End-to-End Known-Interference Cancellation (E2E-KIC) with Multi-Hop Interference

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1 End-to-End Known-Interference Cancellation (EE-KIC) with Multi-Hop Interference Shiqiang Wang, Qingyang Song, Kailai Wu, Fanzhao Wang, Lei Guo School of Computer Science and Engnineering, Northeastern University, Shenyang, China Department of Electrical and Electronic Engineering, Imperial College London, United Kingdom arxiv: v [cs.it] 5 May 06 Abstract Recently, end-to-end known-interference cancellation (EE-KIC) has been proposed as a promising technique for wireless networks. It sequentially cancels out the known interferences at each node so that wireless multi-hop transmission can achieve a similar throughput as single-hop transmission. Existing work on EE-KIC assumed that the interference of a transmitter to those nodes outside the transmitter s communication range is negligible. In practice, however, this assumption is not always valid. There are many cases where a transmitter causes notable interference to nodes beyond its communication distance. From a wireless networking perspective, such interference is caused by a node to other nodes that are multiple hops away, thus we call it multi-hop interference. The presence of multi-hop interference poses fundamental challenges to EE-KIC, where known procedures cannot be directly applied. In this paper, we propose an EE-KIC approach which allows the existence of multi-hop interference. In particular, we present a method that iteratively cancels unknown interferences transmitted across multiple hops. We analyze mathematically why and when this approach works and the performance of it. The analysis is further supported by numerical results. Index Terms Communications, end-to-end knowninterference cancellation (EE-KIC), multi-hop transmission, wireless ad hoc networks I. INTRODUCTION Wireless multi-hop networks have attracted extensive interest due to its flexibility of deployment and adaptability to changing network topologies. These features are particularly useful for many emerging applications today, such as vehicular networking. One big problem in multi-hop networks is its performance degradation compared to single-hop networks. This is illustrated in Fig. (a), where node can only transmit one packet every three timeslots, due to the half-duplex nature of conventional radio transceivers and to avoid collision of adjacent packets. Obviously, if the transmission between the source and destination nodes are carried out in a single hop, node can transmit one packet per timeslot to node. It turns out that in this simple example, multi-hop transmission brings only one third of the throughput of single-hop transmission. A natural question is: Can we close this gap? Efforts have been made to improve the performance of multi-hop networks with advanced physical-layer techniques. In a large network, there may exist other transmitting nodes for which collision needs to be avoided, but we ignore that case here for simplicity. We also ignore packet losses, congestion, etc. Slot Slot Slot Slot x() x() (a) x() Useful Signal x() Slot Slot Slot Slot Interference Signal Figure. Procedure of conventional multi-hop communication (a) and EE- KIC (b), where node sends packets to node via nodes and. These techniques are generally based on the idea that interference signals known to the receiver a priori can be cancelled out from a superposed signal, where the superposed signal contains an unknown signal carrying new data and a set of known interferences. Such techniques are termed as knowninterference cancellation (KIC) []. One representative KIC technique is physical-layer network coding (PNC), where the relay node encodes the superposed signal into a new signal and broadcasts it out to nodes with decoding capability. The typical application of PNC is in twoway relay networks, which have two end nodes exchanging data via a common relay []. In this setting, PNC is able to transfer two packets every two slots for two symmetric data flows in opposite directions. On average, this corresponds to a throughput of 0.5 packet/(slot flow). While PNC can be extended to linear networks with more than two hops [], its throughput cannot exceed 0.5 packet/(slot flow). Another representative KIC technique is full duplex (FD) communication [], [5]. Here, wireless nodes can transmit and receive at the same time, by effectively cancelling its transmitted signal at the receiving antenna in real time. FD can achieve a throughput of packet/(slot flow) for bidirectional singlehop communications (containing two opposite flows), which is the same as what one can achieve for unidirectional single-hop communications. However, it is non-straightforward to directly extend FD to multi-hop communications. End-to-end KIC (EE-KIC) was recently proposed to boost up the throughput of wireless multi-hop networks. Unidirectional EE-KIC supporting a single flow can be achieved We refer to bidirectional data flows as two separate unidirectional data flows in this paper. x() x() x() x() (b) x() x() x() x() x()

