Multifunctional Mimo Systems: a Combined Diversity and Multiplexing Design Perspective

HANZO LAYOUT 4/8/10 12:55 PM Page 73

ACCEPTED FROM OPEN CALL

MULTIFUNCTIONAL MIMO SYSTEMS: A COMBINED DIVERSITY AND MULTIPLEXING DESIGN PERSPECTIVE

MOHAMMED EL-HAJJAR AND LAJOS HANZO, UNIVERSITY OF SOUTHAMPTON

ABSTRACT in demand for high-speed multimedia wireless X services. Advances in channel coding made it W 11 A In this treatise we investigate the design alter- feasible to approach Shannon’s capacity limit in natives of different multiple-input multiple-out- systems equipped with a single antenna [1], but put schemes while considering the attainable fortunately these capacity limits can be further X diversity gains, multiplexing gains, and beam- extended with the aid of multiple antennas. W 1LAA forming gains. Following a brief classification of Recently, multiple-input multiple-output Beamformer different MIMO schemes, where the different (MIMO) systems have attracted considerable MIMO schemes are categorized as diversity research attention and it is considered as one of techniques, multiplexing schemes, multiple the most significant technical breakthroughs in AA m1 access arrangements, and beamforming tech- contemporary communications. niques, we introduce the family of multifunction- Explicitly, MIMO schemes can be categorized al MIMOs. These multifunctional MIMOs are as diversity techniques, multiplexing schemes, AA (Nt-mK) capable of combining the benefits of several multiple access methods, and beamforming as MIMO schemes and hence attaining improved well as multifunctional MIMO arrangements, as performance in terms of both their bit error rate shown in Fig. 1. Diversity is the technique where X as well as throughput. The family of multifunc- the receiver receives several replicas of the same WN 1 tional MIMOs combines the benefits of both transmitted signal, while assuming that at least space-time coding and the Bell Labs layered some of them are not severely attenuated. Spa- The authors space-time scheme as well as those of beam- tial diversity can be attained by employing multi- forming. We also introduce the idea of layered ple antennas at the transmitter or the receiver. investigate the steered space-time spreading, which combines Multiple antennas can be used to transmit and design alternatives of the benefits of space-time spreading, V-BLAST, receive appropriately encoded replicas of the and beamforming with those of the generalized same information sequence in order to achieve different multiple- multicarrier direct sequence code-division multi- diversity and hence obtain an improved bit error ple access concept. Additionally, we compare the rate (BER) performance. On the other hand, input multiple-output attainable diversity, multiplexing, and beamform- multiplexing techniques were designed in order ing gains of the different MIMO schemes in to improve the attainable spectral efficiency of schemes while order to document the advantages of multifunc- the system by transmitting the signals indepen- tional MIMOs over conventional MIMO dent of each of the transmit antennas. In the considering the schemes. context of diversity and multiplexing techniques, attainable diversity the antennas are spaced as far apart as possible CLASSIFICATION OF MULTIPLE-INPUT so that the signals transmitted to or received by gains, multiplexing the different antennas experience independent MULTIPLE-OUTPUT SYSTEMS fading, and hence we attain the highest possible gains, and beam- diversity or multiplexing gain. Additionally, mul- Recently, there has been an urgent demand for tiple antennas can also be used in order to forming gains. flexible and bandwidth-efficient transceivers improve the signal-to-noise ratio (SNR) at the capable of supporting the explosive expansion of receiver or the signal-to-interference-plus-noise the Internet and the continued dramatic increase ratio (SINR) in a multi-user scenario. This can be achieved by employing beamforming techniques, where the antenna gain is increased in The financial support of Vodafone under the auspices of the direction of the desired user, whilst reducing the Dorothy Hodgkin postgraduate award and that of the the gain towards the interfering users. European Community under Seventh Framework Pro- A simple spatial diversity technique, which gramme grant agreement ICT OPTIMIX nINFSO-ICT- does not involve any loss of bandwidth, is consti- 214625 is gratefully acknowledged. tuted by the employmexnt of multiple antennas

