《通信原理》课程教学资源（辅导资料）Selected MIMO Techniques and their Performance.pdf_P21-P25

FLOWS IST-2001-32125 Deliverable No: D14 2.2.3 MIMO techniques for flat fading channels Layered space-time architecture (BLAST) In MIMO systems, the data rate can be increased by transmitting nT independent data streams from nT transmit antennas. An optimal receiver (ML receiver) has to choose out of MnT possible signals, where M is a constellation size for the modulation scheme used. As a result, the complexity of the optimal receiver grows exponentially with the number of transmit antennas. Therefore, suboptimal solutions were proposed, based on layered architectures (BLAST) each layer corresponding to a transmit antenna. In BLAST systems, the data is split into nT independent data streams, transmitted simultaneously from nT antennas. The layered space-time architecture allows signal processing complexity to grow linearly, rather than exponentially, with the promised capacity increase. Such an architecture allows a nT -dimentional signal processing problem to be solved with only nT similar 1-D processing steps. In [Ari00] it has been shown that Foschini’s lower capacity bound is, in fact, the Shannon bound when SNR of the space-time processing in each layer is represented by the corresponding ”matched filter” bound. This proves the optimality of the layered space-time concept. Simulation results have shown that the Shannon capacity for wireless communications can be achieved within 3 dB in average SNR, about 2 dB of which is a loss due to a practical coding scheme used for analysis. So, the layered space-time processing itself is nearly information-lossless. D-BLAST (diagonal BLAST) and V-BLAST (vertical BLAST) systems were proposed by Foschini et al. [BH02]. In V-BLAST, transmit antenna i is assigned to layer i for the entire transmission period. As a result, due to the random channel matrix H different layers pro- vide different error probability. In D-BLAST, a fraction of a coded block of a certain layer is transmitted from all transmit antennas, resulting in the same channel for all layers. In another MIMO system, Multi-Stratum-Space-Time Coding system [WTS01], independently encoded data streams undergo an orthogonal transformation, also leading to the same channel for all layers. A characteristic feature of the BLAST schemes is that signals from layers with low diversity are fed back to construct high diversity channels. This significantly limits the system performance due to error propagation. To provide a high performance, a DFE (decision feedback equalisation) based BLAST scheme requires more receive antennas than transmit antennas; unsatisfactory performance is reported when equal number of antennas are employed at both ends. A parallel detection algorithm is proposed in [Li02] to improve the performance in such scenarios. At each stage, the detector consists of M branches (M beeing the constellation size) each with a sub-detector. In the qth branch, the hypothesis that a transmitted signal s1 represents the point xq of the constellation is made. After subtracting hixq from the received signal y, the qth sub-detector makes a hard decision bq on s2,...,snT . Each branch outputs a different hard-decision {xq, bq} on s. A final decision ˆs is made by selecting the branch with a smallest error. Since the sub-detectors are now functioning for a (nT − 1, nR) system, the diversity is higher which leads to a better performance. Simulation results demonstrate that the proposed parallel detector offers approximately the MLSE performance for a QPSK (5,5) system in a channel with the known channel matrix and significantly outperforms conventional DFE schemes. In [LS02], a general approach to building MIMO layered architectures is formulated, which is based on QR decomposition of the channel matrix H. This approach allows construction of a variety of layered space-time processing structures, including the BLAST and V-BLAST 17 December 2003 Page 22

FLOWS IST-2001-32125 Deliverable No: D14 as special cases. Also, this allows construction of BLAST-type processing to overcome the problem of error propagation. The main computation in using BLAST is the determination of the optimal ordering of nulling and cancellation steps, and the computation of the nulling vector. These steps have computational complexity of order O(n4 T ) [ZB02]. The existing iterative nulling and cancellation algorithms for BLAST have high computational complexity and require repeated matrix pseudo- inversion calculations which may lead to numerical instability. A modification of BLAST proposed in [ZB02] simplifies the implementation. In this scheme, numerical stable unitary transformations are performed on the Cholesky-decomposed matrices to reorder the detection and cancellation steps. This approach is a modification of the decorrelating decision-feedback CDMA multiuser detection method and applying it to BLAST. Here, a (nT , nR) BLAST system is interpreted as a nT -user CDMA system with spreading factor nR. The system assumes perfect channel estimates and a quasi-static channel. The dominant computation of the modified receiver is in the QR-decomposition, the matrix inversion, and reordering and triangularisa- tion of permutations of the Cholesky decompositions. For nT = nR the computational load is reduced by about 3nT times. This algorithm is numerically more stable than the original BLAST and therefore is more suited to fixed-point DSP implementation. In addition to the lower computational load, the proposed algorithm provides the optimal ordering resulting in a better detection performance. In [GC01] it has been shown that V-BLAST receiver processing is equivalent to the operations of generalised decision-feedback equalisers in both the zero-forcing and MMSE modes. Antenna selection The BLAST architecture is an example of spatial multiplexing, i.e. MIMO modulation techniques when the incoming data are divided into multiple substreams and each substream is transmitted on a different antenna. If many transmit antennas are available, simultaneous transmission from all the antennas may be difficult due to hardware costs. Another example of spatial multiplexing is antenna selection. In [HSP01] an antenna selection technique is proposed and analysed for a system with a linear receiver. The technique selects a subset of available transmit antennas. The mobile decides from which antennas it wishes to receive the data substreams. With as little as one extra antenna the subset selection can dramatically improve the performance of linear receivers. It has been demonstrated that the system (4,2) with a zero-forcing linear receiver and the antenna selection significantly outperforms the system (2,2) with the ML receiver. The antenna selection is an inexpensive way to obtain diversity over a multiple antenna fading channel. The paper [BW02] discusses optimum MIMO systems with antenna selection at both the transmitter and receiver. Transmit diversity Both the ML and layered receivers require the number of receive antennas to be equal or more than the number of transmit antennas: nR ≥ nT . For scenarios, where the performance can be improved by optional receive diversity, a different approach based on transmit diversity may be used. In systems with transmit diversity, the same information is transmitted from all transmit antennas. The goal of the first approach is to transmit more bits, the goal of the second approach is to obtain better bits [BH02]. In a system with receive diversity, the symbol s transmitted from a single antenna is received by nR spatially separated receive antennas. If maximum ratio combining is applied, the output 17 December 2003 Page 23

