Y. Xin, Z. Wang, and G.B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. Wireless Commun., vol.2, pp.294-309, Mar. 2003.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of our LRF codes over these constellations. Simulations corroborate our theoretical ndings. I. Introduction Signal space diversity has been by now well documented as a bandwidth and power ecient coding approach, considerably improving the reliability of transmissions over fading channels [2, 3, 4, 6, 11]; see also [9] for a tutorial treatment, recent results, and applications. Pertinent research has focused on developing high (or maximum) diversity constellations (such as rotating QAM) 2, 4, 6, 11] These are constructed using linear code generator matrices, whichmultiply blocks of symbols drawn ....

....coding approach, considerably improving the reliability of transmissions over fading channels [2, 3, 4, 6, 11] see also [9] for a tutorial treatment, recent results, and applications. Pertinent research has focused on developing high (or maximum) diversity constellations (such as rotating QAM) [2, 4, 6, 11]. These are constructed using linear code generator matrices, whichmultiply blocks of symbols drawn from standard constellations to generate blocks of symbols with large diversity gain (## ) and coding gain (## ) Depending on the eld the entries of these matrices are drawn from, they can be ....

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Y. Xin, Z. Wang, and G. B. Giannakis, \Space-time diversity systems based on linear constellation precoding," IEEE Trans. on Wireless Communications, March 2003.

.... complex field were advocated for their fading resilient features in the signal processing for communications literature, in which the focus was placed on frequency selective fading channels, and these matrices appeared under terms such as linear precoding [5 9] linear constellation precoding [10,11], or complex field coding [12] As these matrices are linear operators, to unite the information and coding theoretic approach with the signalprocessing viewpoint, we will collectively call them LCF encoders. A comprehensive treatment of LCF encoding combined with ideal (de ) interleaving for ....

.... LCF ST codes for MIMO flat fading channels were first designed in Reference [9] to ensure space diversity (see also Reference [15] in which the sphere decoding (SD) algorithm of Reference [16] was applied to the same problem) LCF based spacetime coding (STC) was studied thoroughly in References [10,11], in which LCF encoders were generalized to account not only for diversity but also for coding gains. The present paper aspires to motivate, provide a concise exposition devoid of undue rigor, delineate pertinent trade offs, and put forth novel directions for single and multi antenna wireless ....

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Xin Y, Wang Z, Giannakis GB. Space-time diversity systems based on linear constellation precoding. IEEE Transactions on Wireless Communications 2002; to appear.

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Y. Xin, Z. Wang, and G. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Transactions on Wireless Communications, vol. 2, no. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-Time Diversity Systems based on Linear Constellation Precoding," IEEE Trans. on Wireless Communications, vol. 2, no. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space--time diversity systems based on linear constellation precoding," IEEE Trans. Wireless Commun., vol. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space--time diversity systems based on linear constellation precoding," IEEE Trans. Wireless Commun., vol. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. Wireless Commun., vol. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-Time Diversity Systems based on Linear Constellation Precoding," IEEE Transactions on Wireless Communications, vol. 2, no. 2, pp. 294-309, March 2003.

.... the Gaussian integer ring Z(j ) e.g. QAM or PAM) there exists at least one pair of (#,#) for which # g = # g 1 #,#g [1,N t ] enable the full diversity N t N r , and simultaneously full ST transmission rate of N t symbols per channel use (pcu) The N t N t matrix # is Vandermonde as in [4] for dimension N t , and # can be selected as the N t th root of any generator for #. If maximum likelihood (or sphere) decoding is employed at the receiver, then the achieved the diversity order is N t N r . If nullingcancelling (NC) decoding is used, then the guaranteed diversity order is N r (N ....

....for #. If maximum likelihood (or sphere) decoding is employed at the receiver, then the achieved the diversity order is N t N r . If nullingcancelling (NC) decoding is used, then the guaranteed diversity order is N r (N r N t 1) Simulations: FDFR schemes achieve the same diversity as LCF STC [4] and space time orthogonal design (ST OD) but have better performance because they can afford smaller modulations for the same transmission rate. 0 2 4 6 8 10 12 14 16 FDFR (SD) LCF STC FDFR (NC) 0 2 4 6 8 10 12 14 16 E N 0 (dB) FDFR (SD) LCF STC FDFR (NC) 0 2 4 6 8 10 12 ....

Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," Proc. of GLOBECOM, vol. 1, pp. 455-459, San Antonio, TX, Nov. 25--27, 2001.

.... existing MIMO designs aim mainly at one of two objectives: either high performance by enabling the available space diversity, or, high rates by capitalizing on the capacity of MIMO fading channels [14,48,54] ST Orthogonal Designs (OD) 1,46] Linear Constellation Precoding (LCP) ST Codes [61], and ST Trellis Codes (TC) 47] fall under the performance oriented class, while BLAST type architectures, 57,13] and Linear Dispersion (LD) codes [22,24] belong to the rate oriented alternatives. ST OD codes enjoy full diversity (FD) at linear decoding complexity, and for systems with (N t ....

....the constellation they precode. We will henceforth call them LCF codes, to delineate the features they di#er and share with GF codes. For MIMO flat fading channels, LCF ST codes were introduced by [58] and independently by [6] to enable FD at 1 symbol pcu, for any number of antennas (see also [61] reporting the first coding gain analysis of such LCF ST codes) For MIMO frequency and time selective channels, space, multipath, and Doppler diversity modes were enabled via LCF ST coding in [30,18,35,39,63] but again, at transmission rates not exceeding 1 symbol pcu. For N t = 2 antennas, FD ....

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. on Wireless Communications, vol. 2, no. 2, pp. 294--309, Mar. 2003.

....block, we take the indices of the assigned subcarriers to increase by one, in the spirit of the one step frequency hopping in [12] Although alternate frequency hopping patterns can be implemented in practice, we stick to (11) for simplicity. We will choose the unitary precoding matrix as in [4] [21]: # = FK #, 12) where # : diag 1, e j , e j(K 1) is a diagonal matrix with unit amplitude diagonal entries. Notice that our # in (12) is the conjugated version of the precoders used in [19] 21] conjugation does not affect the performance) We will prove that: ....

....(11) for simplicity. We will choose the unitary precoding matrix as in [4] 21] # = FK #, 12) where # : diag 1, e j , e j(K 1) is a diagonal matrix with unit amplitude diagonal entries. Notice that our # in (12) is the conjugated version of the precoders used in [19] [21] (conjugation does not affect the performance) We will prove that: Proposition 1: The equi spaced subcarrier assignment (11) together with the precoder (12) leads to perfectly constant modulus UP OFDMA user transmissions. Proof: Suppose that the symbols in s u (i) are drawn from a PSK ....

Y. Xin, Z. Wang, and G. B. Giannakis, "Space-Time Diversity Systems based on Linear Constellation Precoding," in IEEE Transactions on Wireless Communications, vol. 2, no. 2, pp. 294-309, March 2003.

....transmission rate is: # # ### symbols per channel use (pcu) while the maximum possible transmission rate is # pcu, since we have # # transmit antennas. We call # # and # as full diversity and full rate, respectively. VBLAST achieves full rate # but loses diversity, while LCF STC in [12] achieves full diversity # # at rate # # # symbol pcu, for any # # .In this section, we will present a design we term FDFR LCF STC, which guarantees full rate and full diversity, simultaneously, for any number of antennas. 3.1. Encoding Define the spatial span of each layer as the number of ....

....Define the spatial span of each layer as the number of columns of the ST matrix # which contain one or more of this layer s symbols. And the temporal span as the number of rows of # which one layer s symbols are present. For example, VBLAST in [10] has spatial span one, while LCF STC proposed in [12] has only one layer with spatial span # # , and temporal span # # . Based on these two definitions, we will introduce two lemmas that provide necessary conditions for achieving full rate with full diversity. Lemma 1 (Necessary condition for full diversity) For one LCF coded layer in # to achieve ....

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. on Wireless Communications, 2002.

