Interference Mitigation in MIMO Interference Channel via Successive Single-User Soft Decoding

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1 Interference Mitigation in MIMO Interference Channel via Successive Single-User Soft Decoding Jungwon Lee, Hyukjoon Kwon, Inyup Kang Mobile Solutions Lab, Samsung US R&D Center 491 Directors Pl, San Diego, CA 911, USA {jungwon, Abstract This paper examines a practical way of mitigating interference in multi-input multi-output MIMO) interference channel when each user is constrained to use a point-to-point code. It was recently shown that the capacity region of interference channel with point-to-point codes can be established by a combination of two schemes: treating interference as noise and joint decoding. In practice, a straightforward implementation of a joint decoding receiver could be significantly more complex than treating interference as noise. Thus, as a low-complexity approach to joint decoding, this paper proposes a successive single-user soft decoding receiver, which performs interference-aware detection with a priori log-likelihood ratio LLR) and single-user soft decoding for every user successively. The proposed receiver is compared with a receiver treating interference as noise and a receiver performing interference-aware detection without a priori LLR and single-user decoding for the desired user only. Simulation results show that the proposed receiver significantly outperforms these existing receivers. I. INTRODUCTION Recently, interference management has become the central issue of cellular communication system design. The intercell interference has been one of the most important issues, and with the shrinking cell size, the inter-cell interference is increasingly important as the system performance is limited by interference rather than background noise. Moreover, with the advent of heterogeneous network consisting of macrocells, pico-cells, and femto-cells, interference management has become critical. Traditionally, the most common practice in interference management was to avoid interference altogether by using orthogonal multiplexing schemes. One widely-used scheme is to reuse frequency only among cells placed far away with the adjacent cells using different frequency. Another orthogonal multiplexing scheme is to use code division multiple access CDMA). Even now, orthogonal multiplexing scheme is one of the most popular approach. For example, an interference management scheme called enhanced inter-cell interference coordination eicic) in the 3rd generation partnership project 3GPP) release 10 employs time division multiplexing for data channels. However, all these orthogonal multiplexing schemes cannot achieve the full degrees of freedom available in the channel. Thus, there have been many efforts to achieve universal frequency reuse without using orthogonal multiplexing schemes. In the case of the universal frequency reuse, the cellular channel can be modeled as the interference channel, which was studied extensively in information theory. Research on interference channel in information theory community was mainly focused on finding the capacity region outer-bound and near-capacity achieving transmission and encoding schemes. Relatively less emphasis was placed on the analysis of interference channel when point-to-point codes were used but advanced receivers were employed. However, recently, there has been some active research in this area, as can be seen in [1 3]. Particularly, in [3], the capacity region of an interference channel with point-to-point codes was established by a combination of treating interference as noise and using joint decoding. This paper examines how we can design a receiver such that interference can be minimized in multi-input multi-output MIMO) interference channels when each user is constrained to use a point-to-point code. The MIMO receiver treating interference as noise can be implemented straightforwardly [4]. However, joint decoding is much more complex than treating interference as noise. Thus, it is necessary to develop a joint decoding receiver with a reasonable complexity in order to achieve the capacity of MIMO interference channels with point-to-point codes in practice. For this purpose, this paper proposes a successive single-user soft decoding receiver as a low complexity approach to joint decoding. The rest of the paper is organized as follows. Section II describes a MIMO system model for a Gaussian interference channel. Section III reviews existing MIMO decoding schemes in the presence of interference. In Section IV, a successive single-user soft decoding scheme is proposed. In Section V, the performance of the proposed scheme is evaluated and compared with existing schemes, and Section VI provides concluding remarks. II. SYSTEM MODEL In this paper, a U-user Gaussian interference channel IC) with flat fading is considered. Each user employs a spatial multiplexing SM) scheme with multiple antennas. In the MIMO SM system, the transmitter of user u with N T,u transmit antennas sends N S,u spatial streams to the receiver of user u with N R,u receive antennas, N S,u min{n R,u,N T,u }. For the point-to-point codes, this papers focuses on a bit interleaved coded modulation BICM) scheme in conjunction with binary codes such as convolutional codes, turbo codes,

