The Two-Way Interference Channel: Towards a Redesign of Mobile Communication Systems Peter Rost NEC Europe Labs, Network Research Department, 69115 Heidelberg, Germany Email: [email protected]

Abstract— Full spatial reuse of spectral resources (frequency reuse of 1) is an inevitable consequence of the demanding requirements on mobile communication networks. A prerequisite to obtain full reuse is to either cancel or mitigate inter-cell interference as it otherwise limits the achievable performance. In order to derive new strategies for cellular interference-mitigation, this paper introduces the two-way interference channel and analyzes the achievable uplink-downlink data rates for different inter-cell interference scenarios. Of particular interest is an asymmetric protocol that exploits cross-uplink-downlink interference, i. e. two adjacent cells do not operate simultaneously in uplink or downlink but only one of both is active in uplink and one is active in downlink. Using analytical results, it is shown that under specific conditions this approach provides performance gains over conventional approaches and close to multi-cell MIMO. Although this approach is not able to improve the performance under all channel conditions, it provides a new degree of freedom which might be exploited if inter-cell interference significantly impairs the performance.

I. I NTRODUCTION An increased site density and frequency reuse 1 maximize the spatial reuse of available spectrum in cellular networks and are essential to achieve the challenging goals of IMTAdvanced [1]. Both, however, imply seriously increased intercell interference, which limits the system throughput and requires very efficient inter-cell interference mitigation or cancellation (e. g. multi-cell MIMO transmission and detection). A. Problem description The majority of existing work is focused on multi-cell MIMO under the assumption of perfect compound Channel State Information (CSI) and unlimited inter-site connections [2] for which high-speed low-latency backhaul solutions are mandatory, e. g. to enable coherent transmission of multiple base stations (BSs). Existing backhaul solutions are not able to satisfy the data-rate and latency requirements, which implies that multi-cell MIMO will suffer from high quantization noise and asynchronous transmission. Hence, there is the need to either improve current technologies allowing for multi-cell MIMO implementations [3], or to introduce more practical technologies providing similar gains but avoiding the stringent Part of this work has been performed in the framework of the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement No 257263 (FLAVIA). The authors would like to acknowledge the contributions of their colleagues in FLAVIA, although the views expressed are those of the authors and do not necessarily represent the project.

BS

BS

BS

BS

H

H H

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BS

H

BS

BS

BS

(a) Symmetric DL

BS

(b) Asymmetric UL/DL

Fig. 1. Two UL/DL assignments where solid lines denote intended transmissions and dashed lines denote interference.

requirements of multi-cell MIMO. This paper focuses on the latter and introduces an approach which is able to offer similar gains as multi-cell MIMO but avoids its drawbacks. Multi-cell MIMO relies on the basic assumption that cells align their uplink (UL) and downlink (DL) transmission, i. e., adjacent BSs simultaneously transmit or receive. Multi-cell MIMO is realized by exchanging either quantized signals (after modulation) or en-/decoded data (before modulation). Exchanging quantized signals offers diversity-gains but requires significant backhaul-resources. By contrast, exchanging en-/decoded data is more backhaul-efficient but suffers from error propagation. Furthermore, CSI must be acquired and exchanged among BSs, which requires low-latency backhaul to avoid out-dated CSI. These requirements render multi-cell MIMO across different sites as a less feasible and highly resource-consumptive method. B. A Redesigned Cell Layout In this work, we analyze a setup in which BSs do not align their UL and DL but intentionally create an asymmetric assignment. An asymmetric UL/DL assignment introduces inter-BS interference, which can be alleviated by Successive Interference Cancelation (SIC) based on CSI acquired from pilots (without quantization error) and encoded data exchanged via backhaul. Similar situations appear in TDD-UMTS systems where it might happen that DL-frames of multiple cells are of different length and overlap with UL-frames of other cells [4]. However, in UMTS this is rather considered as curse

