Broadband Wireless Access From the Single Carrier MIMO Signal Processing Perspective

Transcription

1 Broadband Wireless Access From the Single Carrier MIMO Signal Processing Perspective Nenad Veselinovic, Tad Matsumoto and Maru Juntti Centre for Wireless Communications P.O. Box 4500, University of Oulu, Finland {nenad.veselinovic, tadashi.matsumoto, I. INTRODUCTION The scarcity of the frequency spectrum resources and ever growing demand for new broadband services imposes a need for the bandwidth efficient transceiver schemes. Signal transmission and reception using multiple transmit and multiple receive antennas over multiple-input-multiple-output (MIMO) channel is one of the most promising approaches to increasing the lin capacity and achievable data rates [1]. Two ey approaches have been developed to mae effective use of the benefits of the MIMO channels. The first one is the Bell- Labs-Layered-Space-Time-Architecture (BLAST) [2] where independent signals are transmitted from different transmit antennas. Another technique that combines the benefits of transmit diversity and channel coding in an efficient manner is space-time-coding either in a form of space-time-bloccoding (STBC) [3] or space-time-trellis-coding (STTrC) [4]. This paper focuses on STTrC coded systems. STTrC codes have originally been developed for frequency flat fading channels. In order to meet the requirements for high data rate transmission, their extension to frequency selective channels and performance in such scenarios are of great interest. The performance of STTrC codes in unequalized frequency selective channels was studied in [5], where it was shown that the dominant factor on their performance is the inter-symbol-interference (ISI), that causes inevitable error floor in large signal-to-noise ratio (SNR) range. To solve this problem, two research directions have been followed in recent years. One of them is a combination of orthogonal-frequencydivision-multiplexing (OFDM) and decoding [6], which allows one to perform signal processing for a set of frequencyflat fading channels. The other approach is a combination of equalization and decoding for single-carrier communications. The optimal receiver for the frequency selective channels is the maximum a posteriori (MAP) equalizer usually implemented by means of the BCJR algorithm [7]. Its complexity, however, grows exponentially with the number of multipath components. Moreover, in the channel coded systems, the optimal receiver is the one that performs joint equalization and de- This wor was supported by Noia, Eletrobit, Finnish Air Forces, Instrumentointi, National Technology Agency of Finland (Tees), Noia Foundation and Infotech Oulu Graduate School coding and its complexity is exponential in the product of the number of multipath components and the code memory length. Therefore, it is impractical in broadband systems, and low complexity schemes are of a particular interest. The problem of complexity of the optimal joint equalization and decoding can be effectively solved by iterative (turbo) equalization principle that was introduced in [8]. Further complexity reductions have been mainly based on simplifications of the equalization part. This paper focuses on the low complexity turbo equalization for single-carrier communications using STTrC codes. Joint iterative equalization and decoding of STTrC codes is introduced in [9], where the optimal MAP equalizer is used. Its low complexity extension is proposed in [10], where channel shortening taes place first, and the reduced complexity MAP algorithm is performed afterwards. The technique results in relatively low performance degradation when compared to the optimal receiver. In the case of decision feedbac equalization (DFE) combined with STTrC-decoder in an iterative manner, a method for complexity reduction was studied by [11], [12]. This method is based on the decoupling between the real and imaginary parts of the received signal, resulting in a reduced total number of equalizer states. An equalizer based on soft interference cancellation and MMSE filtering was proposed in [13] for a convolutionaly coded system with diversity signal reception. The receiver can be seen as an extension of the idea introduced for code-division-multiple-access (CDMA) in [14]. It was further extended to cover higher order modulations in [15], [16], where further complexity reduction methods