FLOWS IST-2001-32125 Deliverable No: D14 SNR is maximised: after combining the SNR is a sum of SNRs in the diversity branches. In a system with transmit diversity, a receiver observes the superposition of signals transmitted simultaneously from nT antennas. This is equivalent to transmission over a single-input singleoutput channel with the complex Gaussian channel tap [BH02] h = 1 √nT nT i=1 hi1. (2.10) In such a system, no diversity gain is obtained because the transmitted signals cannot be separated. In order to separate the signals transmitted by different antennas, different approaches can be used, for example, modulation diversity or delay diversity. The modulation transmit diversity is based on using orthogonal pulses at different transmit antennas. The receiver uses respective matched filters in nT branches. The orthogonality allows the receiver to separate the contributions of different antennas and to apply maximum ratio combining. In a CDMA system, different orthogonal spreading sequences should be assigned to different transmit antennas. However, this approach loses bandwidth efficiency. The delay diversity allows the system to avoid the loses. To this end, orthogonal prefiltering of the signal before transmission is used. The prefilters introduce intersymbol interference and the receiver faces a frequency selective channel with independent tap fadings. The diversity gain is provided by an equaliser. A particular example of this approach is to transmit the same symbol with a delay (i − 1)Ts from antenna i. However, due to the fact that the same information is transmitted over all antennas, the outage capacity of the MIMO channel can never be reached using delay diversity if nR > 1. Transmit antenna diversity should be used in systems with nR = 1 receive antenna. If multiple receive antennas are available, the data rate should be increased by transmitting independent data from different antennas, as in BLAST. MIMO in multiuser systems Previous results on MIMO systems were all obtained for a single link with no external interference. In [CDG00a, CDG00b, CDG01] attainable MIMO performance is quantified and compared with that of traditional approaches in interference-limited cellular systems. A cellular data system combines: (a) multiple transmit signals, each using a separately adaptive modulation, matched to the instantaneous channel condition; (b) adaptive array processing at the receiver; and (c) aggressive frequency reuse (reuse in every cell). A cell comprises a base station and one mobile user on every frequency channel. The cell is surrounded by six cells, with full frequency reuse in every cell. Each user is randomly located with uniform probability over the cell. The other characteristics and parameters are: inverse distance law; Rayleigh fading; lognormal shadow fading; antenna pattern when sectoring is used; path loss exponent 3.7; fading standard deviation 0, 4 or 8 dB; Ricean K-factor = 0 or 10. Array processing is based on either MMSE or ordered successive interference cancellation (OSIC) MMSE. Adaptive modulation rate algorithm perfectly adapts the transmission rate on each transmit antenna. MIMO system (3,3) suffers more performance degradation than SIMO system (1,3), when going from a noise-limited environment to an interference-limited environment [CDG01]. Increasing the number of receivers brings back the throughput advantage of MIMO systems over SIMO systems. Using adaptive modulation without power control provides a significantly higher throughput than using SINR-based power control. For (3,3) systems OSIC-MMSE technique in all cases outperforms MMSE. Increasing the number of receivers beyond the number of transmitters will add more degrees of freedom for interference cancellation and thus will improve the performance of MIMO systems by providing diversity against fading and cochannel interference. There is almost a two-to-one improvement in performance when using MIMO system (3,6) instead of MIMO system (3,3). Increasing the number of receivers in an SIMO 17 December 2003 Page 24

