T and ˆN k = 1 N 1 N n=0 n ne jπ nk N C NR 1 represent a channe matrix and the AWGN at the kth subcarrier. In principe, compex signa vectors and channe matrices can be transformed into rea vectors and matrices, respectivey [7] [9]. Let Y k R N R, D k R N T, N k R N R,andH k R N R N T represent the received signa vector, the data signa vector, the AWGN vector, and the channe matrix expressed in rea vaues, respectivey. 3) can be rewritten as Y k = H k D k + N k. 4) Because the same signa processing is performed in every subcarrier, the subcarrierindexk is omitted for simpicity in the rest of this paper, which does not confuse readers. The th entry of D, d, is decomposed into a rea signa s and a phase θ as d = s e jθ,wheres = ± andθ = ±π/4. When the decomposition of a scaar is extended to a vector, D is rewritten as foows [7]. D = Ωϕ)Sϕ), 5) [ [ ]] diag cos θ1,, cos θ Ωϕ) = NT diag [ ], 6) sin θ 1,, sin θ NT Sϕ) = [ s 1 ϕ) s NT ϕ) ] T, 7) where diag [V] represents a diagona matrix with entries of a vector V in the diagona positions and superscript T represents transpose of a vector. We ca Ωϕ) R N T N T a rotation matrix, Sϕ) R N T a rea signa vector. We refer ϕ as a phase pattern, which is defined as θ ϕ = π/ + 1 ) 1. 8) =1

880 IEICE TRANS. COMMUN., VOL.E98 B, NO.5 MAY 015 Fig. Basic configuration of the receiver. The phase pattern ϕ ranges from 0 to N T 1. From 5), we can rewrite 4) as Y = Φϕ)Sϕ) + N, 9) Φϕ) = HΩϕ). 10) As is expressed in 9), the channe mode can be regarded that the signa vector Sϕ) is transmitted in the channe Φϕ) R N R N T, which is caed a virtua channe. Whie the size of the channe matrix H k is N R N T, that of the virtua channe Φϕ) isn R N T. In a word, the number of the coumns of the virtua channe Φϕ)ishafofthatofthe channe matrix H k, which means that the number of the spatiay mutipexed streams in the virtua channe ooks haf of that in the channe H k. If the number of the streams is reduced, the streams can be detected with higher performance by inear detectors, such as the OSD. The OSD detects the rea signa vector in a the virtua channes, Φ ϕ) ϕ = 0,, N T 1, where ϕ is a tentative phase pattern. In the OSD, basicay, the transmission signa is detected with an MMSE fiter, and the interference associated with the previousy detected signas is canceed from the received signa vector. This step is iterated by N T times in the OSD. The th-step MMSE fiter W ) ϕ) isdefinedas W ) ϕ) = Φ ) ϕ) [ Φ ) ϕ) ] T σ 1 + n I) Φ ) ϕ), 11) σ s where σ n, σ s,andirepresent the noise power, the signa power, and the unit matrix. In addition, Φ ) ϕ) denotes the virtua channe in the th step. Let Φ ) ϕ) be written as Φ ) ϕ) = [φ ) 1 ϕ),, φ) N T ϕ)], the virtua channe in the th step is defined as Φ ) ϕ) = [0 φ ) ϕ),, φ ) N T ϕ)] where we assume that the signas are detected in the order of the antenna number for simpifying the notation. The th-stream signa is detected as s det, ϕ) = [ w ϕ) ]T Y, 1) where w ϕ) represents the th coumn of W ) ϕ). The hard decision signa s det, ϕ) is defined as foowings. s det, ϕ) = sgn [ s det, ϕ) ] 13) +1 x 0) sgn[x] = 14) 1 x < 0) Using these hard decision signas, the interference canceation is carried out as Y +1) =Y ) φ ) ϕ)s det, ϕ), 15) where Y 1) is set to Y. The soft rea signa vector S det ϕ)and hard decision rea signa vector S det ϕ) are defined as S det ϕ) = [ s det,1 ϕ) s det,nt ϕ) ] T, 16) S det ϕ) = [ s det,1 ϕ) s det,nt ϕ) ] T. 17) The most ikeihood phase pattern is seected by a technique proposed in the foowing section. Figure shows a basic configuration of the receiver. The rea signas are detected by the OSD with the MMSE fiter in each virtua channe, and the detected signas are provided to the virtua channe detector in the MIMO detector. The detector seects the most ikey virtua channe based on the proposed technique described in the foowing section, and outputs the information associated with the signas to the Turbo decoder via the intereaver. The Turbo decoder estimates the og ikeihood ratio LLR) with the signa from the intereaver, and feeds back ony the extrinsic information of the LLR to the MIMO detector. 3. Proposed SHISO Iterative Receiver 3.1 MIMO Detector with Virtua Channes 3.1.1 LLR of Rea Signas The LLR of the rea signa λ s) ϕ) in the virtua channe Φ ϕ) can be defined as λ s) ϕ) = og P s ϕ) =+ Y ) P s ϕ) = ), 18) Y where P s ϕ) = ± Y ) represents an a posteriori probabiity of the rea signa in the th-stream, s ϕ), when Y is received. The numerator of 18) can be approximatey cacuated with the Max-Log-MAP approximation as, og P s ϕ) =+ Y ) og P s ϕ) =+ ) og P Y)

