2864 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 6, JULY 2011 Transmit-Diversity-Assisted Space-Shift Keying for Coocated and Distributed/Cooperative MIMO Eements Du Yang, Chao Xu, Student Member, IEEE, Lie-Liang Yang, Senior Member, IEEE,and Lajos Hanzo, Feow, IEEE Abstract Space-shift keying (SSK) moduation is a recenty proposed mutipe-input mutipe-output (MIMO) technique, which activates ony a singe transmit antenna during each time sot and uses the specific index of the activated transmit antenna to impicity convey information Activating a singe antenna is beneficia in terms of eiminating the interchanne interference and mitigates the peak-to-mean power ratio whie avoiding the need for synchronization among transmit antennas However, this benefit is achieved at a sacrifice, because the transmit diversity gain potentia of the mutipe transmit antennas is not fuy expoited in existing SSK-assisted systems Furthermore, a high-ssk throughput requires the transmitter to empoy a high number of transmit antennas, which is not aways practica Hence, we propose four agorithms open-oop space time space-shift keying (ST-SSK), cosed-oop feedback-aided phase rotation, feedback-aided power aocation, and cooperative ST-SSK to achieve a diversity gain The performance improvements of the proposed schemes are demonstrated by Monte Caro simuations for spatiay independent Rayeigh fading channes Their robustness to channe estimation errors is aso considered We advocate the proposed ST-SSK techniques, which can achieve a transmit diversity gain of about 10 db at a bit error rate (BER) of 10 5, at the cost of imposing a moderate throughput oss that is dedicated to a modest feedback overhead Furthermore, our proposed ST-SSK scheme ends itsef to efficient communication, because the deeterious effects of deep shadow fading no onger impose spatia correation on the signas that are received by the antennas, which cannot readiy be avoided by coocated antenna eements Index Terms Ampify and forward (AF), feedback, phase rotation, power aocation, space-shift keying (SSK), space time, transmit diversity can particuary be usefu for communication systems that rey on distributed antennas in cooperative communication 2) It circumvents the spatia antenna correation that is imposed by the deeterious effects of deep shadow fading, which cannot readiy be avoided by the cassic STBC schemes using coocated antenna eements 3) It eiminates the interchanne interference among transmit antennas, mitigates the peak-to-mean enveope ratio, and achieves fu receiver diversity through ow-compexity singe-stream [1] rather than mutistream receivers [9], [10] 4) It is robust to channe estimation errors at the receiver side [1], because it is not the actua channe reaization but the differences between channes associated with the different transmit antennas, which determines the bit-error-rate (BER) performance The nove contribution of this paper is that we proposed the foowing three agorithms to achieve transmit diversity for SSK moduation: 1) an open-oop space time space-shift keying (ST-SSK) scheme; 2) a feedback-aided phase rotation scheme, and 3) another cosedoop scheme that uses feedback-aided power aocation 1 Furthermore, we proposed an ampify-and-forward (AF)-reaying-aided cooperative ST-SSK scheme to avoid the empoyment of a high number of transmit antennas at the cooperating nodes, which aowed us to mitigate the potentia performance degradation caused by deep shadow fading This paper is organized as foows The origina SSK scheme in [1] is briefy introduced in Section II The proposed transmit-diversityassisted SSK moduation schemes are detaied in Section III Our simuation resuts are provided in Section IV, foowed by our concusions in Section V I INTRODUCTION Space-shift keying (SSK) moduation, which uses the specific index of the activated transmit antennas to impicity convey information, was proposed by Jeganathan et a [1] This idea may be traced back to [2], which was then further deveoped into spatia moduation (SM) by Meseh and Haas [3], [4] Compared with the conventiona mutipeinput mutipe-output (MIMO) schemes [5], eg, space time bock coding (STBC) [6], the Vertica Be Laboratories Layered Space Time (V-BLAST) scheme [5], spatia-division mutipe access (SDMA) [7], and beamforming [8], SSK moduation activates ony a singe transmit antenna at each symbo instant and has the foowing advantages 1) It avoids synchronization among transmit antennas, because ony a singe antenna is activated during a time sot This feature Manuscript received August 26, 2010; revised November 23, 2010, February 10, 2011, and Apri 18, 2011; accepted May 12, 2011 Date of pubication June 13, 2011; date of current version Juy 18, 2011 This work was supported in part by the Research Councis UK through the India UK Advanced Technoogy Centre, by the Engineering and Physica Sciences Research Counci through the China UK Science Bridge, and by the European Union through the CONCERTO Project The review of this paper was coordinated by Dr D W Matoak The authors are with the Schoo of Eectronics and Computer Science, University of Southampton, SO17 1BJ Southampton, UK (e-mai: dy05r@ ecssotonacuk; cx1g08@ecssotonacuk; y@ecssotonacuk; h@ecssoton acuk) Coor versions of one or more of the figures in this paper are avaiabe onine at http://ieeexporeieeeorg Digita Object Identifier 101109/TVT20112157185 II PRELIMINARIES: SPACE-SHIFT KEYING MODULATION Without any oss of generaity, we wi focus our attention on the (N Tx 1)-eement MISO systems, which are iustrated in Fig 1 The extension of our resuts to systems with more than one receive antenna is straightforward A random sequence of independent bits a =[a 1,,a Na ] enters the channe encoder, which produces the vector c =[c 1,,c Nc ],wheren a and N c represent the number of channe encoder input and output bits, respectivey The resuting coding rate r c becomes r c = N a /N c The pseudo randomy intereaved encoded bits Π(c) then enter an SSK bit-to-symbo mapper A group of m =og 2 N Tx bits is then mapped to a consteation vector x with ony a singe nonzero eement me b at the jth position, which is formuated as ] T [ 0 0 meb 0 0 x = jth position (1) where E b represents the average energy of a singe bit Athough the symbo x j = me b does not contain any information, its ocation does Hence, ony the jth transmit antenna wi be activated for transmission The moduated signa is then transmitted over the N Tx - eement wireess channe h, which is contaminated by the additive white Gaussian noise (AWGN) n CN(0,N 0 ),wheren 0 represents the noise variance The received signa is given by y = hx + n 1 The opportunistic power-aocation-assisted SSK proposed for systems with two transmit antennas in [11] may be considered a specia case of our scheme 0018-9545/$2600 2011 IEEE
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 6, JULY 2011 2865 Fig 1 SSK-moduation-aided MISO system with N Tx transmit and a singe receiver antenna Assuming that the channe vector h is perfecty known, the index of the activated antenna ĵ is determined by [12] ( ) ĵ =argmin y me b h j 2 j =argmax j (2 me b R ( h Hj y ) me b h i 2 ) (2) Given the knowedge of the SSK bit-to-symbo mapping rues, the transmitted information sequence is estimated and then correspondingy deintereaved and decoded III TRANSMIT-DIVERSITY-ASSISTED SPACE-SHIFT KEYING MODULATION A Open Loop: ST-SSK for N Tx > 2 The proposed ST-SSK scheme uses L time sots to transmit m =og 2 N Tx bit sequences a i At the th (1 L) time sot, the f(t, a i )th (1 f(t, a i ) N Tx ) transmit antenna is activated according to the information sequence a i, which is formuated as y t 1 h f(t1,a i ) n t 1 y t me b = h f(t,a L i ) + n t (3) y t L n t L h f(tl,a i ) Upon defining y =[y t 1,,y t L] T and h f (ai ) =[h f(t1,a i ),, h f(tl,a i )] T, the transmitted sequence â i is determined at the receiver side according to â i =argmin a i =argmin a i y L h f (a i ) me b y me b t L h f(t,a i ) 2 2 2 (4) Before considering the design of the bit-to-antenna mapping function f(t, a i ), et us first prove the foowing two propositions Proposition 1: For an (N Tx 1) ST-SSK-moduation-aided system that uses L time sots, the transmit diversity order of L is achieved if and ony if, for any two bit