Proceedings of the 15th Asia-Pacific Conference on Communications (APCC 2009)-055
Successive Interference Cancellation Amiable Space-time Codes With Good Multiplexing-Diversity Tradeoff Xiaoming Dai, Sun ShaoHui, Wang Yingming
Runmin Zou
Datang Mobile Communications Equipment Com., Ltd, Email:
[email protected]
School of Information Science and Engineering Central South University Changsha 410083, P. R. China Email:
[email protected]
Invited Paper
Abstract—In this work, we propose two high-rate quasiorthogonal space-time coding (STC) schemes which are designed in conjunction with the successive interference cancellation (SIC) based receiver. The symbols of the proposed STC are of judiciously designed diversity order which can be effectively exploited by the SIC based receiver to cancel interference as well as to obtain diversity gain. The proposed STC scheme’s amicable quasi-orthogonal structure lends itself to efficient low-complexity linear decoding. Simulation results show that the proposed STC scheme achieves better multiplexing-diversity tradeoffs than the existing conventional schemes in noise-limited single-cell scenarios. In the interference-limited multi-cell scenario, the application of proposed SIC-amiable STC to the coordinated multi-point transmission and reception (CoMP) also achieves higher throughput than the conventional schemes.
I. Introduction Ever since the first works on space-time coding (STC) [1], [2] appeared, the research community has spent great efforts on seeking STCs with good complexity-performance tradeoffs. The orthogonal space-time block codes (OSTBCs) [2]–[3] can offer full transmit diversity and low-complexity linear decoding. However, the upper-bound of the maximum possible symbol rate (the number of information symbols per channel use (pcu)) of the OSTBC is 3/4 for cases with more than three transmit antennas [4] when complex modulation is applied (the rate-1 is achieved only for the case with two transmit antennas proposed by Alamouti [2]). The vertical Bell Labs layered space-time architecture (V-BLAST) [5] with an ordered successive interference cancellation (OSIC) based detector can achieve full transmission rate at the cost of diversity gain and is widely acclaimed for providing a reasonable tradeoff between transmission rates and complexity. The STC transmission schemes proposed in [6], [7] can achieve both full diversity and high spectral efficiency. However, the associated maximum-likelihood (ML) decoding complexity is much higher than that of the V-BLAST, especially when the number of transmit antennas or the constellation size is large. While sphere decoding (SD) [8] can be utilized to simplify the implementation of the ML detector for many practical problems, there still exists the issue of the choice of the
appropriate covering radius of the lattice, and the complexity can be still quite high if the number of transmit antennas is large. It has been recently shown in [9] that expected complexity of the SD is exponential for fixed signal-to-noise ratio (SNR), thus, incurring high decoding complexity in the low SNR regime. Therefore, STC designs that can achieve full (of high) transmit diversity and high rate, but requiring only moderate decoding complexity are highly desirable for practical applications. The recently proposed STC transmission schemes [10] which combine the advantages of the OSTBC and V-BLAST can provide both diversity as well as multiplexing gains. The hybrid STC schemes [10] relying on a combination of spatial multiplexing and OSTBC are claimed to achieve good performance-complexity tradeoffs and are well suited to achieve high data rates in asymmetric antenna configurations, where the number of transmit antennas is superior to the number receive antennas (normally occurs in the configurations of the downlink). The hybrid STC schemes based on different tradeoffs between data rate and robustness have received great interest and have been admitted to the IEEE802. 11n [10] and WINNER drafts [11] for future potential applications. In this work, we propose a STC structure that consists of two partially overlapped 2 × 2 orthogonal sub-matrixes in conjunction with the SIC based receiver. The joint design of STC and SIC based receiver efficiently exploits transmit antenna diversity and the merits of the SIC based detector. Hence, it achieves better diversity-multiplexing tradeoffs than its counterparts of the V-BLAST and the hybrid STC schemes [10] under symmetric and asymmetric configurations, respectively, in noise-limited single cell scenario. In interference-limited muti-cell case, coordinated multipoint transmission and reception (CoMP) has been identified as one of the key techniques for the long-term evolution (LTE) advanced (LTE-A) system [12] to enhance the cell edge user performance. The applications of the proposed STC to CoMP in the interference-limited multi-cell scenarios also achieves higher throughput than its counterparts based on the hybrid STC and V-BLAST.