TAYA et a.: AN ITERATIVE MIMO RECEIVER EMPLOYING VIRTUAL CHANNELS WITH A TURBO DECODER FOR OFDM WIRELESS SYSTEMS 881 + max s ϕ)=+ og P s m ϕ)) 1 Y Φ ϕ)s ϕ) σ, m n 19) where PS ϕ)) represents an aprioriprobabiity of S ϕ). In addition, max [a m] denotes the maximum vaue among constraint a m m = 0, under the indicated constraint. Because the exact cacuation of 19) needs ots of compex cacuations, the LLR of the rea signa λ s) ϕ) is cacuated more simpy using the foowing hypothesis [9]. Y Φ ϕ)s ϕ) sdet, ϕ) s ϕ) ) 0) w ϕ) When the term in the eft hand side of 0) is substituted for 19), the maximization with respect to s m ϕ) can be performed independenty. In a word, s m ϕ) can be seected that satisfies s m ϕ) = max [ og P s m ϕ)) s det,m ϕ) s m ϕ) ) ]. Therefore, the terms s m ϕ) m = 1,, N T except m = become common between the numerator and the denominator in 18). Hence, the LLR of the rea signas λ s) ϕ) can be approximatey obtained as λ s) ϕ) Λ s) a, ϕ) 1 { s σ n w ϕ) det, ϕ) s det, ϕ) + } =Λ s) a, ϕ) + s det, ϕ) σ n w ϕ). 1) where Λ s) a, ϕ)representsaprioriinformation of the rea signa s ϕ), which is defined as P s ϕ) =+ ) Λ s) a, ϕ) = og P s ϕ) = ). ) This aprioriinformation is provided by the Turbo decoder foowing the detector. By making a hard decision of λ s) ϕ), rea signa vector S ϕ) can be obtained in a the virtua channes. S ϕ) = [ s 1 ϕ) s NT ϕ) ], 3) s ϕ) = sgn [ λ s) ϕ) ]. 4) The transmitted virtua channe is estimated with the estimated rea signas by a technique proposed in the foowing section. 3.1. LLR of Phase Pattern The proposed detector cacuates the LLR of the phase pattern Λ ϕ ϕ : ϕ ), in order to seect the optimum phase pattern that maximizes an a posteriori probabiity. Here, ϕ is a phase pattern that differs from ϕ. The LLR of the phase patterns is defined as Λ ϕ ϕ : ϕ ) = og P ϕ Y) P Y ϕ) P ϕ) P ϕ = og Y) P Y ϕ ) P ϕ ), 5) where P ϕ Y), PY ϕ), andp ϕ) represent an a posteriori probabiity of the phase pattern, a conditiona probabiity when a signa vector with a phase pattern ϕ is transmitted, an aprioriprobabiity of the virtua channe with the phase pattern ϕ. P ϕ) can be expressed as N T P ϕ) = P θ ), 6) =1 where P θ ) represents aprioriprobabiity of the phase θ of the transmission signa from the th antenna. Using 6), 5) can be rewritten as Λ ϕ ϕ : ϕ ) = og Pθ ) Pθ ) + og P Y ϕ) og P Y ϕ ) =1 = Λ θ θ : θ ) 1 =1 σ n Y Φ ϕ) S ϕ) + 1 Y Φ ϕ ) S ϕ ), 7) σ n where aprioriinformation Λ θ θ : θ )isdefinedas ) θ =+ π 4,θ = π 4 +Λ θ) a, Λ θ θ : θ ) = ) Λ θ) a, θ = π 4,θ =+ π 4, 8) 0 θ = θ ) Λ θ) a, = og P ) θ =+ π 4 P ), 9) θ = π 4 where Λ θ) a, represents aprioriinformation of the th phase θ that is fed back from the decoder. The aprioriinformation Λ θ) a, is defined in the next section. The optimum phase pattern ϕ est that satisfies the foowing equation is seected as foows. Λ ϕ ϕ est : ϕ ) 0 for ϕ ϕ est. 30) For the seected phase pattern ϕ est, the estimated data signa vector D det ϕ est ) can be cacuated according to the definition of D in 5). D det ϕ est ) = Ω ϕ est )S det ϕ est ). 31) The estimated data vector D det ϕ est ) is output to the Turbo decoder through the deintereaver. In other words, the proposed receiver provides the Turbo decoder with those output signas via the intereaver. This means that the detector does not output extrinsic information, which is a big difference from Turbo equaizers: a representative of iterative receivers. Though the definition of the phase is regarded as an appication of the principe of the bit LLR, the definition is not equa to that of the bit LLR. This generates the performance shown in Sec.4