....achieve maximum diversity at a rate higher than one symbol per channel use. 1. INTRODUCTION Future generation communication systems are likely to employ antenna arrays to enhance the data rates and cope with the adverse fading effects of wireless propagation. Linear constellation rotation coding [9] for space time (ST) communications achieves a rate of one symbol per channel use with diversity gain as high as MN , where M and N are the number of transmit and receive antennas, respectively. Practical decoding, however, relies on near optimum algorithms such as sphere decoding to guarantee ....

....transmit antennas. Linear constellation rotation coding can be viewed as a counterpart of a Galois field (GF) block code in complex field (CF) and hence will also be termed Complex field coding (CFC) Instead of having entries from a GF, a CFC generator can have complex entries. It has been shown [9] that CFC allows for large (in many cases, maximum) diversity gain with small or no rate loss. The key point is that in fading channels, the minimum Hamming distance eventually determines the diversity order, or the slope, of the average probability of error curve. Even a square (that is, rate 1) ....

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. on Wireless Communications, 2002 (to appear). 574

....we design as [7] C = # # # # u 1 (1) uN t (2) u 2 (1) u 1 (2) uN t (1) uN t (2) # # # , 5) where u (n) denotes the nth element of the th layer. The outer part of the transmitter is termed LCF encoder . Relying on the algebraic tools developed in [15, 5], we design the LCF encoders of the different groups as: # g = # g 1 #, #g # [1,N t ] 6) where # is to be designed, and # is a unitary Vandermonde matrix with generators i i=1 selected as in [15, 5] With the inner and outer encoders in (5) and (6) after stacking the receive vectors ....

....of the transmitter is termed LCF encoder . Relying on the algebraic tools developed in [15, 5] we design the LCF encoders of the different groups as: # g = # g 1 #, #g # [1,N t ] 6) where # is to be designed, and # is a unitary Vandermonde matrix with generators i i=1 selected as in [15, 5]. With the inner and outer encoders in (5) and (6) after stacking the receive vectors y(n) into one vector, we have y = IN t #H) # . c(N t ) # w. 7) Furthermore, based on (5) and (6) we obtain c(n) P n D # ) n ]s, where the permutation matrix P n , and the diagonal matrix ....

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. on Wireless Communications, 2002.

....Because both classes of multi antenna systems cope with BER performance and transmission rate in a disjoint way, these systems are usually unable to strike the best performance rate tradeoff, and do not offer sufficient design flexibility. Incorporating non redundant ST Constellation Rotation (CR) [10] into a carefully designed LST structure, we propose in this paper a novel system that we term LST CR, to deal with the performance rate tradeoff in a direct and effective way. The LST CR system has the following features: it subsumes V BLAST and ST CR as special cases; it enables high ....

.... to VBLAST, which is well known to enjoy full transmission rate ( # # # ) but suffers from poor performance when # # ; Case 2 ( # # ) In this case, we have # # # and # # # # # , and our LST CR specializes to ST CR, which achieves full diversity gain # with transmission efficiency [10, 11]. Cases 1 and 2 correspond to two extremes among different performance rate tradeoffs. By choosing # # # # , LSTCR is capable of offering great flexibility to meet any desirable performance rate requirement. To make this possible, we have to explore decoding options in LST CR. IV. LAYER ....

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE JSAC, Mar. 2001 (submitted); downloadable from http://spincom.ece.umn.edu/zhiqiang/xiwg01j.ps

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Y. Xin, Z. Wang, and G.B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. Wireless Commun., vol.2, pp.294-309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, Space-time diversity systems based on linear constellation precoding, IEEE Trans. Wireless Commun., Vol. 2, No. 3, pp. 294--309, 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. Wirel. Comm., vol. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. Wirel. Comm., vol. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. on Wireless Commun., vol. 2, no. 2, pp. 294--309, 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. Wirel. Comm., vol. 2, pp. 294--309, Mar. 2003.

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Y. Xin, Z. Wang, and G. B. Giannakis, "Space-time diversity systems based on linear constellation precoding," IEEE Trans. Wireless Commun., vol. 2, pp. 294--309, Mar. 2003.

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