at the receiver, where several techniques can be alize the concept of transmit diversity schemes employed for combining the independently fad- to more than two transmit antennas, contriving ing signal replicas. In case of narrowband fre- the generalized concept of orthogonal space- quency-flat fading, the optimum combining time block codes (OSTBCs). The family of OST- strategy in terms of maximizing the SNR at the BCs is capable of attaining the same diversity combiner output is maximum ratio combining gain as space-time trellis codes (STTC) [4] at (MRC). Additionally, other combining tech- lower decoding complexity when employing the niques have been proposed in the literature, as same number of transmit antennas. However, a shown in Fig. 1, including equal gain combining disadvantage of OSTBCs when compared to (EGC) and selection combining (SC). All three STTCs is that they employ unsophisticated repe- combining techniques are said to achieve full tition coding and hence provide no coding gain. diversity order, which is equal to the number of Furthermore, inspired by the philosophy of receive antennas. STBCs, Hochwald et al. [6] proposed the trans- On the other hand, several transmit — rather mit diversity concept known as space-time than receive — diversity techniques have also spreading (STS) for the downlink of wideband been proposed in the literature [2–5], as shown code-division multiple access (WCDMA) that is in Fig. 1. In [2] Alamouti proposed a witty trans- capable of achieving the highest possible transmit diversity technique using two transmit anten- mit diversity gain. nas, the key advantage of which was the Regretfully, the OSTBC and STS designs of employment of low-complexity single-receive- [3, 6] contrived for more than two transmit antenna-based detection, which avoids the more antennas result in a reduction of the achievable complex joint detection of multiple symbols. The throughput per channel use when complex-val- decoding algorithm proposed in [2] can be gen- ued constellations are used. An alternative idea eralized to an arbitrary number of receive anten- invoked for constructing full-rate STBCs for nas using MRC, EGC, or SC. Alamouti’s complex-valued modulation schemes and more achievement inspired Tarokh et al. [3] to gener- than two antennas was suggested in [7]. Here the strict constraint of perfect orthogonality was relaxed in favor of achieving a higher data rate. The resultant STBCs were referred to as quasi- MIMO techniques orthogonal STBCs [7]. The OSTBC and STS designs offer — at best — the same data rate as an uncoded single- Diversity techniques antenna system, but they provide improved BER performance compared to the family of single- Receive diversity antenna-aided systems, since they attain a diver- Maximum ratio combining (MRC) sity gain. In contrast to this, several high-rate space-time transmission schemes having a nor- Equal gain combining (EGC) malized rate higher than unity have been pro- Selection combining (SC) posed in the literature. For example, high-rate space-time codes that are linear in both space Transmit diversity and time, the family of so-called linear dispersion codes (LDCs), was proposed in [5]. LDCs STBC strike a flexible trade-off between emulating STS space-time coding and/or spatial multiplexing. STTC The attractive concept of LDCs invokes a matrix- based linear modulation framework, where each LDC space-time transmission matrix is generated by a Quasi-orthogonal STBC linear combination of so-called dispersion matri- ces, and the weights of the components are determined by the transmitted symbol vector. Multiplexing techniques OSTBCs and STTCs are capable of providing an attractive diversity gain for the sake of BLAST improving the achievable system performance. However, this BER performance improvement is Multiple access techniques often achieved at the expense of a rate loss, since OSTBCs and STTCs may result in a SDMA throughput loss compared to single-antenna- Beamforming techniques aided systems. As a design alternative, a specific class of MIMO systems was designed for improving the attainable spectral efficiency of the sys- Beamformers designed for SNR gain tem by transmitting different parallel signal Beamformers designed for interference suppression streams independently over each of the transmit antennas, hence resulting in a multiplexing gain. Beamforming techniques This class of MIMOs subsumes Bell Labs’ layered dpace-yime (BLAST) scheme and its rela- LSSTC tives [8]. The BLAST scheme aims to increasie LSSTS the system throughput in terms of the number of bits per symbol that can be transmitted in a given bandwidth at a given integrity. Figure 1. Classification of MIMO techniques. In contrast to the family of BLAST schemes,

74 IEEE Wireless Communications • April 2010 HANZO LAYOUT 4/8/10 12:55 PM Page 75

where multiple antennas are activated by a single user for increasing the user’s throughput, space-division multiple access (SDMA) [9] X W11 employs multiple antennas for the sake of sup- AA1 porting multiple users. SDMA exploits the unique user-specific channel impulse responses X (CIRs) of different users to separate their W received signals. 1LAA On the other hand, in beamforming arrange- Beamformer DOA B1 1 ments [9] typically λ/2-spaced antenna elements Rx1

are used for the sake of creating a spatially STC AA Rx2 selective transmitter/receiver beam, where λ rep- m1 resents the carrier’s wavelength. Beamforming is B employed for providing angular receiver selectiv- LSSTC