than opportunity to improve the throughput. Fig. 1(a) illustrates a typical interference situation, where two user terminals (UTs) are located close to the same cell border. Both receive significant interference from the adjacent cell, which requires either interference avoidance, such as fractional frequency reuse (FFR), or interference mitigation techniques. In this case, the model of the interference channel [5] can be applied such that the two-way communication is a cascade of the same interference channel in UL and DL. By contrast, consider Fig. 1(b) where the left BS operates in DL while the right one receives data in the UL. This asymmetric UL/DL assignment changes the interference situation such that one BS receives interference from the other BS, and both UTs interfere each other. Hence, the two-way communication consists of two different interference channels each involving one BS and one UT as transmitters. This additional degree of freedom can be used to redesign cells or to more efficiently operate existing cellular networks. Instead of applying complex multi-cell MIMO methods, we avoid interference using an asymmetric UL/DL assignment. As further discussed in Section VI, this requires inter-cell coordination to assign adjacent UTs to orthogonal resources. C. Outline and Contributions By contrast to existing work, we discuss the benefits of introducing inter-BS interference for the purpose of avoiding inter-cell interference at UTs. In order to evaluate this novel system architecture, we introduce the two-way interference channel underlying the constraint of a fixed UL-DL rateratio. The proposed protocols are of practical interest as they consider limited inter-BS connection and fixed UL-DL rateratios. We show that how to dynamically create different interference properties in order to relax backhaul-constraints while still providing similar gains as multi-cell MIMO. The underlying system model is introduced and discussed in Section II. Based on this model, we present in Section III approaches for the one-way interference channel, which are applied in Section IV to describe achievable rates of the twoway interference channel. In Section V, we evaluate results for an exemplary setup and Section VI highlights implementation aspects. The paper is concluded in Section VII. II. S YSTEM M ODEL OF THE T WO -WAY I NTERFERENCE C HANNEL Fig. 2 shows an abstract model of the two-way interference channel, which models the previous example of Fig. 1 with two interfering communication pairs. More specifically, we have four half-duplex nodes n ∈ [1; 4] with i.i.d. zero-mean circularly symmetric Gaussian channel inputs Xn ∼ CN (0, Pn ) with variance Pn if node n is transmitting, and Xn = 0 if node n is receiving. The channel output Yn at node n is given by  P  hn,n′ Xn′ + Zn if Xn = 0, Yn = n′ ∈[1;4]\n  0 otherwise. The random variable (r.v.) Zn ∼ CN (0, σn2 ) is the Additive White Gaussian Noise (AWGN) and hn,n′ = hn′ ,n denotes

C3,4 β2

3

4

1

1 α

1

α β1

2

Fig. 2. Two-way interference channel with symmetric inter-cell interference

the channel coefficient between nodes n and n′ . For the sake of readability we simplify this setup and consider a symmetric inter-cell interference scenario, i. e., h3,2 = h4,1 = α. We further abbreviate the inter-terminal interference by h1,2 = β1 and h3,4 = β2 . Given a specific access pattern of the two-way interference channel, s1 , s2 refer to both transmitting nodes and d1 , d2 refer to both receiving nodes in the DL. Motivated by the example in Fig. 1, we refer to nodes 1 and 2 as UTs and nodes 3 and 4 as BSs. Hence, the link from nodes 3 and 4 to both UTs represents the DL in a mobile communication system while the opposite direction is equivalent to the UL. Both BSs, nodes 3 and 4, may be connected by an error-free backhaul link with capacity C3,4 , which is considered to be virtually unlimited in our analysis, i. .e. C3,4 ≈ ∞. Let Rn,n′ , n 6= n′ , be the maximum achievable rate with which a message Wn is transmitted from node n to node n′ . We constrain all results in this work such that a given ratio η of DL to UL rates, η = R3,1 /R1,3 = R4,2 /R2,4 , must be satisfied. This ratio is of particular importance in mobile communication as very high DL-data-rates require a minimum UL-data-rate for signaling. In addition, this ratio simplifies the analysis as the achievable rate region for a specific η is a twodimensional intersection level in the four-dimensional set of all achievable rates. Our analysis assumes that the system is divided into two phases using fraction τ and 1 − τ of the available resources for UL and DL, respectively. Without loss of generality, the following discussion relates to a TDD system. We further use the abbreviation C(x) = log(1 + x) with the dual logarithm. III. P ROTOCOLS FOR THE O NE -WAY I NTERFERENCE C HANNEL This work bases on existing literature on the one-way interference channel for which a variety of approaches has been published. The interference channel can be divided into three main classes: the very strong [6], the strong [7], and the weak interference channel [8]. In the case of very strong and strong interference, the capacity is known and achieved if each receiver decodes the interference signal first and the interference-free useful signal next. By contrast, the capacity of the weak interference channel, 2 2 which satisfies 0 ≤ |α| , |β| ≤ 1, is not known. So far, the