2 Data Bits Encoder Coded Bits Interleaver Interleaved coded bits Modulator Bit-to-Symbol Mapping) Transmit Symbols Symbol-to- Symbol-Vector Mapping Transmit Symbol Vectors MIMO Precoding Precoded Transmit Signal Vectors N S,u Streams N T,u Antennas Fig. 1. MIMO spatial multiplexing SM) transmitter with BICM for user u and low-density parity check codes because a BICM scheme is widely used in wireless communication systems. Fig. 1 shows a MIMO SM transmitter model with BICM. At the transmitter for user u, data bits are encoded, interleaved, grouped into N u bits, and mapped to a M u -ary modulation symbol with M u = Nu. Then a group of N S,u modulation symbols form a transmit symbol vector. This transmit symbol vector consisting of N S,u elements are precoded to form a precoded transmit signal vector consisting of N T,u elements. The precoding is optional for N S,u = N T,u. However, it is assumed that the precoding is always applied in general since even no precoding can be represented as a trivial linear precoding with an identity matrix. This precoded transmit signal vector is then transmitted over N T,u transmit antennas, which goes through a wireless channel. After going through a channel, the signal received by user u at time m in U-user MIMO Gaussian IC is represented as follows: U y u [m] = H u,i [m]x i [m]+z u [m], 1) i=1 y u [m] = [y u,1 y u,nr,u ] T is an N R,u 1) receive signal vector of user u, x i [m] = [x 1 x NS,i ] T is an N S,i 1) transmit symbol vector of user i, z u [m] is an N R,u 1) noise vector of user u, and H u,i [m] = [h u,i,1 [m] h u,i, [m] h u,i,ns,i [m]] is an N R,u N S,i ) effective channel matrix with h u,j,s [m] representing an N R,u 1) channel vector from the s-th stream of user i to all receive antennas of user u. Here, the effective channel matrix combines the effect of the transmitter precoding and the wireless channel. The noise vector is assumed to be independent, identically distributed i.i.d.) circularly symmetric complex Gaussian random vector. Furthermore, the variance of each element of the noise vector is set to σz =1. This noise can model Gaussian noise with any covariance matrix by using noise whitening, in which case the effective channel includes the effect of the noise whitening on top of the transmitter precoding and the wireless channel. Then the probability density function pdf) of the noise vector z u [m] is expressed as f z u [m]) = 1 π exp z u [m] ). ) NR,u In this paper, MIMO Gaussian interference networks with point-to-point codes are considered, the transmitter operation is straightforward as shown in Fig. 1. The challenge lies in the receiver design, which is thoroughly investigated in the following sections. More specifically, various receivers are investigated under the assumption that the channel matrix H u,i [m] for all i is known to each receiver u. For notational simplicity, the time index m is omitted in the following. III. EXISTING DECODING SCHEMES In this section, two existing decoding schemes are reviewed: interference whitening IW) and interference-aware detection schemes. A. Interference Whitening The straightforward approach to handle interference is treating the interference as Gaussian noise and whitening interference [4]. The received signal in 1) can be represented as follows: y u = H u,u x u + U i=1,i u H u,i x i + z u 3) The receiver calculates the covariance matrix R u of U i=1,i u H u,i + z u and then applies Ru 1/ to the received signal vector y u : and ỹ u = Ru 1/ y u 4) = H u,u x u + w u, 5) w u = R 1/ u H u,u = R 1/ u H u,u 6) U i=1,i j H j,i + z u, 7) and the covariance matrix of w u is I. With the interference-whitened received signal ỹ u and the effective channel H u,u, the log-likelihood ratio LLR) of each coded bit can be calculated using various MIMO detectors such as zero-forcing ZF) and minimum mean square error MMSE) equalizers or maximum likelihood ML) detector.

3 Z ^ s L d d L d h / D/DK W >>Z + - ^ h ^ h / - + Fig.. A soft decoding receiver for user j for the proposed successive single-user soft decoding receiver With the ML detector [5], the LLR for the n-th bit of the s-th stream of the u-th user is given as L u b s,n,u ) =log log x u X 1) s,n,u x u X 0) s,n,u exp ỹ u H ) u,u x u exp ỹ u H ) u,u x u, 8) X s,n,u b) is the set of transmit symbol vectors with b s,n,u =b. The sets X s,n,u 0) and X s,n,u 1) partition the set X u transmit symbol vectors equally with Mu NS,u / vectors in each set. With the max-log approximation [5], an approximate LLR can be defined as of all possible M NS,u u L u b s,n,u ) = min x u X s,n,u 1) min x u X 0) s,n,u ỹ u H u,u x u ỹ u H u,u x u. 9) The LLR in 8) or the approximate LLR in 9) is calculated for the j-th user only, de-interleaved, and fed into a decoder, which performs a single-user decoding. B. Interference-Aware Detection without A Priori LLR In the interference whitening approach above, the interference was assumed to be Gaussian. A better approach is to use the discrete nature of the interference when the modulation information of other users is available at the receiver. In [6], an interference-aware detection approach based on the discrete nature of the interference was proposed. This approach is basically a soft version of the joint hard detector [7]. The LLR for user u using the interference-aware detection without a priori LLR can be represented as L u b s,n,u ) =log log and x 1,,x U ) X 1) 1:U,s,n,u x 1,,x U ) X 0) 1:U,s,n,u exp Dx 1,, x U )) exp Dx 1,, x U )), 10) U Dx 1,, x U )= y u H u,i x i, 11) X b) 1:U,s,n,u = i=1 { x 1,, x U ) x u X s,n,u, b) x j X j for j u}. 1) The max-log approximation can also be applied here to obtain an approximate LLR. As in the interference whitening, the LLR 10) or its approximate version is calculated for the j- th user only, de-interleaved, and fed into a decoder, which performs a single-user decoding. IV. SUCCESSIVE SINGLE-USER SOFT DECODING One straightforward implementation of the joint decoding in MIMO interference channels is generating a noiseless version of a series of received signal vector candidates for each message set of all users, calculating the sum of Euclidean distances between a series of received signal vectors and a series of the noise-less version of received signal vector candidates, and finding the message set with the smallest Euclidean distance sum. However, this joint decoding scheme is extremely complex, and a low-complexity alternative is necessary in practice. Although the interference-aware detection in the previous section has a low-complexity, it does not fully exploit the knowledge on the interference. It only exploits the property of interference that the interference symbol at a given time is one of the discrete modulation symbols in the interference signal constellation rather than a Gaussian-distributed symbol.