were proposed as well. In [17], the idea was applied to the multiuser diversity signal detection with convolutional codes. The reduced complexity version of the receiver, based on matched filter approximation, was proposed in [18]. An STTrC coded multiuser system in frequency flat MIMO channels was considered in [19]. It employs iterative multiuser detection schemes similar to those of [14] and [17]. In some situations the unnown cochannel interference (UCCI) can be present in the channel apart from the users that are to be detected. Those users can originate from the undetected users in the same cell, from the other-cell interference, or from other communication systems. In [20] an iterative UCCI suppression method has been studied which is based on the covariance matrix estimation technique. Subspace

2 estimation methods for the UCCI suppression were considered in [21] and [19] in CDMA and SDMA systems, respectively. A non-iterative receiver for detection of STTrC codes in the presence of UCCI was introduced in [22] in frequency flat fading channels. The method of [22] is based on joint detection of all the transmit antennas signals using MMSE receiver presented in [23]. A similar solution was proposed in [24] for the orthogonal transmission using STBC codes in flat fading channels. In [24] and [22], however, the MMSE filters are different so that the outputs of the latter one are the combined signals from all the receive antennas, while the outputs of the former one are the separated outputs for each receive antenna. In this paper new low-complexity turbo equalization schemes for the multiuser MIMO STTrC coded system are derived. The first part of the studied receivers is soft cancellation of both inter-symbol-interference (ISI) and co-channel interference (CCI). The second part is linear MMSE filtering that is used to cope with the residual interference after soft cancellation and UCCI if the latter is present. The degrees-offreedom (DoF) of the MMSE receiver are thereby decreased depending on the significance of the residual interference and UCCI. The receiver can be seen as a combination of those considered in [19] and [24], and their extension to frequency selective channels. Assuming that each transmitter has N T transmit antennas, the receiver is derived for the general case of jointly detecting signals in the N T /n 0 sets containing n 0 transmit antennas of one particular user, where N T is an integer multiple of n 0. The derived receiver s performance in special cases corresponding to n 0 = 1 and n 0 = N T is studied through simulations. The case n 0 = 1 can be seen as an extension of the receiver proposed in [19] to the frequency selective channels. The cases of 1 n 0 N T are a further receiver extensions where several transmit antennas are detected jointly. The aim of joint detection of several transmit antennas signals is to preserve the DoFs of the receiver. In case of n 0 = N T, N T 1 DoFs are preserved. The UCCI mitigation capability of the proposed receiver is attained by using the iterative covariance estimation technique shown in [20]. It should be noted that the receiver proposed in [19] requires the nowledge of the UCCI channel matrix. Unlie [19], the method of [20] requires only a covariance matrix estimate of the UCCI-plus-noise and it is therefore less complex. The rest of the paper is organized as follows. Section II describes system model. Section III presents the proposed receiver and its special cases for which either one antenna or all antennas are detected simultaneously. Section IV describes the use of channel measurement data. Section V presents numerical results. The paper is concluded in Section VI. II. SYSTEM AND RECEIVED SIGNAL MODEL Figures 1 and 2 describe the system model and the th user s transmitter bloc diagram assumed in this paper, respectively. Each of K +K I users encodes bit information sequence c (i), Fig. 1. System model = 1,..., K + K I, i = 1,..., B 0 using a rate 0 /N T STTrC code, where N T and B are the numbers of transmit antennas and frame length in symbols, respectively. The users indexed by = 1,..., K are the users of interest to be detected and the others indexed by = K + 1,..., K I are unnown users. The encoded sequences b (i) Q, i = 1,..., BN T are first grouped in B blocs of N T symbols, where Q = {α 1,..., α 2 0 } denotes the modulation alphabet of M-phaseshift-eying (M-PSK). owever, it