88 IEICE TRANS. COMMUN., VOL.E98 B, NO.5 MAY 015 3.1.3 aprioriinformation Fed Back to the MIMO Detector for Iterative Decoding The Turbo decoder cacuates the bit LLR L d) d,v in the same way as usua Turbo decoders. The bit LLR is defined as L d) d,v = og Pc d,v = 1 Y) Pc d,v = 0 Y), 3) where c d,v represents the vth bit. After the N in iterations of the decoding, the Turbo decoder feeds back the extrinsic bit LLR L ex,v to the MIMO detector as aprioriinformation L a,u via the intereaver. L a,u = π [ L ex,v ], 33) where π[ ] represents a function of the intereaver. Whereas the extrinsic bit LLRs are fed back from the Turbo decoder, the MIMO detector requires the aprioriinformation of the rea signa and the phase. Therefore, we propose a scheme to convert the extrinsic bit LLRs into the aprioriinformation of the rea signas s ϕ) and the phase θ. The proposed conversion can be obtained by the foowing derivation. P s ϕ) =+ ) Λ s) a, ϕ) = og P s ϕ) = ) = og P R[d ] =+1 ) P R[d ] = 1 ) = L a,u, 34) Λ θ) a, = og P ) θ =+ π 4 P ) θ = π 4 = og P d =+1 + j ) + P d = 1 j ) P d = 1 + j ) + P d =+1 j ) P R[d ] =+1 ) P I[d ] =+1 ) P R[d ] = 1 ) P I[d ] = 1 ) + 1 = og P I[d ] =+1 ) P I[d ] = 1 ) + P R[d ] =+1 ) P R[d ] = 1 ) = max [ L a,u + L a,u+1, 0 ] max [ ] L a,u, L a,u+1, 35) where R [a]andi [a] represent a rea part and an imaginary part of a compex number a, respectivey. Note that the u th and u + 1) th bits correspond to the rea part and the imaginary part of the th QPSK signa, respectivey. 3. Procedure of the proposed SHISO receiver The MIMO detector estimates the signa vector D det ϕ est ) based on the proposed scheme described in Sect. 3.1. The vector D det ϕ est ) is output to the Turbo decoder, which feeds back the extrinsic bit LLR to the MIMO detector. This operation is iterated N out times in the proposed receiver. Since the vector D det ϕ est ) is the product of the hard decision rotation matrix Ω ϕ est ) and the soft rea signa vector S det ϕ est ) as is defined in 31), the vector is caed as a semi-hard decision signa vector. This is the reason why the proposed receiver is named as an iterative SHISO receiver. The proposed receiver has the iterative signa processing between the MIMO detector and the Turbo decoder and the iterative processing of the Turbo decoding. To distinguish the two iteration processing. we ca the iterative exchange of the signas between the MIMO detector and the Turbo decoder as outer iteration. N out denotes the number of the outer iterations. The extrinsic bit LLR is exchanged N in times between the two component decoder in the Turbo decoder. we ca this iteration within the Turbo decoder as inner iteration. N in represents the number of the inner iterations. 3.3 Extended MAP Estimation for Virtua Channe Detection The virtua channe is detected based on the MAP in 5), assuming that the rea signas in the virtua channe Φ ϕ)are amost the same to those in Φ ϕ ). However, the assumption does not aways hod true. In this section, we propose a nove estimation criterion for the virtua channe detection where it is taken into account that the rea signas in a virtua channe might be different from those in the others. Our proposed estimation criterion appies an LLR Λ D ϕ : ϕ )of the phase pattern ϕ, which is defined as Λ D ϕ : ϕ ) = og P Y D ϕ)) P D ϕ)) P Y D ϕ) ) P D ). 36) ϕ) Because the rotation matrices Ω ϕ) and the rea signa vectors S ϕ) canbeassumedtobeindependentfromeachother, the LLR of the phase pattern, Λ D ϕ : ϕ ), can be rewritten using 5) as Λ D ϕ : ϕ ) = og P Y Ω ϕ) S ϕ) ) P Ω ϕ)) P S ϕ) ) P Y Ω ϕ )S ϕ) ) P Ω ϕ )) P S ϕ) ) Λ s s : s ) = 0 = og Pθ ) NT Pθ ) + og Ps ϕ)) Ps ϕ)) + og P Y Ω ϕ) S ϕ) ) og P Y Ω ϕ )S ϕ) ) = Λ θ θ : θ ) + Λ s s : s ) 1 σ n + 1 σ n +Λ s) a, Λ s) a, Y Φ ϕ) S ϕ) Y Φ ϕ )S ϕ), 37) s =+, s = ) s =, s =+ ), 38) s = s ) This assumption is aso appied in [7], [9]. The proposed receiver expained in Sec.3.1 attains ony sighty better performance than the receiver proposed in [9], which is described in Sec.4., even though the Turbo code is appied in the proposed receiver. We think that the appication of this assumption imits the performance gain.