AA decoder ity by mitigating the effects of various interfering (Nt-mK) signals, provided that they arrive from sufficient- Serial-to-parallel converter RxN ly different angular directions. Additionally, BK r beamforming is capable of suppressing the K X

STC W effects of co-channel interference, hence allow- Nt1 ing the system to support multiple users by angu- AAN larly separating them. Again, this angular t X separation becomes feasible only on condition W that the corresponding users are separable in NtLAA terms of the angle of arrival of their beams. Beamformer DOA Finally, multifunctional MIMOs, as the term suggests, combine the benefits of several MIMO schemes including diversity gains, multiplexing Figure 2. Multi-functional MIMO system block diagram. gains, and beamforming gains. As mentioned earlier, V-BLAST is capable of achieving the maximum attainable multiplexing gain, while for attaining the maximum achievable multiplex- STBC may attain the maximum achievable ing gain equal to the number of transmit anten- antenna diversity gain facilitated by the number nas. Additionally, beamforming schemes have of independently fading diversity channels. been designed in order to attain an SNR gain. Hence, it was proposed in [10] to combine these Therefore, the appealing concept of multifunc- two techniques in order to provide both antenna tional MIMO schemes designed for combining diversity and spectral efficiency gains. On the the benefits of STBC, BLAST, and beamforming other hand, in [11] the authors presented a schemes arises in order to provide diversity, mul- transmission scheme referred to as double space- tiplexing, and SNR gains. time transmit diversity (D-STTD), which consists Figure 2 shows the block diagram of a gener- of two STBC layers at a transmitter equipped al multifunctional MIMO scheme that can com- with four transmit antennas, while the receiver is bine the benefits of space-time coding (STC), equipped with two antennas. Furthermore, in BLAST, and beamforming. The system’s archi- order to achieve additional performance gains, tecture seen in the figure has Nt transmit anten- beamforming has been combined with both spa- na arrays (AAs) spaced sufficiently far apart in tial diversity as well as spatial multiplexing tech- order to experience independent fading, and niques. STBC has been combined with hence achieve transmit diversity and/or multi- beamforming in order to attain an improved plexing. The LAA number of elements of each SNR gain in addition to the diversity gain [12, AA is spaced at a distance of λ/2 for the sake of 13]. achieving a beamforming gain. Furthermore, the This contribution provides a lighthearted per- receiver is equipped with Nr antennas. According spective on further research advances in the field to Fig. 2, a block of B input information symbols of multifunctional MIMO systems, and demon- is serial-to-parallel converted to K groups of strates how diversity, multiplexing, and beam- symbol streams of length B1, B2, …, BK, where forming gains are achieved by multifunctional B1 + B2 + … + BK = B. Each group of Bk sym- MIMOs. More explicitly, in the next section we bols, k ∈ [1,K], is then encoded by a component elaborate on the design of multifunctional space-time code STCk associated with mk trans- MIMO schemes and describe the evolution of mit AAs, where m1 + m2 + … + mK = Nt. the idea of multifunctional MIMO systems. We The STC employed can be OSTBC, STTC, or quantify the achievable performance of the dif- STS for the sake of attaining a diversity gain. ferent MIMO schemes. A comparison of the dif- The data transmitted from each component STC ferent MIMO schemes expressed in terms of is independent of the data transmitted from all their diversity, multiplexing, and beamforming the other STCs, which results in a multiplexing gains is then presented, followed by our conclu- gain, where the throughput of the multifunction- sions in the final section. al MIMO scheme is K times that of a scheme employing a single STC. The multiplexing gain is MULTIFUNCTIONAL MIMO SYSTEMS attained by considering each STC as a layer in a BLAST scheme. Furthermore, the data is trans- Space-time codes have been designed for the mitted using antenna arrays that can be used for sake of attaining the highest possible diversity attaining a beamforming gain. gain, while the V-BLAST scheme was designed In [10] a dual-functional MIMO scheme was

IEEE Wireless Communications • April 2010 75 HANZO LAYOUT 4/8/10 12:55 PM Page 76