best known inner bound for the weak interference channel has been introduced by Han and Kobayashi in [8]. The authors proposed to divide each transmitter’s message in a private part and common part which are jointly decoded. The common part, however, is decoded at both receivers while the private part is only decoded at the intended receiver. Now let transmitter s1 divide its message into the private message W(s1 ,d1 ) and common message W(s1 ,D) with D = {d1 , d2 }. Both messages satisfy the power constraints P(s1 ,d1 ) and P(s1 ,D) with P(s1 ,d1 ) + P(s1 ,D) ≤ Ps1 . Define the set P containing each possible power allocation tuple. For a specific p ∈ P the rate of message W(·,·) is defined by R(W(·,·) , p). Furthermore, the per-node rates are given by Rs1 (p) = R(W(s1 ,d1 ) , p) + R(W(s,D) , p). The resulting achievable rate region is given by [ RIC ((s1 , s2 ) → (d1 , d2 )) = (Rs1 (p), Rs2 (p)) p∈P

subject to the following constraints  ∀W ⊆ W(sk ,dk ) , W(s1 ,D) , W(s2 ,D) , k ∈ {1, 2} : ! X X R(l, p) = C h2l,dk Pl /σd2k . l∈W

l∈W

RIC is the convex hull of all achievable rate regions over all power allocations. As the capacity of the strong and very strong interference channel is achieved by this approach, we use RIC as an inner bound of the general interference channel. If both transmitters are connected with an unlimited backhaul-link (C3,4 ≈ ∞), the resulting channel can be understood as a broadcast channel. Costa showed in [9] that by using the Dirty Paper Coding (DPC) technique [10] one of both nodes can receive its transmission as it was without interference. The resulting capacity region is given by [11]: n [
RDPC ((s1 , s2 ) → (d1 , d2 )) = Rs′ 1 , Rs′ 2 : Ps′1 +Ps′2 ≤Ps1 +Ps2

Rs′ 1 ,d1 + Rs′ 2 ,d2

≤ log I + 

X

k∈{s1 ,s2 }
′ hs1 ,d2 ) Ps1 /σd21 ∧

Rs′ 1 ,d1

≤ C (1 +

Rs′ 2 ,d2

≤ C (1 + hs2 ,d1 ) Ps′2 /σd22


o ,

 HTk Pk′ Hk ∧

with the unity matrix I, the matrix transpose (·)T and the partial channel matrix Hk = (hk,d1 , hk,d2 ). Similarly, both BSs can exchange the received signals with a central entity such that the capacity region for the UL with unlimited receiver cooperation is given by n RV−MAC ((s1 , s2 ) → (d1 , d2 )) = (Rs1 , Rs2 ) :   X T  Hk Pk Hk  ∧ Rs1 ,d1 + Rs2 ,d2 ≤ log I + k∈{s1 ,s2 }
2 Rs1 ,d1 ≤ C (1 + hs1 ,d2 ) Ps1 /σd1 ∧
o Rs2 ,d2 ≤ C (1 + hs2 ,d1 ) Ps2 /σd22 .