TAYA et a.: AN ITERATIVE MIMO RECEIVER EMPLOYING VIRTUAL CHANNELS WITH A TURBO DECODER FOR OFDM WIRELESS SYSTEMS 883 where Λ s) a, represents aprioriinformation of the rea signa defined in 34). As is simiar to 30), the optimum phase pattern ϕ est that satisfies the foowing equation is seected: Λ D ϕ est : ϕ ) 0 for ϕ ϕ est. 39) Then, the optimum signa vector D det ϕ est ) is cacuated as D det ϕ est ) = Ω ϕ est )S det ϕ est ). 40) This optimum signa vector is output to the Turbo decoder through the deintereaver. Because not ony Λ θ θ : θ )but aso Λ s s : s ) are taken into account in the virtua channe detection, the proposed detection is expected to achieve better performance than the technique expained in Sect. 3.1.. 4. Simuation Resuts In this section, we evauate the BER performance of the proposed receiver by computer simuation. Simuation parameters are isted in Tabe 1. The channe impuse responses are independenty and identicay distributed i.i.d.) and are quasi-static. In addition, the detector is assumed to have the perfect channe state information CSI). We appy the Turbo code introduced in [10]. The Max-og MAP agorithm is appied to a the MAP estimations in this paper. 4.1 SHISO Iterative Receiver Figure 3 shows the BER performance of the proposed receiver with some combinations of the inner iterations and the outer iterations, i.e., N in and N out.however,n out N in is kept to 48 in a the combinations. In addition, the performance of the SISO iterative receiver composed of the Tabe 1 Simuation parameters. N T N R 6 Moduation scheme OFDM-QPSK Channe mode 10-path Rayeigh fading Forward error correction Turbo code, rate 1/3, K = 4 No. of sub carriers 51 Data packet ength 16384 bits MIMO detector and the Turbo decoder is added, which is abeed as LLR of each bit. In the SISO iterative receiver, a technique written in Appendix to impement a soft input soft output iteration receiver is appied. The setting of N out, N in )is6, 8) in the SISO iterative receiver. Obviousy, the performance of the SISO iterative receiver is much worse than that of the proposed receiver. The reason is discussed beow. It is shown that the BER performance with N out, N in ) = 48, 1) is better than the performance with 4, ) by about 0.9dB at BER = 10 5. The reason is aso discussed in the foowing. Figure 4 shows the cumuative distribution function CDF) of misestimated extrinsic bit LLR that is fed back from the Turbo decoder to the MIMO detector. The misestimated extrinsic bit LLR is defined as the extrinsic bit LLR whosesign isdifferent from that of the transmitted bit. Since the extrinsic bit LLR mutipied by the corresponding transmitted bit is shown in the figure, the sign of the misestimated extrinsic bit LLR is ony minus. In the figure, the pot with N out, N in ), end shows the CDF of the misestimated extrinsic bit LLR at the end of a the iterations, whie the pot with N out, N in ), begin shows the CDFs of misestimated extrinsic bit LLR at the beginning of the iterations. Because an extrinsic bit LLR is deat as reiabiity in the MAP estimation, in principe, a misestimated extrinsic bit LLR that is not reiabe, shoud be cose by zero, e.g., L ex,v = og PR[d ]=+1) PR[d ]= 1) 0 in the proposed receiver. If a misestimated extrinsic bit LLR with a big absoute vaue is provided to the MIMO detector, performance of the proposed detector is not improved enough. As is shown in Fig. 4, the distribution of the misestimated bit LLR has a bigger absoute vaue with reativey higher probabiity. Because the SISO iterative receiver circuates the misestimated extrinsic bit LLRs between the MIMO detector and the Turbo decoder. the misestimated extrinsic bit LLR with a big absoute vaue not ony deteriorates the signa detection at Fig. 4 CDF of misestimated extrinsic bit LLR. Fig. 3 BER performance of the proposed receiver. The technique to cacuate the LLR is not a standard technique, but is derived for the iterative MIMO receiver consisting of the MIMO detector with virtua channes and the decorders.