One configuration proposed that combines the benefits of V- interference cancellation procedure can be gen- BLAST and OSTBC. The scheme presented in eralized to arbitrary Nt and K values. can employ two four- [10] considered transmissions over OSTBCs The proposed scheme is applicable to arbi- where several parallel OSTBC blocks were capa- trary STCs and an arbitrary number of layers K. antenna-aided STCs, ble of transmitting independent data. Hence, the For example, for Nt = 3 transmit antennas, a scheme of [10] was capable of attaining the twin-antenna-assisted STC can be employed in while another diversity gain of the OSTBC as well as the multi- parallel with a single-antenna-aided transmission configuration may plexing gain due to using several independent scheme. On the other hand, for a scheme OSTBC layers. However, a drawback of the employing Nt = 8 transmit antennas, several employ four twin- scheme in [10] was that the decoder implement- configurations can be considered. One configu- ed group successive interference cancellation ration can employ two four-antenna-aided STCs, antenna-aided STCs. (GSIC) that did not take into account the anten- while another configuration may employ four na-specific received signal power at the different twin-antenna-aided STCs. The favored configu- The favored OSTBC layers for the sake of ordering the layers ration will depend on the specific application as before interference cancellation. well as on the required performance and configuration will On the other hand, dual-functional MIMO throughput. schemes that combine STBC with beamforming The LSSTC scheme is characterized by a depend on the were proposed in [12, 13]. These schemes bene- diversity gain, a multiplexing gain, and a beam- specific application fit from the diversity gain of the STBCs and the forming gain. However, a drawback of the SNR gain of the beamformer. In [12] the authors LSSTC design is the fact that the number of as well as on the combined conventional transmit beamforming receive antennas Nr should be at least equal to with OSTBC, assuming that the transmitter has the number of transmit antennas Nt for the required performance partial knowledge of the channel, and derived a interference canceller to work. This condition is performance criterion for improving the system not very practical for employing shirt-pocket- and throughput. performance. Furthermore, the scheme present- sized mobile stations (MS) that are limited in ed in [13] combined the twin-antenna-aided size and complexity. The LSSTC scheme can be Alamouti STBC with ideal beamforming, where applied in a scenario where two base stations it was assumed that the transmitter has full (BS) cooperate or a BS is communicating with a knowledge of the channel as well as the signal’s MIMO-aided laptop. Therefore, in order to direction of arrival at the receiver in order to allow communication between a BS and an MS show that the system can attain better perfor- accommodating fewer antennas than the trans- mance while attaining the maximum achievable mitting BS while employing simple linear diversity order at a unity rate. receivers, [11] presented a four-transmit two- Inspired by the performance improvements receive antenna aided scheme that combined the reported in [10, 12, 13], El-Hajjar et al. proposed benefits of Alamouti’s STBC [2] and V-BLAST in [14] a trifunctional MIMO scheme that com- [8]. The scheme of [11] was referred to as bines diversity gain with multiplexing gain and DSTTD and employed a simple linear decoder beamforming gain. The MIMO scheme of [14] that used fewer antennas than the transmitter. was referred to as a layered steered space-time The DSTTD receiver employed a two-stage code (LSSTC), where the parallel data streams decoding algorithm, where the first stage was were encoded by OSTBC layers, and each layer interference cancellation, in order to cancel any might have a different OSTBC structure. Addi- interference imposed by each STBC layer on the tionally, the decoder of the LSSTC scheme other layer. The second decoding stage involved employed an ordering strategy for decoding the the maximum likelihood decoding of the STBC different layers in order to improve the achiev- [2]. able performance. Furthermore, in order to allow multiple users The decoder of the LSSTC scheme may apply to communicate employing a multifunctional GSIC based on the classic Zero Forcing (ZF) MIMO, the layered steered space-time spread- algorithm [10] for decoding the received signal. ing (LSSTS) scheme described below can be The most beneficial decoding order of the STC employed. The LSSTS scheme combines the layers is determined on the basis of detecting the benefits of V-BLAST, STS, and beamforming highest-power layer first for the sake of high cor- with generalized multicarrier direct sequence rect detection probability. For simplicity, let us CDMA (MC DS-CDMA) [15] for the sake of consider the case of K = 2 OSTBC layers, where achieving a multiplexing gain, a spatial and fre- layer 1 is detected first, which allows us to elimi- quency diversity gain, and a beamforming gain. nate the interference caused by the signal of The LSSTS design employs Nt = 4 transmit layer 2. However, the proposed concept is appli- antennas as well as Nr = 2 receive antennas and cable to arbitrary STCs and to an arbitrary num- a linear receiver to decode the received signal. ber of layers K. For this reason, the decoder of The system architecture of the LSSTS scheme layer 1 has to suppress the interference of layer can be seen in Fig. 2 with STS used as the com- 2 originally imposed on layer 1 and generate a ponent STC layers. The LSSTS scheme employs signal that can be decoded using the STBC two twin-antenna-aided STS layers and Nr = 2 detector of [2]. This may be achieved by using receive antennas. The LAA numbers of elements the GSIC algorithm proposed in [10]. Then the of each AA are spaced at a distance of λ/2 for decoder subtracts the remodulated contribution the sake of achieving beamforming. The system of the decoded symbols of layer 1 from the com- can support L users transmitting at the same posite twin-layer received signal. Finally, the time over the same carrier frequencies, because decoder applies direct STBC decoding to the they can be differentiated by the user-specific — second layer, since the interference imposed by spreading code cl, where l ∈ [1,L]. Additionally, the first layer has been eliminated. This group in the generalized MC DS-CDMA system con-