4 However, the interference is a coded signal, which has a special structure. By decoding the interference, the knowledge on the interference statistic can be refined. More specifically, the LLR of each coded bit is updated by decoding interference softly, and with this updated LLR, the probability of each interference modulation symbol can be calculated. This knowledge on the interference modulation symbol can be used by an interference-aware detector with appropriate modification of the interference-aware detector in the previous section. Based on the above observation, we propose a successive single-user soft decoding receiver, which performs interference-aware detection with a priori LLR and single-user soft decoding from user 1 to user U in turn and repeats it as desired. Fig. shows a block diagram for the interferenceaware detector and the single-user decoder for user j. An interference-aware detection is performed for user j, the interference-aware detection calculates the LLR for user j s coded bits treating all the other users as interference. Here, the interference-aware detection uses all the knowledge on the modulation symbols of all users supplied in the form of a priori LLR, the details of which are described below. Then an extrinsic LLR is calculated by subtracting a priori LLR for user j from a posteriori LLR for user j. This extrinsic LLR for user j is deinterleaved and fed into a single-user decoder for user j as a priori LLR. The single-user soft decoder for user j outputs updated LLR for coded bits of user j as a posteriori LLR. Then the extrinsic LLR of the decoder is formed by subtracting the a priori LLR from the a posteriori LLR. This extrinsic LLR is interleaved and fed into the interferenceaware detector. Then next time, the interference-aware detector performs interference-aware detection for user j +1 with this updated a priori LLR for user j, while maintaining the a priori LLR for all the other users. For the above successive single-user soft decoding receiver, the use of a priori LLR for interference-aware detection is essential, and in the following, it is described how it can be accomplished. The a priori LLR L A,i for user i can be used as follow to calculate the probability of each modulation symbol of user i: px i )= s,n) J 1) pb s,n,i =1) pb s,n,i =1)= exp and exp LA,ib s,n,i) s,n) J 0) pb s,n,i =0), 13) LA,ib s,n,i) ) +exp ) LA,ibs,n,i) ), 14) pb s,n,i =0)=1 pb s,n,i =0). 15) In the above, J b) is the set of indices s, n) the n-th bit of the s-th stream of x i has a bit value of b. Using 13), a posteriori LLR for user j can be calculated as follows: L D,j b s,n,j ) ) P {bs,n,j =1 y j } = log 16) P {b s,n,j =0 y j } = log p y, x 1,, x U )) log x 1,,x U ) X 1) 1:U,s,n,j x 1,,x U ) X 0) 1:U,s,n,j p y, x 1,, x U )),17) p y, x 1,, x U )) = exp Dx 1,, x U )) U px i ) π NR,j i=1 18) With 17), the interference-aware detector can generate the a posteriori LLR for user j based on the a priori LLR for all users. A simpler version based on max-log approximation can also be calculated. V. SIMULATION RESULTS This section evaluates the performance of the proposed successive single-user soft decoding receiver over interference channels by Monte Carlo simulation. Two user interference channel is considered with each user transmitting spatial streams equipped with transmit and receive antennas. An i.i.d. Rayleigh fading channel model is assumed. A data packet consists of 360 data bits. Using turbo codes with the rate R c =1/3, 1/ or 5/6, a coded packet s length becomes 360/R c. A random interleaver is used to permute the bit sequence from turbo codes with generator polynomials 7, 5). The modulation orders considered in this section are 4 and 16 QAM with Gray mapping so that each symbol on the constellation has only 1 bit difference from neighbor symbols. For fair comparisons, existing receivers are simulated with 8 inner iterations at the decoder, while the proposed receiver is simulated with 4 iterations at the decoder per user and successive soft-decoding is performed once per user. Fig. 3 and Fig. 4a) demonstrate the performance of three receivers considered in this paper for various levels of singleto-interference ratio SIR). It is observed that the proposed scheme outperforms regardless of the SIR level and the PER gain of the proposed scheme increases as the SIR level decreases. Since the proposed scheme tries to decode the interference, large interference power improves the performance of the proposed scheme, rather than impairing it. This implies that the proposed scheme is robust against large interference power, while the other schemes are not. Fig. 4 shows the effect of the interference code rate on the proposed and existing receivers. Since two existing receivers do not decode interference signals, their performance is independent of interference code rate as can be seen in Fig. 4a) and Fig. 4b). However, the proposed receiver