884 IEICE TRANS. COMMUN., VOL.E98 B, NO.5 MAY 015 the MIMO detector, but aso degrades the Turbo decoding. Though the performance shown in Fig. 4 is not that of the SISO receiver, the simiar performance probaby appears at the decoder output signas, because ony the extrinsic LLRs ony repace the semi-hard decision signas in the SISO receiver. The performance of the SISO receiver can be expained with the performance in Fig. 4. Anyway, the misestimated extrinsic bit LLRs degrades the SISO iterative receiver for the reason expained above. As is described above, the MIMO detector outputs the hard decision signas associated with the phase to the Turbo decoder in the proposed SHISO receiver. When the misestimated extrinsic bit LLRs are fed back to the MIMO detector, the misestimated bits are incuded in the hard decision signas with a certain probabiity due to the wrong feedback information. However, since the ampitude of the hard decision signas is rounded to 1 that is is much smaer than that from misestimated extrinsic bit LLR, the damage from the misestimated bits is imited in the proposed SHISO receiver, especiay, in the Turbo decoder. As is shown in Fig. 4, for instance, the absoute vaue of the misestimated bit LLR happens to reach to 10, which is much bigger than 1. Therefore, the proposed SHISO iterative receiver achieves better performance than the SISO iterative receiver, which is proven by Fig. 3 where the SISO iterative receiver is abeed as LLR of each bit. Generay speaking, SISO iterative receivers are we-known to achieve the best performance when the distribution of the input signa is Gaussian. However, when the misestimated extrinsic bit LLR has distribution that the big vaue appears at high probabiity, SISO iterative receivers is not aways optimum and might has worse performance than HISO iterative receivers. On the other hand, the misestimated extrinsic bit LLR with N out, N in ) = 48, 1) is smaer than that with the others at the end of the iteration. This means that no inner iteration, i.e., N in = 1, reduces the possibiity to feed back the misestimated extrinsic bit LLR with a big absoute vaue to the decoder. This is the reason why the proposed receiver with N in = 1 achieves better performance than that with N in > 1 as shown in Fig. 3. 4. Receiver with Proposed Extended MAP Estimation Figure 5 shows the BER performance when the extended MAP estimation expained in Sec.3.3 is appied. The BER performance with N out, N in ) = 48, 1) is better than that with 4, ) by about.5db at BER = 10 5. Apparenty, the proposed receiver with N in = 1 achieves the best performance in the other combinations, whie Turbo decoders usuay improve decoding performance by increasing the number of turbo iterations that corresponds to that of the inner iterations. Whereas the inner iteration does not seem to contribute to the performance improvement, the outer iteration makes the receiver achieve such a performance. The outer iteration pays an important roe to attain such a performance, even though some signa processing is incuded in the outer iteration. The reason is aso discussed beow. Fig. 5 BER performance with the extended MAP estimation. Fig. 6 CDF of misestimated extrinsic bit LLR. Figure 6 shows the CDF of the misestimated extrinsic bit LLR that is fed back from the Turbo decoder to the MIMO detector. Simiar to Fig. 4, the misestimated extrinsic bit LLR with N out, N in ) = 48, 1) is much smaer than the others at the end of the iterations. Hence, the performance shown in Fig. 6 strongy supports that the proposed receiver with N out, N in ) = 48, 1) achieves better performance than that with N in. Whie the misestimated bit LLRs at the end of the iterations are bigger than those at the begging in the Fig. 4, however, ony the LLR with N out, N in ) = 48, 1) at the end of the iterations is smaer than that at the begging in Fig. 6. The reason coud be considered as foows. Because the estimation criterion with the LLR in 5) can not cacuate the margina distribution with high precision, the iterative SHISO MIMO detector with the LLR outputs the data vector D det ϕ est ) that has error symbos associated with the misestimated extrinsic bit LLRs. When the data vector is provided to the Turbo decoder, the probabiity that the Turbo decoder enhances the absoute vaues of the misestimated extrinsic bit LLRs is increased. On the other hand, because the extended MAP estimation with the LLR in 36) estimates the margina distribution with higher accuracy, the MIMO detector based on the extended MAP estimation generates the data vector D det ϕ est )inwhichthe

TAYA et a.: AN ITERATIVE MIMO RECEIVER EMPLOYING VIRTUAL CHANNELS WITH A TURBO DECODER FOR OFDM WIRELESS SYSTEMS 885 Fig. 7 Performance comparison with Turbo coded detectors. Fig. 8 Performance comparison with conventiona detectors. error symbos are ess correated with the misestimated extrinsic bit LLRs as the aprioriinformation. As is shown in Fig. 6, the absoute vaues of the misestimated bit LLRs tend to raise as the number of the inner iteration is increased. When the extended MAP criterion is appied to the SHISO receiver with N in, N out = 48, 1), the absoute vaues of the misestimated extrinsic bit LLRs is probaby made to reduce as the number of the outer iterations increases. The theoretica anaysis in detai is our future task. Hence, the extended MAP estimation with N out, N in ) = 48, 1) is expected to enabe the MIMO receiver to achieve much better performance than the other