sequences a i and a j (i j) and for any two time instances and n ( n), the foowing conditions are satisfied 1) The indices of the antennas that are activated to signa the bit sequence a i and a j are different from each other at any time sot, which is formuated as f(t, a i ) f(t, a j ) 2) When transmitting a i and a j, the difference between the activated channes channe impuse response (CIR) taps at the th time sot, which is denoted by Δh t = h f(t,a i ) h f(t,a j ), must be a random variabe, which is independent of the CIR taps during the nth time sot, that is represented as Δh tn = h f(tn,a i ) h f(tn,a j ) Proof: Transmitting the bit sequences a i and a j (i j), the Eucidean distance between the corresponding received signas without noise is formuated as me b d = hf (ai ) h f (aj ) L F = me b L = me b L hf(t,a i ) h f(t,a j ) Δh t 2 (5) A diversity order of L is achieved if and ony if Δh t, [1,L] are independent compex-vaued Gaussian variabes As a resut, i j, n, i, j [1,N Tx ],, n [1,L], wehavef(t, a i ) f(t, a j ), and h f(t,a i ) h f(t,a j ) must be independent of h f(tn,ai ) h f(tm,aj ) Proposition 2: For an (N Tx 1) ST-SSK-moduation-aided system, the maximum achievabe transmit diversity order cannot be higher than (N Tx 1) Proof: Assume that we have L = N Tx when a transmit diversity order of N Tx is achieved According to Proposition 1, the Eucidean distance d between a i and a j is a sum of N Tx independent Δh t vaues However, for N Tx transmit antennas, there are at most (N Tx 1) independent Δh vaues Hence, achieving a diversity order that is higher than (N Tx 1) becomes impossibe Let us now consider the design of the bit-to-antenna mapping function We propose a shift-mapping function f s (t, a i ) for scenarios with an even number of time sots and propose what we refer to as a shift-swap-mapping function f s w (t, a i ) for scenarios with an odd 2
2866 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 6, JULY 2011 TABLE I EXAMPLE OF THE ACTIVATED TRANSMIT ANTENNA WHEN (a) N Tx =3, N Rx =1USING SHIFT BIT-TO-ANTENNA MAPPING f s(, a i ) AND (b) N Tx =4,N Rx =1USING SHIFT SWAP BIT-TO-ANTENNA MAPPING f s w (, a i ) AND THE SHIFT MAPPING f s(, a i ) propose a scheme that is particuary for N Tx =2, which feeds back a phase vaue from the receiver to the transmitter to maximize the Eucidean distance d min = d = E b h 1 h 2 and, hence, achieve transmit diversity The objective function that is used for our design may be written as arg max d 2 min =argmax h 1 h 2 e j 2 =argmax h 1 2 + h 2 2 2R ( h H 1 h 2 e j) =argminr ( h H 1 h 2 e j) =argminr ( h H 1 h ) 2 e j(+φ) (6) where we have h H 1 h 2 = h H 1 h 2 e jφ Expicity, the minimum of (6) is achieved for number of time sots More expicity, the agorithms are described as foows 1) f s (t, a i ) when N Tx > 2 and L is an even number Set v =[1, 2,,N Tx ] Set [f(t, a 1 ),f(t, a 2 ),,f(t, a NTx )] = Shift(v, 1), where Shift(v, 1) represents a eft circuar shift of ( 1) positions 2) f s w (t, a i ) when N Tx > 2 and L is an odd number Create a shift-mapping function foowing the aforementioned steps Randomy group the ast (N Tx )/2 bit sequences (a (NTx /2)+1,,a NTx ) into (N Tx )/4 pairs Within each pair, eg, a (NTx /2)+1 and a (NTx /2)+2 grouped as a pair, swap the mapping resuts of f(t, a (NTx /2)+1) and f(t, a (NTx /2)+2) for a (N Tx /2) The exampes of the activated transmit antenna index for N Tx =3 using the shift mapping of f s (t, a i ) and for N Tx =4 using the shift swap bit-to-antenna mapping of f s w (t, a i ) are shown in Tabe I, respectivey The shift-mapping resuts for N Tx =4 are aso shown in Tabe I within the brackets The proposed bit-to-antenna mapping functions have guaranteed that the transmit diversity order of L is achieved if we have L (N Tx 1) The proposed ST-SSK scheme may be modeed using the same structure as the orthogona STBC [13] or the unitary space time moduation [14], [15], which is given by the product of the channe matrix and an (N Tx L)-eement coding matrix denoted as C However, for our ST-SSK scheme, every coumn vector of C contains ony a singe nonzero eement, which is different from the other