76 IEEE Wireless Communications • April 2010 HANZO LAYOUT 4/8/10 12:55 PM Page 77

sidered, the subcarrier frequencies are arranged to guarantee that the same STS signal is spread (1Tx, 1Rx) V-BLAST (4Tx, 4Rx) to and hence transmitted by the specific subcar- STBC (2Tx, 1Rx) LSSTC (4Tx, 4Rx) 1 STBC (4Tx, 4Rx) riers having the maximum possible frequency LAA=1 separation so that they experience independent LAA=4 fading and achieve the maximum attainable fre- LSSTS (4Tx, 2Rx) -1 quency diversity. 10 LAA=1 V=1 The LSSTS system employs the generalized V=4 MC DS-CDMA scheme of [15], where the input data is serial-to-parallel converted to two paral- 10-2

lel streams that are transmitted using twin- BER antenna-aided STS [6]. The transmitted signal is spread to the two transmit antennas with the aid 10-3 — — of the orthogonal spreading codes of {cl,1 cl,2}, l — — = 1, 2, …, L. The spreading codes cl,1 and cl,2 are generated from the same user-specific 10-4 — spreading code cl as in [6]. The output of the two STS blocks modulate a group of subcarriers, where the subcarrier sig- 10-5 nals are superimposed on each other in order to -10 -5 0 5 10 15 20 25 30 35 40 form the complex-valued modulated signal for Eb/N0 [dB] transmission. Finally, according to the lth user’s channel information, the signal of the lth user is Figure 3. BER performance comparison of the SISO, STBC, V-BLAST, weighted by the transmit beamformer weight LSSTC, and LSSTS schemes, while communicating over a correlated vector determined for each subcarrier of the lth Rayleigh fading channel associated with a normalized Doppler frequency of user, which is generated for the nth AA. Assum- fd = 0.01. ing that the system employs a modulation scheme transmitting D b/symbol, the bandwidth efficiency of the LSSTS aided generalized MC lar, which suggests that V-BLAST does not attain DS-CDMA system is given by 2D b/channel use. a high diversity gain, but is capable of attaining a Assuming that the K users’ data are transmit- high multiplexing gain. Additionally, Fig. 3 shows ted synchronously over a dispersive Rayleigh that the STBC system employing (Nt,Nr) = (2,1) fading channel, decoding is carried out in two attains better BER performance than the SISO steps. First, interference cancellation is per- and V-BLAST schemes due to the diversity gain formed according to [11], followed by the STS attained by the STBC. Further diversity gain can decoding procedure of [6]. Finally, after combin- be attained by the four-antenna-aided STBC ing the l = 1st user’s identical replicas of the employing four receive antennas, which results in same signal transmitted by spreading over the a diversity order of 16. As shown in Fig. 3, the number of subcarriers, the decision variables four-antenna-aided STBC scheme employing corresponding to the symbols PV transmitted in four receive antennas is capable of attaining ~ V ~ –5 each subblock can be expressed as x1 = ∑v=1 x1,v, around 15 dB gain at a BER of 10 over the where V is the number of subcarriers employed twin-transmit-antenna-aided STBC system using by the generalized MC DS-CDMA. Therefore, Nr = 1. However, a drawback of the four-anten- the decoded signal has a diversity order of 2V. na-aided system, while employing complex-valued More explicitly, second order spatial diversity is constellations, is that it results in a throughput attained from the STS operation, and a diversity loss where four symbols are transmitted in eight order of V is achieved as a benefit of spreading time slots, resulting in a rate of 1/2. by the generalized MC DS-CDMA scheme, Observe in Fig. 3 that the LSSTS scheme where the subcarrier frequencies are arranged in employing (Nt,Nr) = (4,2) and V = 1 attains such a way as to guarantee that the same STS identical BER performance to that of the twin- signal is spread to and hence transmitted by the transmit-antenna-aided STBC system. This specific V number of subcarriers having the max- means that the LSSTS scheme employing V = 1 imum possible frequency separation, so they has a diversity order of 2 similar to the twin- experience as independent fading as possible. antenna-aided STBC. On the other hand, the LSSTS scheme attains twice the throughput of RESULTS AND DISCUSSION the twin-transmit-antenna- aided STBC scheme. In this section we compare the BER perfor- Additionally, when V is increased from 1 to 4, mance of the different MIMO schemes to that the achievable BER performance improves due of the classic single-input single-output (SISO) to the additional frequency diversity gain system. We compare binary phase shift keying attained. (BPSK) modulated systems, while considering A further performance improvement is transmissions over correlated Rayleigh fading attained by the LSSTC scheme in conjunction channels associated with a normalized Doppler with (Nt,Nr) = (4,4) compared to the LSSTS frequency of 0.01. scheme. The LSSTC scheme employs more According to Fig. 3, the V-BLAST system antennas than the LSSTS scheme and hence employing (Nt,Nr) = (4,4) antennas has slightly attains both a higher diversity order as well as better BER performance than the SISO system, better BER performance. Furthermore, Fig. 3 despite its quadrupled throughput. Also observe shows the performance improvements attained in Fig. 3 that the slope of the BER curves of by beamforming, where the LSSTC scheme both the V-BLAST and SISO systems are simi- employing LAA = 4 attains around 6 dB perfor-