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Possible UL/DL assignments in the two-way interference channel

IV. P ROTOCOLS FOR THE T WO - WAY I NTERFERENCE C HANNEL Based on the previous discussion, we define in this section achievable rates for the two-way interference channel with BS cooperation. We distinguish two ways of operating the system. The first is to align UL and DL of adjacent cells as shown in Fig. 3(a). Alternatively, we consider cross-UL-DL interference where one BS transmits while the second one is receiving as shown in Fig. 3(b). In the following, we use τ RIC ((·, ·) → (·, ·)) to denote that all rate pairs are scaled with τ . A. Symmetric UL and DL alignment At first, we model the two-way interference channel by two separate interference channels where both BSs transmit at the same time and do not cooperate (C3,4 = 0). The corresponding achievable rate region is given by [  τ ηRIC ((1, 2) → (3, 4)) Rsym = 0 0≤τ ≤1

 ∩ (1 − τ )RIC ((3, 4) → (1, 2)) .

Factor η enforces the constraint of asymmetric UL/DL rates. Lets assume that C3,4 ≈ ∞ and both BSs obtained perfect CSI of the compound channel, then the BSs can apply multicell MIMO and the achievable rate region is given by [  τ ηRV−MAC ((1, 2) → (3, 4)) Rsym ∞ = 0≤τ ≤1

 ∩ (1 − τ )RDPC ((3, 4) → (1, 2)) .

We do not consider UT-cooperation as this requires significant data exchange between both terminals (supposedly using their radio interface), and there is currently no existing standard implementing or foreseeing mobile terminal cooperation. B. Asymmetric UL and DL alignment In the second case, we consider the asymmetric scenario in which only one of both BSs transmits while the second one is listening. This setup is illustrated in Fig. 3(b) for the case that UT 2 transmits in the UL and BS 3 transmits in the DL. For the case that both BSs do not exploit the backhaul connection, it follows for the achievable rate region: Rasym = {(R3,1 , R2,4 ) ∈ RIC ((3, 2) → (1, 4)) : R3,1 = ηR2,4 } . 0

R4 [bpcu]

/2

1.5

Fig. 4. Setup for the analysis of the two-way interference channel. Labels indicate the actual channel between two nodes.

sr p q

1.5

R4 [bpcu]

p q

p q

p q c b q p sr q p rs cb R3 = R4 bcrs q p

c rs bc b t u

t u

0.5

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t u

Fig. 5.

0

0.5 1.0 R3 [bpcu]

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Achievable DL rate regions for dUT = 230 m and η = 5/3

This equation already reflects the additional degree of freedom, e. g. both BSs or UTs may be well separated (β ≪ α) which avoids interference or they experience a (very) strong interference channel (β > 1), which allows for interference cancellation. Hence, the achievable rates may be increased as the interference situation with β is preferable over α. Finally, we consider the case that both BSs receive over the backhaul the message of the other BS in addition to their own message. Then, under the assumption of CSI at the receiver (which can be acquired using pilots instead of backhaul) we can apply a perfect interference cancellation no matter how strong the interference is. This implies for the given scenario that h3,4 = 0, which gives the following achievable rate region n Rasym = (R3,1 , R2,4 ) ∈ RIC ((3, 2) → (1, 4)) : ∞ o R3,1 = ηR2,4 h3,4 = 0 .

V. ACHIEVABLE G AINS THROUGH A SYMMETRIC UL/DL This section analyzes the performance of an exemplary interference channel with unlimited backhaul, which is illustrated in Fig. 4. Both BSs are placed at distance dBS = 500 m [1] from each other and each UT is located at distance dUT from its assigned BS. As indicated in Fig. 4 we apply an exponential path-loss model with θUT = 3 (for BSUT and UT-UT links) and θBS = 2.5. Throughout this section we assume a cell-edge SNR at dUT = 250 m of 2 2 |h1,3 | P3 /σ12 = |h3,1 | P1 /σ32 = 0 dB (and similar for the second communication pair).

c rs b

R3 = R4

0.5 0

Fig. 6.