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Successive Interference Cancellation Amiable Space-time Codes With Good Multiplexing-Diversity Tradeoff
(a) NT = 3. Fig. 1.
(b) NT = 4.
The proposed codeword matrixes for NT = 3 and NT = 4 transmit antennas.
II. The Proposed SIC-Amiable STC Scheme A. The System and Channel Model We consider a discrete-time baseband channel model and assume quasi-static flat Rayleigh fading. For a multipleantenna communication system with NT transmit and NR receive antennas, the transmitted and received signals are given by ρ HS + V (1) Y= NT where Y denotes the matrix of complex received signals with the size of NR ×T . S ∈ CT ×NT represents the matrix of complex transmitted signals, H ∈ CNR ×NT denotes the channel matrix, and the additive noise V ∈ CNT ×NR is CN(0, 1) (zero-mean, unit-variance, complex-Gaussian) distributed that is spatially and temporally white. ρ is the SNR at each receive antenna. The channel coefficients hi, j , i = 1, ..., NR, j = 1, ..., NT are modeled as independent identically distributed (i.i.d.) complex circular Gaussian random variables, each with a CN(0, 1) distribution. B. Review of the SIC Based Receiver The OSIC based detector detection [5] (which is a application of the SIC to multiple-input multiple-output (MIMO) system) starts by searching the “strongest” data with the highest signal-to-interference-and-noise ratio (SINR). The order of detection of the substreams is chosen to maximize the signal-to-noise ratio (SNR) at each stage. The SIC based receiver has been widely acclaimed for providing a reasonable tradeoff between performance and complexity for MIMO system [5]. However, one main disadvantage of any system using nulling and canceling based approach has the drawback that errors occurred in detecting the transmitted symbols are propagated further into subsequent symbols due to interference subtraction. If the previous detecion/desisions are correct, the diversity order of the ith interference cancellation (IC) stage of the V-BLAST system [13] is NR − NT + i. As a result, the detection of the first stage suffers the most severe interferences. The error propagation resulted from low diversity of early detection stages will severely degrade the overall performance. It has been shown in [13] that the total error rate is dominated by the first-step bit error rate (BER). Furthermore, errors in channel estimates further exacerbates the detrimental effects of the error propagation. As mentioned beforehand, the overall system performance is limited by the symbols with the worst performance, this