is straightforward to extend the receiver derivations to quadrature-amplitude-modulation (QAM) schemes. The coded sequence is then interleaved so that the positions within blocs of length N T remain unchanged but the positions of the blocs themselves are permuted within a frame according to the user-specific interleaver pattern. Thereby the ran properties of the STTrC codes are preserved [25]. The interleaved sequences are then headed by user-specific training sequences consisting of T N T symbols. The entire frame is serial-to-parallel converted, resulting in the sequences b (n) (i), n = 1,.., N T, i = 1,..., B + T and transmitted with N T transmit antennas through the frequency selective channel. Fig. 2. Transmitter bloc diagram After coherent demodulation in the receiver, the signals from each of N R receive antennas are sampled in time domain to capture the multipath components. Observing the signals from different transmit antennas of different users as the virtual users and arranging them in the vector form similarly as in [19], [17] we form the space-time representation of the received signal at time instant i given by y(i) = u(i) + I u I (i) + n(i), i = 1,..., T + B, (1) }{{}}{{}}{{} desired UCCI noise where y(i) C LN R 1 is space-time sampled received signal vector, given by y(i) = [r T (i + L 1),..., r T (i)] T (2)

3 where r(i) = [r 1 (i),..., r NR (i)] T, (3) L is the number of paths of the frequency selective channel and r m (i) denotes the signal sample obtained after matched filtering at the mth receive antenna. Channel matrix has the form of and = (l) = (0)... (L 1) (0)... (L 1) h (1) 1,1 (l)... h(n T ) 1,1 (l)... h (1) K,1 (l)... h(n T ) , K,1 (l) h (1) 1,N R (l)... h (N T ) 1,N R (l)... h (1) K,N R (l)... h (N T ) K,N R (l) where h (n),m (l) denotes the l-th path complex gain between th user s nth transmit antenna and mth receive antenna. The UCCI channel matrix I is defined similarly. The vectors u(i) and u I (i) denote the desired and unnown users sequences, respectively, which are defined as u(i) = [b T (i + L 1),..., b T (i),..., b T (i L + 1)] T (4) and u I (i) = [b T I (i + L 1),..., b T I (i),..., b T I (i L + 1)] T, (5) with b(i) = [b (1) 1 (i),..., b(n T ) 1 (i),..., b (1) K (i),..., b(n T ) K (i)]t, (6) Vector n(i) C LN R 1 contains the spatially and temporally white additive Gaussian noise (AWGN) samples with covariance E{n(i)n (i)} = σ 2 I. III. TURBO MIMO EQUALIZERS The receiver first associates the signals from transmit antennas of the th user to the N T /n 0 sets of size n 0, so that antennas indexed by n = 1,..., n 0 belong to the first set, those indexed by n = n 0 + 1,..., 2n 0 belong to the second set etc. Thereby the number of transmit antennas N T is assumed to be an integer multiple of n 0. owever, the receiver derivation for the more general cases of users having different numbers of transmit antennas and/or different sets of transmit antennas having different sizes is straightforward. Without loss of generality the receiver derivation is presented for the first set of transmit antennas of the th user in Section III-A. The derivation is exactly the same for the rest of transmit antenna groups and the rest of users, with a difference only in indexing. The SISO channel decoding part and the extrinsic probabilities calculation are presented in Section III-B. The special cases Fig. 3. and b I (i) = [b (1) K+1 (i),..., b(n T ) K+1 (i),..., b(1) K+K I (i),..., b (N T ) K+K I (i)] T. (7) ˆR = 1 T Iterative receiver bloc diagram of n 0 = 1 and n 0 = N T are considered in more detail in Section III-C. For n 0 = 1, only one antenna is detected at a time and the receiver can be viewed as an extension of the receiver presented in [19] to the frequency selective channel. For n 0 = N T all the transmit antennas are detected jointly, resulting in the preserved DoFs of the receiver. A. SC/MMSE Equalizer Derivation Fig. 3 shows the receiver bloc diagram. First, an estimate Ĥ of the channel matrix is obtained based on the training sequence u(i), i = 1,..., T. Then, the covariance matrix R of the UCCI-plus-noise is estimated. In the first iteration only the training sequence is used for this purpose, resulting in T i=1 (y(i) Ĥu(i))(y(i) Ĥu(i)). (8) Starting from the second iteration we mae use of the soft feedbac from the SISO decoding when estimating the covariance matrix. Let us denote the soft feedbac vector as u(i). Its elements are obtained by replacing the corresponding elements of u(i) by their soft estimates, defined as b (n) 2 0 (i) = α q P app SISO (b(n) (i) = α q), (9) q=1 where P app SISO denotes a posteriori information obtained after SISO decoding (to be defined in (25)). The covariance matrix estimate is now obtained by ˆR = 1 T (y(i) T Ĥu(i))(y(i) Ĥu(i)) (10) + 1 B i=1 T +B i=t +1 (y(i) Ĥu(i))(y(i) Ĥu(i)). The estimate ˆR is, therefore, dependent on the iteration index. owever, for the simplicity of notation we omit this