two schemes More importanty, the coding matrix C that is conceived for our ST-SSK scheme varies according to the input information vector a i By contrast, for the other two schemes, the coding matrix is constant and is designed offine As a resut, athough the ST-SSK scheme is inferior to the conventiona STBC schemes in terms of throughput, it retains the beneficia properties of the origina SSK moduation, eg, ow compexity that is achieved in the absence of interantenna synchronization, which is beneficia in cooperative/distributed MIMOs, as mentioned in the Introduction B Cosed Loop: Feedback-Aided Phase Rotation for N Tx =2 Based on Proposition 2, it is now pausibe that, using the open-oop ST-SSK moduation scheme proposed in Section III-A, we can ony achieve a transmit diversity order of one for N Tx =2, because there is ony an N Tx 1=1independent Δh vaue In this section, we + φ =(2k +1)π, k Z (7) As a resut, the Eucidean distance becomes d = E b ( h 1 + h 2 ) due to having two independent channe gains Hence, a transmit diversity order of two is achieved In fact, as ong as we have R(h H 1 h 2 e j ) > 0, a diversity order of two can be guaranteed Moreover, is expected to have a uniform distribution between 0 and 2π A scaar quantizer with uniformy distributed quantization eves constitutes an adequate yet ow-compexity quantizer design C Cosed Loop: Feedback-Aided Power Aocation Our proposed feedback-aided power aocation scheme is detaied as foows First, the channe s fading coefficients h j associated with different transmit antennas are estimated at the receiver side Second, the transmit antenna with the owest channe gain is identified at the receiver, and its index is fed back to the transmitter using og 2 N Tx bits Upon receiving the feedback information, the transmitter wi aocate zero power to the antenna with the owest channe gain and increase the power that is aocated to other antennas from a vaue of me b to me b +(me b /N Tx 1) For exampe, two bits [0 0] wi be fed back to the transmitter if we have h 1 < h i, 1 <i 4 for a system with four transmit antennas and a singe receive antenna The power that is aocated to the first transmit antenna is zero, whereas the power for the other antennas is increased from 2E b to (2 + (2/3))E b The proposed scheme deactivates the transmit antenna that is associated with the owest channe gain and equay aocates the tota transmit power to the other transmit antennas so that the statistica properties of the resuting effective channes are changed, and a certain degree of transmit diversity is achieved, simiar to the cassic antenna seection schemes [16] D Cooperative ST-SSK Design The proposed ST-SSK is designed to achieve fu diversity gain However, we aso note that the foowing potentia probems may be encountered 1) A high ST-SSK throughput ony becomes achievabe at the cost of empoying a high number of transmit antenna eements, which is impractica for shirt-pocket-sized handhed devices 2) A shadowing-induced power oss may be imposed on the mutipe-antenna-aided transmitter, which resuts in a significant performance degradation at the destination To mitigate these potentia probems, we invoke the proposed scheme for achieving cooperative diversity [17], [18], where mutipe
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 6, JULY 2011 2867 Fig 2 AF-reaying-aided ST-SSK scheme with N Tx reays to aid the SN singe-eement reay nodes (RNs) may share their antenna eements to form a virtua antenna array (VAA) We propose an AF-reaying-aided ST-SSK scheme (see Fig 2), where the signa processing at the RNs exhibits a ow compexity, because our ST-SSK design dispenses with interantenna synchronization Let us now consider the ST-SSK mapping function f s (t, a i ) for scenarios with an even number of time sots According to the mapping function f s (t, a i ), the antennas are activated one by one to transmit the same signa Therefore, the symbo vector that is transmitted at the nth (1 n N Tx ) antenna is equivaent to a right circuar shift of the symbo vector that is transmitted by the (n 1)th antenna Against this background, we specify the mapping function that