receiver configurations. When the LLR in 36) is appied, the extended MAP estimation with N out, N in ) = 48, 1) seects the estimated data vector D det ϕ est ) that imits the increase of the misestimated bit LLR, because the proposed estimation cacuates the margina distribution more exacty. The performance of the proposed receiver with extended MAP estimation is compared with that of the other configurations in Fig. 7. The receiver named as Phase ony in the figure feeds back ony the extrinsic bit LLR associated with the virtua channes to the MIMO detector from the Turbo decoder. LLR of each bit denotes the SISO iterative receiver. As is seen in Fig. 3, the performance of the proposed receiver is much better than that of the SISO iterative receiver. The proposed receiver achieves better per- If non-inear detectors such as the MLD detector are appied, BER performance is graduay changed with respect to the number of spatiay mutipexed streams for exampe, [8]), whie performance of inear detectors changes drasticayas thenumber of spatiay mutipexed streams exceeds N R. Hence, there is not a strong reason to compare our proposed receiver with N R N R MIMO MLD or SISO MAP receivers. As a resut, there are a ot of receivers for comparison with the proposed iterative SHISO MIMO receiver. For instance, the MLD in 16QAM 3x MIMO, 8PSK 4x MIMO, the SISO MAP with the same rate 1/3 Turbo decoder in 64QAM x MIMO, the SISO MAP with haf rate forward error correction codes in 16QAM xmimo, and so on. Because an overoaded MIMO system is our target in the paper, we restrict oursevesin 6 MIMO systems to evauate performance. The receivers drawn in Fig. 7 are seected as reference receivers, because they have been regarded as reference receivers in MIMO systems. formance than the receiver with ony the phase information by approximatey 0.5dBatBER= 10 6. Moreover, the proposed receiver with the extended MAP estimation achieves a gain of.5dbatber = 10 5, compared with the proposed receiver. The BER performance of the proposed receiver with the extended MAP estimation is compared with that of the SISO MAP iterative receiver with the Turbo code, the vertica Be aboratories ayered space-time V-BLAST) [18] with the same code, and the iterative SISO receiver with the convoutiona code [9] in Fig. 8. In the figure, the SISO MAP iterative receiver with the Turbo code and the iterative SISO receiver with convoutiona code are abeed as SISO MAP and Convoutiona code, respecitivey. In the SISO MAP iterative receiver, the MAP detection with brute force search is performed. For fair comparison, the extrinsic bit LLR is circuated between the MAP detector and the Turbo decoder in the SISO MAP iterative receiver. As is we-known, when the number of the receive antennas is ess than that of the streams, inear MIMO detectors such as the V-BLAST, do not have capabiity to detect the signa streams due to ack of the number of degrees of freedom. Even though the Turbo decoder foows the V- BLAST detector, the performance is much worse than the others. The performance of the V-BLAST has an irreducibe error at BER of 0.5. The iterative SISO receiver with the convoutiona code [9] achieves much better performance than the V-BLAST, because the non-inear signa detection is performed in addition to the inear detection in the the receiver. However, the performance of the iterative receiver is inferior to the SISO MAP iterative receiver. The proposed receiver with the extended MAP estimation achieves furthermore better performance than the SISO MAP iterative receiver by.7db at BER = 10 5, surprisingy. In principe, the MAP achieves the best performance when the misestimated bit LLR comes cose by zero owing to ow reiabiity of the bit. However, some misestimated bit LLRs grow high when the Turbo decoder is appied as is shown above. This degrades the SISO MAP iterative re-

886 IEICE TRANS. COMMUN., VOL.E98 B, NO.5 MAY 015 Fig. 9 BER convergence performance of the proposed receiver. Fig. 10 Compexity in terms of the number of mutipications. ceiver. Anyway, the proposed receiver with the extended MAP estimation attains a gain of 3.0dB at BER = 10 5, compared with the iterative receiver with the convoutiona code [9]. Performance comparison with various other receivers, e.g., the SISO MAP receiver with the same Turbo decoder in 64QAM MIMO is one of our future tasks. As is shown in Fig. 8. the BER performance of the proposed receiver is steeper than that of the conventiona receiver. The steep BER performance is typica to iterative decoding such as Turbo decoding, even though N out, N in ) = 48, 1); the turbo iteration as the inner iteration is not performed. In principe, such a performance can not be obtained without a Turbo decoder, which corresponds to the inner decoder in the propose receiver. Athough the inner iteration is not usefu, hence, the Turbo decoder as the inner decoder pays a crucia roe to improve the performance. Fig. 11 Compexity in terms of the number of additions. 4.3 Convergence Performance The BER convergence performances are shown in Fig. 9 at E b /N 0 = 1 db. The white points,, ) indicate the BER performance of the Turbo decoder outputs when the inner iteration is once finished. The back points,, ) indicate the BER performance when the outer iteration is once finished. However, some circes are omitted for cear view. It is obviousy shown that the BER convergence with N in = 1 is faster than that with N in > 1. 