4 dependence, since the receiver derivation is identical for all the iterations. Moreover, only in the first iteration Eq. (8) is used for estimation of R, while in all the subsequent iterations Eq. (10) is used. Let the th user be the user of interest. Let us further denote where e <γ> u <1> (i) = ũ(i) ũ(i) e <1>, (11) = [ 0,..., 0, 1,..., 1, 0,..., 0 }{{}}{{}}{{} [(L 1)K+ 1]N T +(γ 1)n 0 n 0 (LK +1)N T γn 0 ] and and γ = 1,..., N T /n 0 denote elementwise vector product and antenna set index, respectively. The vectors ũ(i) are obtained by replacing the elements of u(i) by their soft estimates, i.e. an element is 2 0 b(n) (i) = α q PSISO(b ext (n) (i) = α q), (13) q=1 where PSISO ext denotes the extrinsic information obtained after SISO decoding (to be defined in (26)). The signals b (n) (i), n = 1,..., n 0, are jointly detected by filtering the signal y <1> (i) = y(i) Ĥu<1> (i), i = T + 1,..., B + T, (14) using a linear MMSE filter whose weighting matrix W <1> (i) satisfies the following criterion [W <1> (i), A <1> (i)] = (15) arg min W,A W y <1> (i) A β <1> (i) 2, subject to the constraint [A] j,j = 1, j = 1,..., n 0 to avoid the trivial solution [W <1> (i), A <1> (i)] = [0, 0]. β <1> (i) C n0 1 is defined by β <1> (i) = [b (1) (i),..., b(n0) (i)] T, (16) The n 0 th column of the matrix W <1> (i) C LN R n 0 can be derived as where M <1> w (n0) (i) = M <1> 1 + h (n0) (i) 1 h (n0) M <1> (i) 1 h (n0) (i) = ĤΛ<1> (i)ĥ + }{{ ˆR n 0 } n=1 R <1> cov h (n), (17) h(n), (18) and h (n) is the [(L 1)KN T + N T + n]-th column of the matrix Ĥ. The matrix Λ<1> (i) is defined as Λ <1> (i) = I E{u <1> (i)u <1> (i) }. (19) Note that Eq. (19) holds only for the M-PSK case, although it is straightforward to extend the receiver derivation to the more general signal constellations. Assuming that the MMSE filter output z <1> (i) C n0 1 can be viewed as the output of the equivalent Gaussian channel [26] we can write z <1> (i)y <1> (i) = W <1> (i) (20) = Ω <1> (i)β <1> (i) + Ψ <1> (i), where matrix Ω <1> (i) C n0 n0 contains the gains of the equivalent channel defined as T Ω <1> (i) = E{z <1> (i)β <1> (i)} = W <1> (i)π <1> (21), (12) with Π <1> (i) = [h (1)... h(n0) ]. The vector Ψ <1> (i) C n0 1 is the equivalent additive Gaussian noise with covariance matrix Θ <1> (i) = E{Ψ <1> = W <1> (i)ψ <1> (i)} (22) (i)rcov W <1> (i) Ω <1> (i)ω <1> The outputs of the equivalent channels z <γ> (i) and their parameters Ω <γ> (i) and Θ <γ> (i) for γ = 1,..., N T /n 0 are passed to the APP bloc that calculates the extrinsic probabilities needed for SISO decoding, as described in Section III-B. B. APP Bloc and SISO Decoding The SISO channel decoding algorithm used in this paper is a symbol-level maximum-a-posteriori (MAP) algorithm from [27]. For the sae of simplicity we omit the full derivation of the MAP algorithm and we refer to [27] and [19]. It should be note that the input required by the decoder is the probability P (S i, S i+1 ) associated with the transition between two trellis states S i and S i+1 of the STTrC code. The transition probability can be calculated as P (S i, S i+1 ) = N T PMMSE(b ext (n) n=1 where d i,i+1 n with the transition (S i, S i+1 ). P ext (i) = di,i+1 n ), (23) Q are the encoder outputs that are associated MMSE (b(n) (i) = α q) are extrinsic probabilities obtained by the MMSE detection. For the 1st set of jointly detected signals (n = 1,..., n 0 ) the extrinsic probabilities are calculated in the APP bloc as P ext MMSE(b (n) (i) = α q) = n 0 p=1,p n P (z <1> (i) f) (24) f B dn P ext SISO(b (n) (i) = d n), for q = 1,..., 2 0 and n = 1,..., n 0, where B dn = {f Q n0 1 f n = d n }. Based on the transition probabilities P (S i, S i+1 ) the SISO channel decoder calculates the a posteriori probabilities for the symbols b (n) (i), defined as P app SISO (b(n) Ω <1> (i) = α q) = P (b (n) (i) = α q z <1> (i), (25) (i), Θ <1> (i), i = T + 1,..., T + B). (i).