is dedicated to the nth antenna eement as {fs n (t, a i )} N Tx n=1, where the information bits are mapped to the nth antenna eement according to f s (t, a i ), except that the other (N Tx 1) antenna eements that are indicated in f s (t, a i ) are ignored We arrange for the singeantenna-eement-aided source node (SN) to perform the bit-to-antenna mapping according to fs 1 (t, a i )Therth (1 r N Tx ) RN first performs a right circuar shift of the received signa by (r 1) positions and then activates the ampify and retransmit functions so that the ST-SSK mapping function f s (t, a i ) may be competed by the N Tx RNs in a distributed manner More expicity, during the first transmission period, which is aso referred to as the broadcast interva, the received signa at the destination node (DN) is represented by y SD = P S h SD + n SD (8) where P S denotes the transmit power at the SN, whereas the L-eement Rayeigh fading vector h SD =[h SD,, fs 1(t 1,a i ) h SD fs 1(t L,a i ) ]T has a zero mean and a variance of σsd 2 The received signa vector y SD has L eements, whereas the AWGN vector n SD has the same size and a variance of N0 D Simiary, the signa that is received at the rth RN may be represented by y SRr = P S h SRr + n SRr (9) where the L-eement vector h SRr =[h SRr fs 1(t 1,a i ),,hsrr fs 1(t L,a i ) ]T has a source reay (SR) channe output power of σsr 2, whereas the L-eement AWGN vector n SRr has a zero mean and a variance of N0 R The L-eement received signa vector y SRr shoud be right circuary shifted by (r 1) positions and then ampified by a factor of α = P R /(P S σsd 2 + N 0 R),whereP R denotes the transmit power at the RNs The retransmitted signa at the rth RN is then formuated as ȳ SRr = α( P S hsr r + n SRr ) (10) where the fading channe vector becomes h SRr =[h SRr fs r(t 1,a i ),, h SRr fs r(t L,a i ) ]T It is shown that the ST-SSK mapping function f s (t, a i ) is therefore formed at the N Tx RNs using ow-compexity signa processing Furthermore, the tota power that is shared by the SN and the RNs shoud now be normaized as P S + P R = me b 2L (11) In the second transmission period, which is aso referred to as the cooperation interva, the signa that is received at the DN is given by N Tx y RD = ȳ SRr h RDr + n RD r=1 N Tx = α( P hsr r S + n SRr )h RDr + n RD r=1 = α P S hsr RD + n RD (12) where the L-eement equivaent fading channe vector becomes hsr RD =[ h SR RD SR RD f s(t 1, a i ),, h f s(t L, a i ) ]T = [ N Tx r=1 (hsrr h RDr ) fs(t1,a i ),, N Tx r=1 (hsrr h RDr ) fs(tl,a i )] T, whereas the equivaent noise matrix n RD = N Tx r=1 α nsrr h RDr + n RD has a variance of α 2 σrd 2 N 0 R + N0 D,whereσRD 2 denotes the power of the fading channe between the RNs and the DN It is shown that the noise at the RNs has aso been ampified and forwarded to the DN Finay, the transmitted sequence â i is determined at the DN according to â i =argmin a i yt SD P S h SD + fs 1(t,a i ) 2 yt RD IV SIMULATION RESULTS α P S hsr RD 2 (13) f s(t,a i ) The uncoded BER versus the E b /N 0 performance of a system with N Tx =4, N Rx =1antennas and using the proposed open-oop ST-SSK moduation scheme discussed in Section III-A is characterized in Fig 3 When the transmission time duration L increases from 1 to 3, the achievabe throughput decreases from 2 (bits/symbo) to 2/3 (bits/symbo) At the same time, the achievabe transmit diversity order increases from one to three, which is iustrated in Fig 3 by the increased sope of the BER curves Moreover, when the number of time sots increases to L =4, the sope of the BER curves remains the same as the sope of L =3, which demonstrated that the maximum