IEEE Wireless Communications • April 2010 77 HANZO LAYOUT 4/8/10 12:55 PM Page 78

The design of the Number Diversity Multiplexing Beamforming Nt Nr LAA V multi-functional of layers order order gain MIMO scheme will 2 Nr 1 1 1 2 × Nr 1 1

depend on the OSTBC 4 Nr 1 1 1 4 × Nr 1/2 1 application 8 Nr 1 1 1 8 × Nr 1/2 1 considered and on 2 2 1 1 2 1 2 1 the number of V-BLAST 4 4 1 1 4 1 4 1 antennas that can be ZF-SIC afforded on the 8 8 1 1 8 1 8 1

transmitter and 4 4 LAA 1 2 4 2 LAA

receiver. LSSTC 8 8 LAA 1 2 16 1 LAA

8 8 LAA 1 4 4 4 LAA

LSSTS 4 2 LAA V 2 2 × V 2 LAA

Table 1. Comparison of the gains achieved by various MIMO schemes.

mance improvement at a BER of 10–5 over its Table 1 compares the diversity, multiplexing, counterpart employing LAA = 1, provided that and beamforming gains of the different MIMO the direction of arrival (DOA) is perfectly schemes for different configurations. In Table 1 known. Finally, a comparison between the STBC Nt and Nr stand for the number of transmit and and LSSTC schemes using (Nt,Nr) = (4,4) reveals receive antennas, respectively, while LAA repre- that the STBC arrangement attains better per- sents the number of elements per transmit AA formance than the LSSTC scheme employing and V denotes the number of subcarriers LAA = 1. This is due to the fact that the STBC employed by the generalized MC DS-CDMA sys- scheme has a higher diversity gain, while the tem. Additionally, the number of layers repre- LSSTC scheme attains a throughput four times sents the number of antenna layers used for that of its STBC counterpart. transmitting different data symbols at the same Therefore, the design of the multifunctional time for the sake of attaining a multiplexing gain. MIMO scheme will depend on the application As shown in Table 1, the OSTBC schemes considered and the number of antennas that can are capable of attaining a full diversity order of be afforded on the transmitter and receiver. For (Nt × Nr), while achieving no multiplexing or example, as mentioned previously, for a hand- beamforming gain. In contrast, in the case of held device the LSSTC scheme is not a practical four- and eight-antenna-aided OSTBC schemes choice due to the limited size and complexity of employing complex-valued constellations, the the small device. On the other hand, the LSSTS multiplexing gain is 1/2, resulting in half the scheme can be considered a good choice for a throughput of the SISO scheme. For example, in system with a small-sized receiver that requires the four-antenna-aided OSTBC scheme, four high robustness and throughput. symbols are transmitted in eight time slots; simi- larly for the eight-antenna aided STBC scheme, eight complex-valued symbols are transmitted in DIVERSITY AND MULTIPLEXING OF 16 time slots. On the other hand, as shown in MIMO SYSTEMS Table 1, the V-BLAST scheme can attain a multiplexing gain of Nt, since the different antennas According to our previous discussions, different transmit different symbols in the same time slot. MIMO schemes have different structures and For example, for the V-BLAST scheme employ- hence different BER as well as throughput per- ing (Nt,Nr) = (4,4), the transmitter transmits formance. Explicitly, the OSTBC scheme is four different symbols from the four different capable of attaining the highest possible spatial antennas in the same time slot, which results in a diversity gain while having no multiplexing gain; quadrupled multiplexing gain in comparison to in fact, some STBC structures result in through- that of the SISO scheme. Observe in Table 1 put loss. On the other hand, the V-BLAST that the diversity order of V-BLAST employing scheme is capable of achieving the maximum ZF-SIC is 1 for different (Nt,Nr) configurations. possible multiplexing gain while attaining low The diversity order of the V-BLAST scheme diversity gain, depending on the choice of V- employing ZF-SIC is (Nr – Nt + 1). BLAST decoder employed. Furthermore, several The LSSTC scheme combines the benefits of multifunctional MIMO schemes that can attain a STBC, V-BLAST, and beamforming, as dis- combination of diversity, multiplexing, and cussed earlier. This becomes clear in Table 1, beamforming gains have been introduced. where it is shown that the LSSTC scheme attains