4.4 Computationa Compexity The number of mutipications and additions performed in the MIMO detectors are compared with those in the SISO MAP iterative receiver in Fig. 10, and Fig. 11, respectivey. When N out, N in ) = 48, 1), the number of mutipications in the proposed receiver is 30.3% of that required in the SISO MAP iterative receiver and the number of additions required in the proposed receiver is 3.% of that in the other. Therefore, it can be said that the proposed receiver is ess compex than the SISO MAP iterative receiver. 5. Concusions This paper proposes a nove receiver caed as a iterative SHISO receiver empoying virtua channes with a Turbo decoder for MIMO-OFDM systems where the number of spatiay mutipexed streams is more than twice as many as that of the receive antennas, e.g., N T, N R ) = 6, ). In the proposed iterative SHISO receiver, the extrinsic bit LLR is fed back from the decoder to the MIMO detector as an a priori information, and the rea signa and the hard decision signa of the phase are provided to the Turbo decoder. Moreover, this paper proposes a new estimation criterion, named as extended MAP estimation, for the MIMO detector to seect the most ikey virtua channe. The performance of the proposed receiver is verified in a 6 MIMO system by computer simuation. If the product of the number of the outer iterations and that of the inner iterations is set to 48, the proposed receiver with the inner iteration N in equa to 1 achieves better performance than that with N in > 1. Even when the extended MAP estimation is appied to the proposed receiver, the combination of N out, N in = 48, 1) makes the receiver achieve the

TAYA et a.: AN ITERATIVE MIMO RECEIVER EMPLOYING VIRTUAL CHANNELS WITH A TURBO DECODER FOR OFDM WIRELESS SYSTEMS 887 best performance in that with the other combinations. In other words, the inner iteration does not seem to contribute to the performance improvement and the outer iteration enabes the receiver to achieve the steep BER performance. The outer iteration pays a roe of Turbo iteration of Turbo decoding, even though some signa processing is incuded in the outer iteration. Because such a steep BER performance is typica to iterative decoding such as Turbo decoding, in principe, such a performance can not be obtained without a Turbo decoder, which corresponds to the inner decoder in the propose receiver. Athough the inner iteration is not usefu, hence, the Turbo decoder as an inner decoder pays a crucia roe to improve the performance. The proposed receiver with the extended MAP estimation achieves better performance than the origina SHISO MIMO receiver by.5dbatber= 10 5. The proposed receiver with the extended MAP estimation attains by 3.0dB better performance than the SISO MAP iterative receiver at BER = 10 5, because the misestimated extrinsic bit LLR provided by the detector deteriorates the Turbo decoding in the SISO MAP iterative receiver. Besides, the proposed receiver has ower computationa compexity than the SISO MAP iterative receiver. In summary, the proposed receiver achieves better transmission performance with reativey ow computationa compexity compared with the SISO MAP iterative receiver. Performance comparison with various other receivers, e.g., the SISO MAP receiver with the same Turbo decoder in 64QAM MIMO is one of our future tasks. Acknowedgments This research is supported by Strategic Information and Communication R&D Promotion Program SCOPE) conducted by the Ministry of Interna Affairs and Communication MIC) of Japan. References [1] R. Chang and R. 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[17] H.E. Gama and E. Geraniotis, IIterative mutiuser detection for coded CDMA signas in AWGN and fading channes, IEEE J. Se. Areas Commun., vo.18, no.1, pp.30 41, Jan. 000. [18] G.J. Foschini, Layered space-time architecture for wireess communication in a fading environment when using muti-eement antennas, Be Labs Tech. J., vo.1, no., pp.41 59, 1996. Appendix: LLRs of Rea Signas and Phases The iterative detector with virtua channes cacuates the LLRs of both the rea signa and the phase in order to output soft signas to the Turbo decoder. First, the detector obtain the LLR of the phase λ θ), using the Max-Log-MAP approximation, λ θ). Λ θ) = og P θ =+ π 4 Y ) P θ = π 4 Y ) =Λ θ) a, + max θ =+ Λ θ) π a,m + J ϕ) 4 m max θ = Λ θ) π a,m + J ϕ), A 1) 4 m J ϕ) = 1 Y Φ ϕ) S ϕ), A ) σ n where Λ θ) a, represents the aprioriinformation of the phase θ

888 IEICE TRANS. COMMUN., VOL.E98 B, NO.5 MAY 015 fed back from the Turbo decoder via the converter defined in 35) The LLR of the phase is provided to an sicer to extract ony the sign from the LLR. When the sign is positive, θ = π/4 is estimated as a transmitted phase. Otherwise, θ = π/4 is estimated. This processing is regarded as a hard decision. After the processing is appied for a the phases θ = 1,.., N T, the most ikeihood virtua channe can be estimated by using 5), 6), and 10). Next, the LLR of the rea signa in the most ikeihood virtua channe is cacuated as s =+ ) Y Λ s) ϕ est ) = og P P s = Y ) =Λ s) a, + max φ s =+ Λ s) m max φ s = m Λ s) a,m + J s φ) a,m + J s φ), A 3) J s φ) = 1 Y Φ ϕ σ est )Sφ). A 4) n In A 4), ϕ est is the phase pattern associated with the most ikeihood virtua channe. In addition, φ represents the set of the rea signas; Sφ) φ s =+ means the set of the rea signa vectors having s =+ astheth entry. The MIMO detector outputs the extrinsic bit LLR to the Turbo decoder. The extrinsic bit LLR is defined as Λ s) ex, =Λs) Λ θ) ex, =Λθ) ϕ est ) Λ s), A 