gives us the hint that improving the performance of the first layer will be the most effective means to enhancing the overall performance of the SIC based system. C. Proposed Codeword Based on the observations of Section II-B, we propose the codewords for three and four transmit antennas as shown, respectively, in Fig. 1(a) and Fig. 1(b), where rows and columns represent transmit antennas and symbol intervals, respectively, and (·)∗ denotes the conjugate of the argument (·). The proposed STC schemes’ symbol rates r of the three and four transmit antennas are 5/3 and 2, respectively. With NR = 3 receive antennas, the mathematical model of the proposed STC for three transmit antennas can be expressed as ⎡ ⎡ ⎤ ⎤⎡ ⎤ ⎢⎢⎢ y11 y12 y13 ⎥⎥⎥ ⎢⎢⎢ h11 h12 h13 ⎥⎥⎥ ⎢⎢⎢ s1 s∗2 s5 ⎥⎥⎥ ρ ⎢⎢ ⎢ ⎢⎢⎢ ⎥⎥⎥ ⎥ ⎥ ∗ ⎢⎢⎣⎢ h21 h22 h23 ⎥⎥⎥⎦⎥ ⎢⎢⎢⎣⎢ s1 −s1 s3 ⎥⎥⎥⎦⎥ ⎢⎣⎢ y21 y22 y23 ⎥⎦⎥ = 3 h y31 y32 y33 s4 s∗3 s1 31 h32 h33 ⎡ ⎤ ⎢⎢⎢ v11 v12 v13 ⎥⎥⎥ ⎢ ⎥ + ⎢⎢⎢⎢ v21 v22 v23 ⎥⎥⎥⎥ ⎣ ⎦ v31 v32 v33 (2) which can be rewritten as the following equivalent form ⎡ ⎡ ⎤ ⎤ ⎤ ⎡ ⎢⎢⎢ y11 ⎥⎥⎥ ⎢⎢⎢ h11 h12 0 h14 0 ⎥⎥⎥ ⎢⎢⎢ v11 ⎥⎥⎥ ⎢⎢⎢ h ⎥ ⎢⎢⎢ v ⎥⎥⎥ ⎢⎢⎢⎢ y12 ⎥⎥⎥⎥ 12 ⎥ ⎢⎢⎢ 21 h22 0 h24 0 ⎥⎥⎥⎥⎥ ⎡ ⎢⎢⎢ ⎥⎥⎥ ⎥ ⎤ ⎢⎢⎢⎢ ⎢ ⎥ s y h 0 h 0 h ⎢⎢⎢ 13 ⎥⎥⎥ ⎢⎢⎢ 31 ⎥⎥⎥ ⎢⎢ 1 ⎥⎥ ⎢⎢⎢ v13 ⎥⎥⎥⎥⎥ 32 34 ⎢ ⎥ ⎢⎢⎢ y∗ ⎥⎥⎥ ⎢⎢⎢ −h∗ h∗ h∗ ⎥ ⎢ 0 0 ⎥⎥⎥⎥ ⎢⎢⎢⎢ s2 ⎥⎥⎥⎥ ⎢⎢⎢⎢ v∗21 ⎥⎥⎥⎥⎥ ⎢⎢⎢ 21 ⎥⎥⎥ ⎢⎢⎢ 12 11 13 ρ ⎥ ⎢ ⎥⎢ ⎥ ⎢⎢⎢ y∗ ⎥⎥⎥ = ⎢⎢⎢ −h∗ h∗ h∗ 0 0 ⎥⎥⎥⎥ ⎢⎢⎢⎢ s3 ⎥⎥⎥⎥ + ⎢⎢⎢⎢ v∗22 ⎥⎥⎥⎥ 22 21 23 ⎢⎢⎢ 22 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎥ ⎥ ⎢ 3 ⎢ ⎥ ⎢⎢⎢ −h∗ h∗ h∗ ⎢⎢⎢ y∗23 ⎥⎥⎥⎥ 0 0 ⎥⎥⎥⎥ ⎢⎢⎢⎣ s4 ⎥⎥⎥⎦ ⎢⎢⎢⎢ v∗23 ⎥⎥⎥⎥ 32 31 33 ⎢⎢⎢ ⎢⎢⎢ ⎥⎥⎥ ⎥ ⎢ ⎥ ⎢ ⎢⎢⎢ h13 ⎢ v ⎥⎥⎥ 0 h12 0 h11 ⎥⎥⎥ s5 ⎢⎢⎢ y31 ⎥⎥⎥ ⎥⎥⎥ ⎢⎢⎢⎢⎢ 31 ⎥⎥⎥⎥⎥ ⎢⎢⎢ y ⎥⎥⎥ ⎢⎢⎢⎢ h ⎢⎢⎣ v32 ⎥⎥⎦ 0 h22 0 h21 ⎥⎥⎦ Δ ⎢⎣ 32 ⎥⎦ ⎢⎣ 23 =s y33 h33 0 h32 0 h31 v33 Δ
=y
Δ
=Hequivalent
Δ
=v
(3) It is easy to derived the Hequivalent for NR = 2 (or NR > 3) for the codeword for four transmit antennas. With a SIC detector, the symbol s1 has the highest diversity order (assumed to be detected first in general) and the first layer BER is substantially reduced. As a result, the error propagation is, thus, significantly mitigated in the detection of subsequent layers. The symbols of lower diversity orders of the proposed codeword can benefit from accurate detection of the previously detected symbols with higher diversity orders. The reliable estimates from the previously detected symbols are
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Proceedings of the 15th Asia-Pacific Conference on Communications (APCC 2009)-055
III. Simulation Results In this work, we evaluate the proposed STC scheme and compare it with the V-BLAST and the hybrid STC1 under the conventional single-user MIMO (SU-MIMO) based and joint transmission based CoMP-SU-MIMO (CoMP serves a single user equipment) scenarios.2 The perfect channel state information (CSI) was assumed to be known at the receiver for both scenarios. A. SU-MIMO Fig. 2 compares the uncoded average BER performance for the proposed codeword of 16-quadrature amplitude modulation (16-QAM) and the V-BLAST of 4-QAM based on FSIC, 1 The
codewords of the hybrid STC schemes [10] of NT = 3 and
s1 s2 s3 T NT = 4 antennas are, respectively, expressed as G3 = s∗ −s∗ s∗ , and 2 1 4
s1 s2 s3 s5 T G4 = s∗2 −s∗1 s∗4 s∗ . Therefore, the symbol rates are 2 and 3 for the GSTC 6 based schemes of three and four transmit antennas, respectively. 2 In the downlink, CoMP techniques are mainly categorized into two methods: coordinated scheduling and/or beamforming and joint processing/transmission [12].