2868 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 6, JULY 2011 Fig 3 Uncoded BER versus E b /N 0 for N Tx =4,N Rx =1for the foowing three approaches: 1) the ST-SSK scheme that uses L =1/2/3, respectivey, and the shift swap bit-to-antenna mapping f s w, as shown in Tabe I(b); 2) the ST-SSK scheme that is combined with feedback-aided power aocation; and 3) the origina SSK moduation Fig 4 Uncoded BER versus E b /N 0 for ST-SSK with N Tx =2, N Rx =1 using perfect phase feedback, 1-bit quantized phase feedback, and 1-bit power aocation feedback aided, respectivey The performance of the origina openoop ST-SSK moduation is aso incuded for comparison achievabe diversity order of an ST-SSK-moduation-aided system is three (N Tx 1=3) Further BER improvements can be achieved by combining the ST-SSK scheme with the feedback-aided power aocation in Section III-C Fig 4 characterizes the uncoded BER versus the E b /N 0 performance for a throughput of R =1 (bits/symbo) and N Tx =2, N Rx =1 The foowing four scenarios are compared: 1) perfect phase feedback; 2) 1-bit feedback-aided phase rotation; 3) 1-bit feedback-aided power aocation; 4) the origina open-oop SSK moduation Fig 5 Uncoded BER versus E b /N 0 for the N Tx = L =2AF-reayingaided ST-SSK scheme, where the transmit power at the SN and the RNs are normaized as P S = P R =1/2 The unit channe power is assumed for a inks, ie, σsr 2 = σ2 RD = σ2 SD =1 The performance of the direct transmission without reaying and of the origina ST-SSK scheme are aso incuded for comparison For our proposed ST-SSK scheme, a diversity order of two resuts in a significant power gain, which is shown in Fig 4 Hence, we observe that our ST-SSK scheme that reies on perfect phase feedback approaches the performance of the Aamouti G2 STBC Moreover, using as few as a singe bit to quantize the feedback phase information imposes ony a modest performance degradation of about 1 db The achievabe BER performance that is recorded for using a 1-bit feedback for either phase information or power aocation is simiar to one another The uncoded BER versus E b /N 0 performance of our AF-reayingaided ST-SSK with N Tx = L =2 is shown in Fig 5 A unit channe power is assumed for both the source reay (SR) and the reay destination (RD) inks, as we as for the source destination (SD) ink, ie, σsr 2 = σ2 RD = σ2 SD =1 It is shown in Fig 5 that the cooperative diversity provides a significant performance improvement over both the direct transmission regime and its ST-SSK counterpart If a perfect phase feedback is avaiabe for the two SR inks and the two RD inks, the performance of the cooperative ST-SSK scheme is further improved, which is demonstrated in Fig 5 Moreover, assuming that a 10-dB power oss occurred for the SD ink due to a deep shadow fade, Fig 5 shows that the performance degradation of the AF reaying scheme is ony 5 db at a BER of 10 5, because the SD inks ony contribute haf the overa diversity order in our proposed cooperative ST-SSK scheme When using piot-assisted channe estimation, the resuting estimated channe may be formuated as ĥ = h e g + h, whereh e represents the variance of the channe estimation error and the vector g is constituted by N Tx -dimensiona random Gaussian variabes with a zero mean and unit variance, whereas the N Tx -eement vector h represents the actua CIR The coded BER performance versus the variance h e of the channe estimation error recorded for the various transmission schemes is iustrated in Fig 6, where a rate r c =1/3 convoutiona code with a constraint ength of seven is empoyed It is demonstrated in Fig 6(a) that, for N Tx =2, the origina open-oop SSK scheme is sensitive to channe estimation errors The proposed cosed-oop scheme that uses the phase information and the feedbackaided power aocation regimes are both ess sensitive to sma channe estimation errors, eg, to h e < 005 However, the sensitivity to high channe estimation errors becomes simiar for a three schemes It
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 6, JULY 2011 2869 V C ONCLUSION In this paper, the foowing four nove schemes have been proposed: 1) the open-oop ST-SSK moduation, which is designed for systems with more than two transmit antennas; 2) the cosed-oop feedback-aided phase rotation, which is conceived for systems with two transmit antennas; 3) the cosed-oop feedback-assisted power aocation; 4) the AF-reaying-aided ST-SSK scheme, which is designed to achieve a usefu transmit diversity for SSK moduation The proposed ST-SSK schemes significanty improved the achievabe uncoded BER performance over independent and identicay distributed (iid) Rayeigh fading channes