5 The decoder extrinsic probability is then calculated as P ext SISO(b (n) (i) = α q) = P app SISO (b(n) (i) = α q) PMMSE ext (b(n) (i) = α q). (26) The similar procedure is repeated for all N T /n 0 groups of transmit antennas that are jointly detected, in order to obtain all probabilities PSISO ext (b(n) (i) = α q) for n = 1,..., N T. The parameter Q ext is an ad-hoc parameter that was introduced in [8] and [19]. It is shown in [19] that if the value of Q ext is appropriately chosen so as to be between 0 and 1, the receiver performance can be significantly improved. This is due to the fact that the extrinsic information in the initial iterations is not accurate enough, especially with relatively small signal-tonoise-ratio (SNR) values. By imposing the parameter Q ext the effect of this inaccuracy is reduced, at the expense of slower receiver convergence. The result of simulations conducted to evaluate the influence of this parameter on the receiver performance is presented in Section V. The receiver complexity is dominated by the MMSE part which requires inversion of the matrix M <γ> (i) as well as by the APP bloc which calculates the extrinsic information of the MMSE detector. The overall complexity is therefore O{max(L 3 NR 3, )}. It can be seen that the complexity of 20n0 the MMSE part does not depend on the number of antennas to be jointly detected. The complexity of the APP part of the receiver, however, increases exponentially with n 0. C. Special Cases of n 0 = 1 and n 0 = N T Receiver #1, n 0 = 1, transmit antennas detected oneby-one. Since the complexity of the receiver depends exponentially on n 0, this option has the lowest complexity. Signal from only one antenna is detected at a time, while the rest of the antennas are cancelled by the soft feedbac and the MMSE filtering, together with CCI and ISI. By doing this, effective DoFs of the receiver are preserved. It should be noted that the number of effective DoFs depends on the reliability of the soft feedbac information, which can be seen from Eq. (18). In the ideal case of perfect feedbac (which is not realistic in practice) the number of effective DoFs reaches its maximum value, which is equal to LN R 1. The fact that feedbac is non-perfect in reality will result in number of effective DoFs that is smaller than LN R 1, since the matrix Λ <γ> (i) h (1) h(1) is in general a non-zero matrix. The preserved DoFs are then used to suppress UCCI, if it is present. If the number of effective DoFs is large enough so that in the asymptotic case of large SNR the matrix M <γ> (i) does not have a full ran, then the ISI, CCI and UCCI can be perfectly suppressed. Otherwise, the receivers performance saturates to an error floor for large SNR values. Receiver #2, n 0 = N T, all transmit antennas detected jointly. In this case, the complexity of the receiver is the largest. owever, the N T 1 effective DoFs of the receiver are now perfectly preserved. This can be seen from Eq. (18). The signals from N T antennas can be seen as being passed jointly to the receiver output by the third term on the righthand side of Eq. (18). The jointly detected signals are then optimally separated in the APP bloc. In general, when n 0 out of N T antennas are detected jointly, the n 0 1 DoFs are perfectly preserved, while at most N T n 0 ones are preserved by soft cancellation, depending on the feedbac reliability. Also one should notice that in the theoretical case of the perfect feedbac, the proposed receivers performance will be identical for any n 0 value. IV. PRACTICAL CONSIDERATIONS Understanding receiver behavior and evaluating its performance in realistic situations is of great importance. One possibility is to perform this evaluation using different channel models [28], [29]. Another possibility is to evaluate performances using realistic channel impulse response obtained directly through measurement campaigns. The advantages of this approach compared to the one based on model are that the results actually reflect practical situation. In the last part of this paper the field measurement data is used to evaluate receiver performance dependency on the practical channel impairments. The channel impulse response data is obtained by using multidimensional channel sounder, described in detail in [30], [31]. The details of the spatiotemporal structure of the channel in the given measurement area can be found in [31]. The receiver was stationary during measurement, while the transmitter was moving at a waling speed. Three different regions can be identified along the route. First, the static non-line-of-site (S-NLOS) region, where transmitter was stationary and the line-of-site (LOS) was obstructed by the metal container. Second, the dynamic- NLOS (D-NLOS) region, where the transmitter was moving but LOS was still obstructed. Third, the LOS region, where LOS between transmitter and receiver exists. V. NUMERICAL EXAMPLES Performance of the proposed receivers was evaluated through computer simulations. The channel estimates were assumed to be perfect. All users transmitted with the same power, and fading was constant over each transmitted frame, but changed independently frame-by-frame. In case of the modelled channel, the fading was assumed to be frequency selective with the number of paths L = 5, each of which is Rayleigh distributed and uncorrelated. It was assumed that antennas are spatially uncorrelated, and that signals at all receive antennas have the same average powers. E s /N 0 is defined as the signal-to-noise-ratio per symbol per receive antenna. The exponentially decaying power delay profile with decay exponent τ was assumed, so that τ = 0 results in the equal-average-power-multipath and τ in the flat-fading