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Uncoded BER
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V−BALST, 4−QAM (6 bits/s/Hz),ZF−LD V−BALST, 4−QAM (6 bits/s/Hz),FSIC V−BALST, 4−QAM (6 bits/s/Hz),OSIC New codeword, 16−QAM (6.7 bits/s/Hz),ZF−LD New codeword, 16−QAM (6.7 bits/s/Hz),FSIC New codeword, 16−QAM (6.7 bits/s/Hz),OSIC
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Fig. 2. Simulated BER curves of the proposed STC scheme and the VBLAST with 3 × 3.
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Uncoded BER
then utilized in detection of subsequent symbols, thus, result in a better overall BER performance. Therefore, the judiciously designed diversity orders of the symbols of different layers are efficiently exploited by the SIC based receiver to suppress interfering signals as well as to obtain diversity gain. The diversity gain obtained in the SIC detection process can be leveraged to increase the transmission rate, thus, achieving a better multiplexing-diversity tradeoff (demonstrated by numerical results in Section III-A). The unequal diversity order based STC scheme lends itself to the efficient SIC based detector, even for the fixed-order SIC (FSIC) one, where the symbols at the SIC receiver side are processed in accordance with data index, s1 is detected first, and the s2 is detected second, and so on. i.e., s1 , s2 ,...,srNT . The FSIC based detector achieves almost identical performance to the OSIC based one for the proposed codeword which has been verified by simulation in Section III-A. The top-left and down-right 2 × 2 sub-matrixes of proposed codeword in Fig. 1(a) are orthogonal, thus, it greatly alleviates the self interference. The quasi-orthogonal structure makes it amicable for the low-complexity linear detector, and it also alleviates the error propagation in the SIC process. The classical equal-diversity based quasi-orthogonal spacetime block codes (Q-OSTBC) proposed in [14] that provide symbol rate 1 for four transmit antennas and symbol rate 3/4 for eight transmit antennas by relaxing the strict orthogonality requirement of OSTBC. As explained beforehand, the equaldiversity based Q-OSTBCs can not benefit from the SIC based receiver and have smaller symbol rates than the proposed STCs. The diversity-embedded codes proposed in [15] provide unequal error protection for different sets of bits based on nonuniformly spaced signal points. Similar idea presented in [16] is to design a codebook which allows many levels of diversity for different information streams which is different from the joint design of SIC and STC proposed in this paper.
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Hybrid STC [11], 8−PSK (6 bits/s/Hz),ZF−LD Hybrid STC [11], 8−PSK (6 bits/s/Hz),OSIC New codeword, 16−QAM (6.7 bits/s/Hz),ZF−LD New codeword, 16−QAM (6.7 bits/s/Hz),OSIC −3
10
4
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12 14 SNR (dB)
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Fig. 3. Simulated BER curves of the proposed STC scheme and the hybrid STC [10] with 3 × 2.