Moreover, the proposed cooperative ST-SSK scheme eiminates the practica probem of empoying a high number of transmit antennas whie simutaneousy mitigating the performance degradation caused by shadow fading Fig 6 Coded BER performance versus the variance of the channe estimation error h e at a fixed SNR per bit vaue using the foowing five approaches: 1) the origina open-oop SSK moduation; 2) the proposed cosed-oop scheme that uses perfect and quantized phase feedback for N Tx =2; 3) the proposed feedback-aided power aocation scheme for N Tx =2; 4) the proposed openoop ST-SSK scheme for N Tx =4; and 5) a combination of ST-SSK and feedback-aided power aocation for N Tx =4 (a) Coded N Tx =2 (b) Coded N Tx =4 is aso demonstrated in Fig 6(b) that, for sma channe estimation errors, the proposed ST-SSK scheme is significanty ess sensitive than the origina SSK scheme Moreover, the empoyment of the proposed feedback-aided power aocation can reduce the sensitivity to channe estimation errors, provided that these errors are confined to reativey sma vaues However, the sensitivity to high channe estimation errors becomes simiar for a three schemes The reason for these observations is that the vaue of Δh has been increased by using the proposed schemes As a resut, the proposed schemes became robust to sma channe estimation errors REFERENCES [1] J Jeganathan, A Ghrayeb, L Szczecinski, and A Ceron, Space-shift keying moduation for MIMO channes, IEEE Trans Wireess Commun, vo 8, no 7, pp 3692 3703, Ju 2009 [2] Y A Chau and S H Yu, Space moduation on wireess fading channes, in Proc IEEE 54th Veh Techno Conf, 2001, vo 3, pp 1668 1671 [3] R Y Meseh, H Haas, S Sinanovic, C W Ahn, and S Yun, Spatia moduation, IEEE Trans Veh Techno, vo 57, no 4, pp 2228 2241, Ju 2008 [4] R Meseh, H Haas, C W Ahn, and S Yun, Spatia moduation A new ow-compexity spectra-efficiency-enhancing technique, in Proc 1st Int Conf Commun Netw China, Oct 2006, pp 1 5 [5] G J Foschini, Layered space time architecture for wireess communication in fading environments when using mutipe antennas, Be Labs Tech J, vo 2, pp 41 59, 1996 [6] S M Aamouti, A simpe transmit diversity technique for wireess communications, IEEE J Se Areas Commun,vo16,no8,pp1451 1458, Oct 1998 [7] L Hanzo, M Munster, B J Choi, and T Keer, OFDM and MC-CDMA for Broadband Mutiuser Communications, WLANs and Broadcasting Hoboken, NJ: Wiey, 2003 [8] L Hanzo, J S Bogh, and S Ni, 3G, HSDPA, HSUPA and FDD Versus TDD Networking: Smart Antennas and Adaptive Moduation New York: Wiey/IEEE Press, 2008 [9] M Tsai and S Yousefi, A new iterative joint detection and decoding agorithm for V-BLAST architecture, IEEE Signa Process Lett,vo16, no 10, pp 905 908, Oct 2009 [10] S Sugiura, S Chen, and L Hanzo, Reduced-compexity iterative Markov chain MBER detection for MIMO systems, IEEE Signa Process Lett, vo 16, no 3, pp 160 163, Mar 2009 [11] M Renzo and H Haas, Improving the performance of space-shift keying (SSK) moduation via opportunistic power aocation, IEEE Commun Lett, vo 14, no 6, pp 500 502, Jun 2010 [12] J Jeganathan, A Ghrayeb, and L Szczecinski, Spatia moduation: Optima detection and performance anaysis, IEEE Commun Lett, vo 12, no 8, pp 545 547, Aug 2008 [13] C Yuen, Y L Guan, and T T Tjhung, Power-baanced orthogona space time bock code, IEEE Trans Veh Techno, vo 57, no 5, pp 3304 3309, Sep 2008 [14] C Yuen, Y Guan, and T T Tjhung, Singe-symbo-decodabe differentia space time moduation based on QO-STBC, IEEE Trans Wireess Commun, vo 5, no 12, pp 3329 3334, Dec 2006 [15] C Yuen, Y Guan, and T Tjhung, Unitary differentia space time moduation with joint moduation, IEEE Trans Veh Techno, vo 56, no 6, pp 3937 3944, Nov 2007 [16] R S Bum and J H Winters, On optimum MIMO with antenna seection, IEEE Commun Lett, vo 6, no 8, pp 322 324, Aug 2002 [17] J Laneman and G Worne, Distributed space time-coded protocos for expoiting cooperative diversity in wireess networks, IEEE Trans Inf Theory, vo 49, no 10, pp 2415 2425, Oct 2003 [18] A Sendonaris, E Erkip, and B Aazhang, User cooperation diversity Part I: System description, IEEE Trans Commun, vo 51, no 11, pp 1927 1938, Nov 2003