5 a) SIR = 3 db a) Desired signal and interference code rate: 0.33 and b) SIR = 3 db b) Desired signal and interference code rate: 0.33 and 0.83 Fig. 3. SIR. PER using 4 QAMs with code rates of 0.33 for various levels of Fig. 4. PER using 4 QAMs at SIR 0 db with various code rates. exhibits better performance with lower interference code rate, which makes intuitive sense because the proposed receiver performs interference decoding. Fig. 5 shows the effect of the interference modulation order. It can be observed that the curves of the interference-aware detection and successive single-user decoding in Fig. 5a) are shifted to the right in Fig. 5b). In other words, the performance of these two schemes is degraded as the interference modulation order increases. From Figs. 3, 4, and 5, it can be seen that the proposed scheme performs well when interference can be decoded well, i.e., INR is large compared to its modulation and code rate. Fig. 6 plots the error rates of both the desired signal and the interference when the proposed receiver is used. The proposed receiver here performs the desired signal decoding followed by the interference decoding. After the interference decoding, the desired signal is decoded once more and then the decoding operation stops. In other words, the desired signal is decoded twice, as the interference is decoded only once. Here, 4 QAMs are used by the desired signal and the interference, and SIR is set to 0 db. From the figure, it can be seen that the desired signal decoding can be done quite well even though the interference decoding can be quite poor. Since the receiver is not interested in the error of the interference itself, only the decoding performance of the desired signal is important. This essentially distinguishes the interference channel situation from the multiple access channel situation, a receiver is interested in decoding all the signals rather than only one signal. VI. CONCLUSION This paper investigated the problem of mitigating interference in multi-input multi-output interference channels with

6 a) Desired signal and interference modulation: 4 QAM and 4 QAM Desired Signal w/ Code Rate 0.33 Interference Signal w/ Code Rate 0.33 Desired Signal w/ Code Rate 0.33 Interference Signal w/ Code Rate Fig. 6. PER using 4 QAMs with various code rates b) Desired signal and interference modulation: 4 QAM and 16 QAM [3] F. Baccelli, A. E. Gamal, and D. N. C. Tse, Interference networks with point-to-point codes, IEEE Trans. Inf. Theory, vol. 57, pp , May 011. [4] J. Winters, Optimum combining in digital mobile radio with cochannel interference, IEEE J. Select. Areas Commun., vol., pp , July [5] B. M. Hochwald and S. Brink, Achieving near-capacity on a multipleantenna channel, IEEE Trans. Commun., vol. 51, pp , Mar [6] R. Ghaffar and R. Knopp, Interference suppression strategy for cell-edge users in the downlink, Accepted for publication in IEEE Trans. Wireless Commun., 011. [7] J. Lee, D. Toumpakaris, and W. Yu, Interference mitigation via joint detection, IEEE J. Select. Areas in Commun., vol. 9, pp , May 011. Fig. 5. orders. PER using code rates 0.50 at SIR 0 db for various modulation point-to-point codes and bit interleaved coded modulation. A successive single-user soft decoding scheme was proposed as a practical way of implementing joint decoding. Then it was shown by simulation that the proposed scheme achieves a dramatic performance improvement compared to the scheme treating interference as noise as well as the scheme performing interference-aware detection without a priori LLR and singleuser decoding for the desired user only. REFERENCES [1] S. Weber, J. G. Andrews, X. Yang, and G. de Veciana, Transmission capacity of wireless ad hoc networks with successive interference cancellation, IEEE Trans. Inf. Theory, vol. 53, pp , Aug [] J. Blomer and N. Jindal, Transmission capacity of wireless ad hoc networks: Successive interference cancellation vs. joint detection, in Proc. IEEE Int. Conf. on Commun., 009.