OSIC, and zero-forcing linear detector (ZF-LD) for three transmit and three receive antennas (represented by 3 × 3). Fig. 2 shows that the proposed codeword obtains about 2.5 dB and 5 dB gain over the V-BLAST at the BER of 1 × 10−3 for the OSIC and FSIC, respectively. As explained in Section II-C, the FSIC based receiver achieves almost identical performance to the OSIC for the proposed codeword (i.e., renders the ordering operation unnecessary for the proposed codeword in practical applications). The proposed codeword with ZF-LD achieves about 8 dB gain over that of the V-BLAST at the BER of 1 × 10−2 . In fact, the proposed codeword using ZF-LD even gives better performance than the V-BLAST with more complex SIC based receiver as shown in Fig. 2. The proposed codeword achieves higher transmission rate of 6.7 bits/s/Hz (=5/3*4) than the V-BLAST of 6 bits/s/Hz (=3*2) at lower signal-to-noise-ratio (SNR) ranges for FSIC, OSIC and ZFLD receivers. The uncoded BER curve of the proposed STC scheme has a larger slope rate than that of the V-BLAST in the high-SNR regime, which implies that the proposed STC scheme has a better diversity gain. Therefore, the proposed STC achieves a better diversity-multiplexing tradeoff, which is consistent with the analysis of Section II-C. B. CoMP-SU-MIMO Two cells with perfect network synchronization and zero backhaul delay are assumed for the CoMP-SU-MIMO. The perfect receive timing without mismatching is also assumed
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Successive Interference Cancellation Amiable Space-time Codes With Good Multiplexing-Diversity Tradeoff
−1
Uncoded BER
10
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V−BALST, 4−QAM (8 bits/s/Hz),ZF−LD V−BALST, 4−QAM (8 bits/s/Hz),FSIC V−BALST, 4−QAM (8 bits/s/Hz),OSIC New codeword, 16−QAM (8 bits/s/Hz),ZF−LD New codeword, 16−QAM (8 bits/s/Hz),FSIC New codeword, 16−QAM (8 bits/s/Hz),OSIC
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Fig. 4. BER curves of the proposed STC scheme and the V-BLAST with (2 + 2) × 4 for CoMP-SU-MIMO.
be efficiently exploited by the SIC based detector to cancel interference as well as to obtain diversity gain. The STCs’ quasi-orthogonal structure alleviates the error propagation which is inherent in the SIC based system, it is also amicable for the low-complexity linear decoding. Two STC schemes designed based on the proposed SIC- and LD-amenable principle for three and four antennas achieve better multiplexdiversity tradeoffs than the conventional schemes. The SICamenable principle can be extended to more than four transmit antennas. Numerical results demonstrated that the proposed SIC-amiable STCs outperforms the conventional schemes in both noise-limited single-cell and interference-limited multicell scenarios. References
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Uncoded BER
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Hybrid STC [11],4−QAM (6 bits/s/Hz),ZF−LD Hybrid STC [11],4−QAM (6 bits/s/Hz),FSIC Hybrid STC [11],4−QAM (6 bits/s/Hz),OSIC New codeword, 8PSK (6 bits/s/Hz),ZF−LD New codeword, 8PSK (6 bits/s/Hz),FSIC New codeword, 8PSK (6 bits/s/Hz),OSIC 4
6
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Fig. 5. BER curves of the proposed STC scheme and the hybrid STC scheme [10] with (2 + 2) × 3 for CoMP-SU-MIMO.
since the received timing difference can be compensated by adjusting a linear phase [17]. For further details, interested readers can consult [18] The proposed SIC-amiable STC for four transmit antennas is compared with its counterparts of the V-BLAST and hybrid STC. Each cell is equipped with two antennas and the data send to the UE is shared among the cells, represented by (2 + 2) × NR i.e., each cell sends half data to the UE. We applied 16-QAM and 4-QAM for the proposed codeword and the V-BLAST, respectively. Therefore, the spectral efficiency of both schemes are the same, i.e., 8 bits/s/Hz (=2*4=4*2). Fig. 4 illustrates that the proposed STC scheme with OSIC receiver gives about 4 dB gain over the VBLAST at the BER of 1 ×10−2 . About 7.4 dB gain is obtained by the proposed STC scheme with the ZF-LD at the BER of 3 × 10−2 . As expected, the BER performance of the proposed STC based on FSIC is similar to that of the OSIC. Fig. 5 depicts that the proposed codeword obtains about 2.8 dB and 1.8 dB gain over the hybrid STC at the BER of 3 × 10−2 and 1 × 10−2 for the LD and OSIC, respectively. As explained in Section II-C, the FSIC based receiver achieves similar performance as the OSIC for the proposed codeword. IV. Conclusions This paper proposed a quasi-orthogonal STC scheme designed in conjunction with the SIC based receiver.The judiciously designed diversity order based STC schemes can
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