78 IEEE Wireless Communications • April 2010 HANZO LAYOUT 4/8/10 12:55 PM Page 79

a diversity gain, a multiplexing gain, and a beam- [5] B. Hassibi and B. M. Hochwald, “High-Rate Codes that A comparison forming gain. In the case of the (N ,N ) = (4,4) Are Linear in Space and Time,” IEEE Trans. Info. Theory, t r vol. 48, July 2002, pp. 1804–24. configuration, two twin-antenna STBC layers are [6] B. Hochwald, T. L. Marzetta, and C. B. Papadias, “A between the BER implemented, which results in a diversity order Transmitter Diversity Scheme for Wideband CDMA Sys- of 4 and a multiplexing order of 2. This is due to tems Based on Space-Time Spreading,” IEEE JSAC, vol. performance as well the fact that four symbols are transmitted from 19, no. 1, 2001, pp. 48–60. [7] H. Jafarkhani, “A Quasi-Orthogonal Space-Time Block the four transmit antennas in two time slots. Code,” IEEE Trans. Commun., vol. 49, no. 1, 2001, pp. 1–4. as the diversity, Additionally, when LAA elements are used per [8] P.W. Wolniansky et al., “V-BLAST: An Architecture for AA, a beamforming gain can be attained. In the Realizing Very High Data Rates over the Rich-Scattering multiplexing, and (N ,N ) = (8,8) configuration, two different Wireless Channel,” Int’l. Symp. Signals, Sys., Electronics, t r Pisa, Italy, Sept. 1998, pp. 295–300. beamforming gains schemes can be implemented. The first scheme [9] L. Hanzo, J. Blogh, and S. Ni, 3G, HSPA and FDD versus is a two-layer one with each layer consisting of a TDD Networking: Smart Antennas and Adaptive Modu- of the different four-antenna STBC scheme. The other configu- lation, Wiley-IEEE Press, 2008. ration employs four layers of the twin-antenna [10] V. Tarokh et al., “Combined Array Processing and Space-Time Coding,” IEEE Trans. Info. Theory, vol. 45, MIMO schemes STBC scheme. The two configurations result in no. 4, 1999, pp. 1121–28. the different diversity and multiplexing gains [11] E. N. Onggosanusi, A. G. Dabak, and T. A. Schmidl, reveals that multi- shown in Table 1. “High Rate Space-Time Block Coded Scheme: Perfor- Finally, in the LSSTS scheme four transmit mance and Improvement in Correlated Fading Chan- functional MIMOs nels,” IEEE WCNC, vol. 1, Mar. 2002, pp. 194–99. and two receive antennas are employed, where [12] G. Jongren, M. Skoglund, and B. Ottersten, “Combin- are capable of the transmit antennas are separated into two ing Beamforming and Orthogonal Space-Time Block STS layers. The diversity order achieved by the Coding,” IEEE Trans. Info. Theory, vol. 48, Mar. 2002, attaining an improved LSSTS scheme is (2 V) as discussed earlier. pp. 611–27. × [13] J. Liu and E. Gunawan, “Combining Ideal Beamform- The multiplexing order of the LSSTS scheme is ing and Alamouti Space-Time Block Codes,” Elect. Lett., performance over 2, since four symbols are transmitted in two time vol. 39, Aug. 2003, pp. 1258–59. slots. Moreover, the LSSTS scheme is capable of [14] L. Hanzo et al., Near-Capacity Multi-Functional MIMO the now classic attaining a beamforming gain when L > 1 ele- Systems: Sphere-Packing, Iterative Detection and Coop- AA eration, Wiley-IEEE Press, 2009. stand-alone STBC ments per AA are used. [15] L.