FLOWS IST-2001-32125 Deliverable No: D14 system also improves the performance significantly. In fact, SIMO system (1,6) is close to the MIMO system (3,6); however, this implies a constellation with 2048 points, while the MIMO system can achieve this capacity with 16 constellation points. MIMO links outperform SIMO links when practical modulations are used. The combination of adaptive modulation, aggressive frequency reuse and multiple antenna transmission can significantly increase the data throughput in a cellular system. 2.3 Frequency-selective channels Frequency-selective channels are more realistic than flat fading channels. Obviously, receivers operating in such channels require more complicated signal processing. Maximum-likelihood sequence estimation (MLSE) receivers are known to provide best performance; however, their complexity increases exponentially with the number of antennas and the channel memory. Therefore, a number of suboptimal schemes were proposed. Some of them we consider in this section. 2.3.1 Models of frequency-selective channels We describe a frequency-selective MIMO channel with nT transmit antennas and nR receive antennas as a discrete-time complex baseband model. Received signals are sampled at the symbol rate. The sampled impulse response from transmitter i to receiver j, including transmit and receive filters, is denoted by hij = [hij (0), hij (1),...,hij (L)]T . (2.11) The signal transmitted at time k is a nT × 1 vector s(k). The received vector y(k) is y(k) = nT i=1 Hisi(k) + n(k) (2.12) where n(k) is an nR × 1 additive white Gaussian noise vector with spatial covariance E{n(k)n(k)} = σ2 InR , (2.13) Hi is a channel matrix between i th transmit antenna and all receive antennas Hi = [hT 1i, hT 2i,..., hT nRi] T , (2.14) and si(k)=[si(k), si(k − 1),...,si(k − L)]T . (2.15) The signal-to-noise ratio for every receive antenna is defined by averaging over all possible channel realizations as ρj = Es nT σ2 nT i=1 E{|hij | 2 }. (2.16) A framework for modelling multi-antenna multipath channels based on the notion of virtual spatial angles has been proposed in [Say01]. The virtual angles are fixed a priori and are determined by the number of antennas at the transmitter and receiver and the spacing between the antennas. The model essentially corresponds to a coordinate transformation via fixed spatial basis functions at the transmitter and receiver. The advantage of this channel representation is that it provides a natural link between the physical propagation environment and the channel statistics induced by it, while beeing still a linear model. The model facilitates realistic estimates of channel capacity. 17 December 2003 Page 25

FLOWS IST-2001-32125 Deliverable No: D14 2.3.2 Capacity of multipath MIMO channels According to [RC98], the information capacity (in bits/transmission) for the discrete-time spatio-temporal communication channels is given by C(H, S) = 1 N K k=1 log2 1 + λk(S)|λk(H)| 2 σ2 (2.17) where H is the channel matrix with singular values λk(H), S is the matrix of transmitted symbols with singular values λk(S), σ2 is the noise variance, N is the length of a data block, and the dimension K defines the number of parallel spatio-temporal channels in the MIMO channel. The parameter K is bounded by K ≤ min (Nν,(N + L)nR,NnT ) (2.18) where ν is the number of multipaths created by reflections and scattering from physical objects and L is the maximum length of the channel impulse responses. Under the practical assumption N >> L, as the SNR increases the capacity slope for the MIMO channel approaches a constant ρ = min(ν, nR, nT ). If there is no multipath (ν = 1), then the high SNR capacity advantage of MIMO communication is limited as compared to SISO channels. If the multipath is severe, i.e. ν > min(nR, nT ), the capacity can be multiplied by adding antennas to both sides of the channel. This capacity improvement occurs with no penalty in average radiated power or frequency bandwidth. Results of measurement of MIMO channel capacity for 5.2-GHz band (HIPERLAN, or IEEE 802.11a) in micro-cellular environments were presented in [MST+02]. The method used for the measurements is based on first extracting parameters of multipath components (delays, directions of departure, directions of arrival, path amplitudes), and then obtaining different channel realisations by assigning random phases to the multipath components. Numbers of antenna elements varied from 1 to 8; cell size was approximately 30 m x 40 m; the frequency bandwidth was up to 100 MHz. It has been obtained that despite an almost uniform distribution of the path arrival and departure angles, the capacities are up to 30% lower than would be expected from the simple model. A relatively small number of multipath components, and especially the different powers carried by them, limits the channel capacity. When assigning equal powers to the multipath components, the capacities become very similar to the ”ideal” case. The frequency-selectivity of the channel adds additional diversity, so that the outage capacity becomes closer to the mean capacity. The measured outage capacity exhibited no significant increase if the inter- element spacing is increased above half of the wavelength. For 5.2-GHz the wavelength is 5.8 cm, i.e. in practice, we can position the antenna elements as close as 2.9 cm without affecting the channel capacity. 2.3.3 MIMO techniques for frequency-selective channels One of approaches to deal with the frequency-selectivity in MIMO channels is to partition the channel transfer functions between transmit and receive antennas into a large number of parallel (approximately) independent memoreless frequency subchannels and apply in each subchannel the techniques developed for flat fading channels. Computationally efficient FFT schemes can be used to implement such partitioning. This approach is especially useful for systems with multicarrier modulation, for example OFDM. The discrete matrix multitone (DMMT) combined with powerful codes was shown in [RC98] to allow achievement of the MIMO channel capacity. A cyclic prefix longer than the channel memory is inserted in every data block to eliminate the interference caused by the channel. If the length of channel impulse responses is long relative to the data block length, the long prefix reduces the system throughput. Another approach is to exploit a time-domain equalisation to shorten the channel memory [AD01, LP02]. 17 December 2003 Page 26