6 Fig. 4. Performance of iterative SC-MMSE receiver in STTr coded system, K I = 0, (K, N R ) = (1, 1), (3, 3) and (5, 5), (B, T ) = (150, 15), N T = 2, frequency selective channel with L = 2 Rayleigh distributed paths, i.i.d. between paths and antennas, all paths are of equal average powers. Fig. 6. Receiver #2 s performance vs. per antenna E s/n 0, (K, K I, N R ) = (1, 0, 1), (B, T ) = (150, 15), N T = 2, (n 0, l 0 ) = (2, 1), τ = 0 Fig. 5. Receivers #1 s and #2 s performance vs. per antenna E s/n 0, (K, K I, N R ) = (1, 0, 1), (B, T ) = (150, 15), N T = 2, (n 0, l 0 ) = (1, 1) and (2, 1), τ = 0 channels, respectively. The 4-state QPSK code with N T = 2 presented in [32] was used to encode signals of all MIMO users. All the users transmit with the same powers. The Log- MAP space-time trellis decoder shown in [27] and [19] was used. User specific random interleavers were assumed. In Fig. 4 the symbol error rate (SER) performances are compared for different simulation scenarios. Number of multipath components is L = 2 with τ = 0. The simulation scenarios (K, K I, N R ) = (1, 0, 1), (K, K I, N R ) = (3, 0, 3) and (K, K I, N R ) = (5, 0, 5) are compared. The performance of the receiver obtained with assumption of perfect feedbac, resulting in ideal ISI and CCI removal prior to decoding, is presented for comparison. It can clearly be seen that the simultaneous increase in the number of users and the number Fig. 7. Receiver #1 s and #2 s performance vs. per antenna E s/n 0, (K, K I, N R ) = (2, 1, 3), (B, T ) = (150, 15) and (300, 30), N T = 2, (n 0, l 0 ) = (1, 1) and (2, 1), SIR=0 and 3dB (two antennas used by UCCI), τ = 0 and of receive antennas yields almost the same performance of the iterative receiver and the corresponding ML lower bound. Note that the required number of receive antennas is thereby equal to the number of users and not to the total number of transmit antennas. Similar behavior can be observed from Figs. 5 and 6, which present results for (K, K I, N R ) = (1, 0, 1) and (K, K I, N R ) = (3, 0, 3), respectively, for the number of multipath components L = 5. It can be seen that the receiver is capable of achieving maximal diversity order thereby almost completely removing ISI and CCI. In Fig. 7, SER performances of the both receivers are presented vs. per-antenna E s /N 0 for (K, K I, N R ) = (2, 1, 3). In this scenario the UCCI uses two antennas in the same way as the desired users. The curves are plotted with SIR, frame length B, and channel decay exponent τ as param-

7 BER circle : rec. #1 cross : rec. #2 diamond : rec. #4 E s /N 0 = 12 db N T =2, N R = snapshot index Fig. 8. BER vs. snapshot index, (N T, N R ) = (2, 1), E s/n 0 = 12dB, Q ext = 0.5, L eff = 11, transmit antennas #1 and #8 used, receive antenna #1 used, ρ (1,8) = 0.48 in the S-NLOS region, ρ (1,8) = 0.56 in the D-NLOS region, ρ (1,8) = 0.98 in the LOS region eters. For comparison the single-user bound described by (K, K I, N R ) = (1, 0, 3) is also presented. It can be seen again that the both receivers are robust against interference over a wide range of E s /N 0 values. owever, due to the lac of effective DoFs the performance curves tend to saturate to an error floor with high E s /N 0 values. This can be solved in a straightforward manner by adding more receive antennas. owever, it should be noted from Fig. 7 that the error floor can be reduced by increasing frame length while eeping the ratio T/B constant. This behavior can be explained by two reasons: First, increasing the frame length results in more samples for R estimation; Second, the feedbac becomes more accurate with the increased frame length. It can also be seen by comparing the results for τ 0 and τ from Fig. 7 that the gain from using receiver #2 is larger if the number of significant multipath components is smaller. This is due to the fact that in the rich multipath environment (τ 0) the number of effective DoFs is much smaller than the number needed to perfectly suppress the UCCI. Therefore, preserving one DoF with the receiver #2 does not have any significant impact on the receivers performance. On the other hand, in the flat-fading (τ ) the number of effective DoFs is comparable to the number needed to suppress the UCCI, and preserving one DoF improves performance. The performances of the both receivers improve with increased SIR and in the absence of UCCI they are expected to approach the corresponding single user