5) a, Λ θ) a,. A 6) This LLR is converted to the bit LLR and then inputted into the Turbo decoder. Akihito Taya received his B.E. degree from Kyoto University, Japan, in 011. He graduated from graduate schoo of informatics, Kyoto University in 013. He is now with Hitachi, Ltd. He has a considerabe interest in mobie radio communications, especiay in spatia mutipexing. He is a member of the IEICE and a member of the IEEE. Satoshi Denno received the M.E. and Ph.D. degrees from Kyoto University, Kyoto, Japan in 1988 and 000, respectivey. He joined NTT radio communications systems abs, Yokosuka, Japan, in 1988. In 1997, he was seconded to ATR adaptive communications research aboratories, Kyoto, Japan. From 000 to 00, he worked for NTT DoCoMo, Yokosuka, Japan. In 00, he moved to DoCoMo communications aboratories Europe GmbH, Germany. From 004 to 011, he worked as an associate professor at Kyoto University. Since 011, he is a fu professor at graduate schoo of natura science and technoogy, Okayama University. From the beginning of his research career, he has been engaged in the research and deveopment of digita mobie radio communications. In particuar, he has considerabe interests in channe equaization, array signa processing, Space time codes, spatia mutipexing, and mutimode reception. He received the Exceent Paper Award from the IEICE in 1995. Koji Yamamoto received the B.E. degree in eectrica and eectronic engineering from Kyoto University in 00, and the M.E. and Ph.D. degrees in informatics from Kyoto University in 004 and 005, respectivey. From 004 to 005, he was a Research Feow of the Japan Society for the Promotion of Science JSPS). Since 005, he has been with the Graduate Schoo of Informatics, Kyoto University, where he is currenty an Associate Professor. From 008 to 009, he was a Visiting Researcher at Wireess@KTH, Roya Institute of Technoogy KTH) in Sweden. His research interests incude game theory, spectrum sharing, and cooperative muti-hop networks. He received the PIMRC 004 Best Student Paper Award in 004, the Ericsson Young Scientist Award in 006, and the Young Researcher s Award from the IEICE of Japan in 008. He is a member of the IEEE. Masahiro Morikura received the B.E., M.E., and Ph.D. degrees in eectronics engineering from Kyoto University, Kyoto, Japan in 1979, 1981, and 1991, respectivey. He joined NTT in 1981, where he was engaged in the research and deveopment of TDMA equipment for sateite communications. From 1988 to 1989, he was with the communications Research Centre, Canada, as a guest scientist. From 1997 to 00, he was active in the standardization of the IEEE80.11a based wireess LAN. He received the Paper Award and the Achievement Award from IEICE in 000 and 006, respectivey. He aso received the Education, Cuture, Sports, Science and Technoogy Minister Award in 007. Dr. Morikura is now a Fu Professor in the Graduate Schoo of Informatics, Kyoto University. He is a member of IEEE.

TAYA et a.: AN ITERATIVE MIMO RECEIVER EMPLOYING VIRTUAL CHANNELS WITH A TURBO DECODER FOR OFDM WIRELESS SYSTEMS 889 IEEE. Daisuke Umehara received the B.S. degree from Nagoya University in 1994, M.I. degree from the Japan Advanced Institute of Science and Technoogy in 1996, and the D.E. degree from the Tokyo Institute of Technoogy in 1999. He is currenty an Associate Professor at the Graduate Schoo of Science and Technoogy, Kyoto Institute of Technoogy. He has been engaged in research work on channe modeing, moduation and coding, and medium access contro protoco. He is a member of the Hidekazu Murata received the B.E., M.E., and Ph.D. degrees in eectronic engineering from Kyoto University, Kyoto, Japan, in 1991, 1993, and 000, respectivey. In 1993, he joined the Facuty of Engineering, Kyoto University. From 00 to 006, he was an Associate Professor at the Tokyo Institute of Technoogy. He has been at Kyoto University since October 006 and is currenty an Associate Professor in the Department of Communications and Computer Engineering, Graduate Schoo of Informatics. His major research interests incude signa processing and its hardware impementation, with particuar appication to cooperative wireess networks. He received the Young Researcher s Award from the IEICE of Japan in 1997, the Ericsson Young Scientist Award in 000, the Young Scientists Prize of the Commendation for Science and Technoogy by the Minister of Education, Cuture, Sports, Science and Technoogy in 006, and the Paper Award of the IEICE in 011 and 013, and IEE ICC best paper award in 014. He is a member of the IEEE. Susumu Yoshida received the B.E., M.E., and Ph.D. degrees, a in eectrica engineering, from Kyoto University, Kyoto, Japan, in 1971, 1973, and 1978, respectivey. From 1973, he had been with the Facuty of Engineering, Kyoto University and was a fu professor there since March 199 unti his retirement from Kyoto University in March, 013. During the ast 35 years, he has been mainy engaged in the research of wireess persona communications. His current research interests incude highy spectray efficient wireess transmission techniques and wireess distributed networks. From 1990 to 1991, he was a visiting schoar at WINLAB, Rutgers University, U.S.A. and Careton University in Ottawa, Canada. He served as a Genera Co-Chair of IEEE VTC 01- Spring, Yokohama, and a Genera Chair of the APWCS 01, Kyoto. He received the IEICE Achievement Award, Ericsson Teecommunication Award, IEICE Best Paper Award and Okawa Prize in 1993, 007, 011, and 013, respectivey.