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Sym, no BS-coop Sym, perfect BS-coop Asym, no BS-coop Asym, with BS-coop

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/2

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Achievable DL rate regions for dUT = 150 m and η = 5/3.

Fig. 5 shows the results if both UTs are located at dUT = 230 m (α = 0.8 in the standard interference channel of Fig. 2), and η = 5/3, which is commonly used in IEEE 802.16m [12]. In this setup, the asymmetric UL-DL assignment creates two interference channels with strong interference between both paths. If we do not allow for BS cooperation (e. g. multi-cell MIMO), the asymmetric case Rasym 0/∞ clearly outperforms the symmetric case Rsym . Due to the strong interference between 0 both UTs and both BSs (β ≫ 0), both asymmetric cases provide the same performance. However, one might expect the rate region to be rectangular but it is a pentagon due to the asymmetric ratio η = 5/3. The common rate of both cells is limited by the time share that both obtain, and the maximum rate of both is limited by the UL. All protocols are outperformed by symmetric assignment and perfect BS cooperation (multi-cell MIMO) which, however, is much more complex and a theoretical outer bound for the symmetric case. Fig. 6 shows the results if both UTs are located at dUT = 150 m. Hence, both UTs interfere each other (β1 = 0.6 based on exponential path-loss), both BSs have a good direct link (β2 = 4), and the inter-cell interference is lower (α = 0.3) than in the previous example. Due to the decreased inter-cell interference, the symmetric case without backhaul Rsym im0 proves its performance and outperforms the asymmetric cases. This shows that the applicability of the asymmetric UL/DL assignment strongly depends on the channel conditions, which is further detailed by the next example. Consider Fig. 7 which shows the performance for varying values of dUT , η = 1, and rates relative to the symmetric, noncooperative case Rsym . Symmetric, perfect BS cooperation 0 (multi-cell MIMO) outperforms all other protocols due to its ability to cancel inter-cell interference and to exploit multi-cell diversity. Since the inter-BS interference is strong enough that it cannot be ignored and must be alleviated, the asymmetric, cooperative protocol Rasym applies SIC and hence outper∞ forms Rasym . An asymmetric assignment of UL/DL improves 0 the rates by up to 50% at the cell-edge while the performance drops below Rsym towards the cell-center. However, asymmet0

t u

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Relative Rate [%]

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cbq p rs

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Achievable DL common-rate for variable UT distance.

Cell 1:

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UL UL DL DL

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UL DL DL

must use orthogonal resources. This can be achieved based on CSI-feedback, e. g. if UTs indicate a preferred sub-band (standardized in IEEE 802.16m and 3GPP LTE). The previous analysis showed that multi-cell MIMO is able to exploit inter-cell interference while the asymmetric approach avoids this interference and creates different interference-situations with possibly preferable properties. However, the results for multi-cell MIMO are a theoretical outer bound as they assume perfect CSI of the compound channel at both BSs and (in the case of UL) perfect quantization of the received signal. Both are the main obstacles in realistic systems due to the strong latency and data-rate requirements. This makes the asymmetric approach an attractive alternative as the backhaul requirements of the asymmetric approach are much less stringent than those of multi-cell MIMO. VII. C ONCLUSIONS

0

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Fig. 8. Example for the different, overlapping regions with symmetric and asymmetric UL/DL assignment.