bounds. In Fig. 8 the proposed receiver s performance sensitivity to the spatial correlation at the transmitter is presented. For that purpose field measurement data is used. It is found in Fig. 8 that the rec. #1 s performance is far better in the NLOS region than in the LOS region. On the contrary, rec. #2 s performance is almost constant regardless of the propagation condition. This is due to the larger spatial spread at the transmitter side in the NLOS region resulting in the lower spatial correlation among the transmit antenna elements. Since the receiver #1 performs spatial separation of transmit antenna elements streams using MMSE filtering, its performance is better in the NLOS case. The receiver #2 s superiority is due to the joint detection of signals transmitted using two transmit antenna elements. Thereby, the separation of two transmit antennas signals is performed in the MAP bloc itself instead of the MMSE receiver. The improvement achieved by the rec. #2 over the rec. #1 is larger in the LOS region. Therefore, preserving the degrees of freedom of the MMSE receiver by joint detection is more beneficial in the LOS than in the NLOS regions. For comparison the performance of receiver which is optimal for STTr code is also shown in Fig. 8. The receiver is denoted as rec. #4. It is shown that the receiver #4 outperforms both of the previously mentioned receivers, showing very robust behavior regardless of the environment. This is due to the fact that receiver #4 separates different transmit antennas in the SfISfO decoder itself, and not in the MMSE or MAP bloc. STTr code, in turn is nown to be rather robust against spatial correlation. VI. CONCLUSIONS New iterative receiver schemes for the STTrC-coded multiuser system in frequency selective channels have been derived for single-carrier broadband signalling. It has been shown through computer simulations that the receiver that jointly detects signals from all the transmit antennas of the user of interest performs slightly better than the receiver that detects only one antenna at a time. In the presence of relatively strong UCCI the gain from joint detection is larger if the channel has less multipath components. This is due to the fact that preserving DoFs of the receivers with the joint detection has a greater impact on performance if the number of effective DoFs is comparable to the number needed to perfectly suppress UCCI. The complexity of the MMSE part of the receiver is independent of the number of antennas n 0 that are to be jointly detected. owever, the complexity of the APP part, that calculates the extrinsic probabilities needed for SISO channel decoding, grows exponentially with n 0. It has been shown that the performance of both receivers improves by increasing frame length, due to the improved feedbac reliability. The performance also improves with higher SIR values. The gain from joint detection, however, is smaller if the feedbac is more reliable. In a multiuser scenario without UCCI the proposed receivers can achieve corresponding single user bounds. Thereby, the required number of receive antennas is equal to the number of users and not to the total number of transmit antennas. Furthermore, the receivers single-user performances are very similar to each other and relatively close to the performance of the ML receiver with perfect feedbac. Performance sensitivity

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Theory, vol. 44, no. 2, pp , Mar Abstract Iterative multiuser detection in single-carrier broadband multiple-input multiple-output (MIMO) system is studied in this paper. A minimum-mean-squared-error (MMSE) low complexity multiuser receiver is derived for space-division-multipleaccess (SDMA) space-time trellis coded (STTrC) systems in frequency selective fading channels. The receiver uses MMSE filtering to jointly detect several transmit antennas of the user of interest, while the interference from the undetected transmit antennas, co-channel interference (CCI) and inter-symbolinterference (ISI) are all cancelled by the soft cancellation. The performances of two extreme receiver cases are evaluated. In the first case only one transmit antenna of the user of interest is detected at a time and the remaining ones are cancelled by soft cancellation. In the second case all the transmit antennas are detected jointly. The comparison of the two cases shows the improvement with the latter one both in single user and multiuser communications and in the presence of unnown cochannel interference (UCCI). It is further shown that in the multiuser case the proposed receivers approach the corresponding singleuser bounds. The number of receive antenna elements required to achieve single-user bound is thereby equal to the number of users and not to the total number of transmit antennas. The receiver with joint antenna detection shows more robust performance to the spatial correlation than the antenna by antenna detection. BROADBAND WIRELESS ACCESS FROM TE SINGLE CARRIER MIMO SIGNAL PROCESSING PERSPECTIVE, Veselinovic N., Matsumoto T., Juntti M.