-L. Yang and L. Hanzo, “Performance of Generalized Multicarrier DS-CDMA over Nakagami-m Fading Channels,” and V-BLAST CONCLUSION IEEE Trans. Commun., vol. 50, June 2002, pp. 956–66. schemes. In this article a brief classification of the family BIOGRAPHIES of MIMO schemes is presented based on their MOHAMMED EL-HAJJAR received his B.Eng. degree (with distinction) in electrical engineering from the American Uni- attainable diversity, multiplexing, and beamform- versity of Beirut (AUB), Lebanon, and an M.Sc. degree ing gains. We also investigate the design of the (with distinction) in radio frequency communication sys- novel class of multifunctional MIMO schemes tems from the University of Southampton, United King- that are capable of combining the benefits of dom. Since October 2005 he has been working toward his several MIMO schemes and hence attaining Ph.D. degree with the Communications Group, School of Electronics and Computer Science, University of Southamp- diversity, multiplexing, and beamforming gains. ton. He is the recipient of several academic awards from More explicitly, we introduce the dual-functional AUB as well as the University of Southampton. His research MIMO scheme of [10] followed by the LSSTC interests include sphere packing modulation, space-time scheme that combines the benefits of STBC, V- coding, differential space-time spreading, adaptive transceiver design, and cooperative communications. In BLAST, and beamforming. Then we discuss the 2008 he completed his Ph.D. thesis and joined Ensigma in design of the DSTTD followed by the LSSTS Chepstow, Wales, United Kingdom as a wireless system arrangement that combines the advantages of architect. STS, V-BLAST, and beamforming with those of LAJOS HANZO [F] ([email protected]), FREng, FIET, received generalized MC DS-CDMA while supporting his degree in electronics in 1976, his doctorate in 1983, multiple users. Finally, a comparison between and his D.Sc. degree in 2004. During his 34-year career in the BER performance as well as the diversity, telecommunications he has held various research and aca- multiplexing, and beamforming gains of the dif- demic posts in Hungary, Germany, and the United King- dom. Since 1986 he has been with the School of Electronics ferent MIMO schemes reveals that multifunc- and Computer Science, University of Southampton, where tional MIMOs are capable of attaining improved he holds the chair in telecommunications. He has co- performance over the now classic standalone authored 19 Wiley-IEEE Press books on mobile radio com- STBC and V-BLAST schemes. munications totaling in excess of 10,000 pages, published 684 research papers at IEEE Xplore, acted as TPC Chair of IEEE conferences, presented keynote lectures, and been REFERENCES awarded a number of distinctions. Currently he is directing [1] L. Hanzo, T. H. Liew, and B. L. Yeap, Turbo Coding, an academic research team working on a range of research Turbo Equalisation and Space Time Coding for Trans- projects in the field of wireless multimedia communica- mission over Fading Channels, Wiley-IEEE Press, 2002. tions sponsored by industry, the Engineering and Physical [2] S. M. Alamouti, “A Simple Transmit Diversity Technique Sciences Research Council (EPSRC) United Kingdom, the for Wireless Communications,” IEEE JSAC, vol. 16, no. European IST Program, and the Mobile Virtual Centre of 8, 1998, pp. 1451–58. Excellence (VCE), United Kgindom. He is an enthusiastic [3] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space- supporter of industrial and academic liaison, and he offers time Block Codes from Orthogonal Designs,” IEEE a range of industrial courses. He is also an IEEE Distin- Trans. Info. Theory, vol. 45, no. 5, 1999, pp. 1456–67. guished Lecturer as well as a Governor of both the IEEE [4] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-Time Communications Society and the VTS. He is the acting Edi- Codes for High Data Rate Wireless Communication: Perfor- tor-in-Chief of IEEE Press. For further information on mance Criterion and Code Construction,” IEEE Trans. Info. research in progress and associated publications please Theory, vol. 44, Mar. 1998, pp. 744–65. refer to http://www-mobile.ecs.soton.ac.uk.

IEEE Wireless Communications • April 2010 79