ric assignment is much less complex than multi-cell MIMO and therefore provides a better tradeoff of complexity and performance for large dUT while towards the cell-center noncooperative symmetric assignment provides the best tradeoff. This makes a mixed approach attractive where resources are assigned to both symmetric and asymmetric assignment. UTs at the cell center would then be served in the symmetric part while those at the cell edge would be served in the asymmetric part. Such an approach provides performance close to multicell MIMO while being much less complex. VI. I MPLEMENTATION A SPECTS In the asymmetric scenario, one cell is in UL while the other one is in DL. Hence, a value η ≈ 1 is preferable for the asymmetric assignment of UL and DL. In the case of η 6≈ 1, only one of both communication pairs may be optimized for η while the other one operates at an inverse η. However, in this case, it is an option to operate the system in a time-share of asymmetric and symmetric assignment. As mentioned, the asymmetric UL/DL assignment does not provide the best performance for all possible scenarios, but for scenarios with high inter-cell interference. Hence, it is preferable to schedule UTs depending on their channel conditions as well as data rate demand (in terms of η). Fig. 8 shows an example for 3GPP LTE [13] using DL to UL switch periodicity of 5 ms (switching subframes 1 and 6 are not shown). In this particular setup, UTs experiencing very high inter-cell interference may be scheduled in subframes 3 and 8 while all other UTs with moderate or no inter-cell interference are scheduled in the remaining subframes. This additional degree of freedom allows for inter-cell interference mitigation in full-reuse systems. If inter-UT interference cannot be canceled, e. g. if UT-cooperation is not supported, adjacent UTs

This paper introduced the two-way interference channel in order to analyze asymmetric UL/DL assignments of adjacent cells. It shows that this method is able to introduce a new degree of freedom and can improve the performance if existing approaches are not able to. The approach creates a new interference channel with parameters different to those of conventional inter-cell interference. Our future work will further investigate this approach on system-level and whether the shown link-level gains can be transferred to system-level. R EFERENCES [1] ITU-R, “Requirements, evaluation criteria and submission templates for the development of IMT-Advanced,” International Telecommunication Union (ITU), Tech. Rep. M.2133, 2008. [2] S. Shamai and B. Zaidel, “Enhancing the cellular downlink capacity via co-processing at the transmitting end,” in IEEE Vehicular Technology Conference (VTC), vol. 3, Rhodes, Greece, May 2001, pp. 1745–1749. [3] G. Fettweis, J. Holfeld, V. Kotzsch, P. Marsch, E. Ohlmer, Z. Rong, and P. Rost, “Field trial results for LTE-advanced concepts,” in IEEE Intnl. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Dallas (TX), USA, March 2010. [4] I. Tardy, O. Grondalen, and G. Vezzani, “Interference in TDD based LMDS systems,” in IST Mobile and Wireless Summit, Tessaloniki, Greece, June 2002. [5] C. Shannon, “Two-way communication channels,” in 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, 1961, pp. 611–644. [6] A. Carleial, “A case where interference does not reduce capacity,” IEEE Trans. Inform. Theory, vol. IT-21, no. 5, p. 569, September 1975. [7] H. Sato, “The capacity of the Gaussian interference channel under strong interference,” IEEE Trans. Inform. Theory, vol. IT-27, no. 6, pp. 786– 788, November 1981. [8] T. Han and K. Kobayashi, “A new achievable rate region for the interference channel,” IEEE Trans. Inform. Theory, vol. IT-27, no. 1, pp. 49–60, January 1981. [9] M. Costa, “On the Gaussian interference channel,” IEEE Trans. Inform. Theory, vol. IT-31, no. 5, pp. 607–615, September 1985. [10] ——, “Writing on dirty paper,” IEEE Trans. Inform. Theory, vol. IT-29, no. 3, pp. 439–441, May 1983. [11] S. Vishwanath, N. Jindal, and A. Goldsmith, “Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels,” IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2658–2668, October 2003. [12] IEEE Computer Society, “Air interface for broadband wireless access systems,” Tech. Rep., July 2010. [13] 3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA); Further advancements for E-UTRA physical layer aspects (Release 9),” 3GPP, Tech. Rep., Mar. 2010.