2 by equipping nodes with FD transceivers [6]; bidirectional EE-KIC supporting two opposite flows can be achieved by leveraging both PNC and FD techniques [7]. It was shown that both unidirectional and bidirectional EE-KIC can achieve a throughput of packet/(slot flow) when ignoring a few idle timeslots caused by propagation delay. This implies that the throughput of EE-KIC is (almost) the same as the single-hop counterparts. The basic concept of EE-KIC is shown in Fig. (b). The source node starts the transmission by sending out its first packet x() to node in slot. Then, in slot, node sends its second packet x() and node relays the first packet x() to node. Node can receive x() while transmitting x() due to its FD capability. In slot, node sends x(), node sends x(), and node sends x(). Now, node can receive x() because it can cancel out x() transmitted by itself as well as x() transmitted by node. It can cancel out x() because it has received x() before and knows its contents. Node can receive x() due to its FD capability. Slot and all remaining slots are then analogous. With this approach, node is able to transmit one packet per slot, and node is able to receive one packet per slot starting from slot. In this example as well as existing work [6], [7], multihop interference has not been considered, i.e., it has been assumed that the signal transmitted by node is negligible at node, for instance. If this is not the case, the existing EE-KIC scheme becomes inapplicable. Consider slot in Fig. (b) as an example, if the signal transmitted by node causes strong interference at node, node may not be able to correctly receive x() from node. Unfortunately, such non-negligible multi-hop interference widely exist in practical scenarios. It is quite possible that two nodes are not close enough to correctly receive the transmitted data, but also not far away enough to ignore the transmitter s interference signal [8]. Therefore, we need to investigate whether and how EE- KIC works in scenarios with multi-hop interference. In this paper, we propose an EE-KIC scheme that is feasible for such scenarios. II. SYSTEM MODEL Similar to related work [], [6], [7], we focus on a chain topology with N nodes. We note that these nodes can be part of a larger network with arbitrary topology, and the chain subnetwork can be obtained via MAC protocols that support EE- KIC [6]. Nodes in the chain topology are sequentially indexed with,,..., N, where node is the source node, node N is the destination node. We use t to denote the timeslot index starting at, and use x(t) to denote the signal (containing data packet ) that the source node (indexed ) sends out in timeslot t. Let h ji denote the channel coefficient from node j to node i. We consider frequency-flat, slow-varying channels in this paper, so that h ji does not vary over our time of interest. We only focus on unidirectional EE-KIC in this paper, and refer to it as EE-KIC. We use x(t) to denote both the data packet and its corresponding signal in this paper. Useful Signal x(t ) x(t ) x(t ) Known Interference Signal Unknown Interference Signal Figure. Useful and (multi-hop) interference signals at node. We also assume that h ji is known a priori, while anticipating that techniques similar to blind KIC [] or correlation-based approaches [9] may be applied for cases with unknown h ji. We assume that when a node receives a superposed signal, it can successfully cancel out all its known signals. For example (see Fig. ), when N = 7, node knows the signals sent by nodes 5 and 6 because they were previously relayed by node. Thus, node can cancel out the signals transmitted by nodes 5 and 6 as well as its own transmitted signal (due to FD capability). Node intends to receive the signal sent by node, while nodes and are potential multi-hop interferers transmitting unknown signals for node. For an arbitrary node i (node in the above example), after cancelling out all known signals from nodes i (itself), i +,..., N, the remaining received signal in slot t is i y i (t) = h ji x (t j ) + z i (t), () j= where x (t i ) is the packet that node i intends to receive (which is sent by node i ), i j= h ji x (t j ) is the sum of unknown interference signals sent by nodes,..., i, and z i (t) is the noise signal with power σ. Residual interference caused by imperfect KIC can be considered as part of the noise, and we do not specifically study it in this paper. We use P T to denote the transmission power so that E [ x(t) ] = P T. The variables t j in () stand for the slot index when the packet has been sent out by node for the first time (see definition of x(t) earlier). We always have t = t > t >... > t i > t i due to the packet relaying sequence. The specific values of t j are related to the interference strength. For single-hop interference (see Fig. (b)), we always have t j t j =. For multi-hop interference, it is possible that t j t j > (see next section), which means that we may need to wait for more than one slot before we can cancel out all interferences and successfully decode the packet. We define j = t t j to denote the total delay incurred for transmitting the packet from node to node j. For simplicity, we assume that packets can always be correctly received if the signal-to-interference-plus-noise ratio (SINR) is larger than a threshold. In practice, this can be achieved by a properly designed error-correcting code. For the convenience of analysis later in this paper, we assume. III. INTERFERENCE CANCELLATION SCHEME We focus on how to cancel 5 the unknown multi-hop interferences, i.e., the i j= h ji x (t j ) terms in (). Cancellation 5 Strictly speaking, instead of cancelling, we aim to reduce the strength of unknown interferences to a satisfactory level so that the packet can be correctly decoded. For simplicity, we use the term cancel in this paper.

3 Slot Slot Slot Slot Slot 5 Slot 6 Slot Slot Slot 5 x() 5 x() x() 5 x() x() 5 x() x() 5 x(5) x() x() 5 x(6) x(5) x() 5 x() x() x(9) 5 x() x() x(0) x() 5 x(5) x() x() x() 5 Figure. Example with N = 5 showing the packet transmission procedure when there exists multi-hop interference. of known interferences is analogous with existing KIC work, so we do not consider it here. A. Constructive Example We first illustrate the interference cancellation procedure using a constructive example with N = 5, as shown in Fig.. Same as in the existing EE-KIC approach, node transmits one packet x(t) in every slot t {,,...}. Because there is no unknown multi-hop interference at the receiver of node, according to (), the signal that node receives in slot t (after cancelling any known interferences) is y (t) = h x (t) + z (t), from which it can successfully decode packet x(t). Node sends out its received packet in the next slot, so that the received signal at node in slot t is y (t) = h x (t) + h x (t ) + z (t), where h x (t ) carries the packet that node intends to receive, and h x (t) is the interference signal 6. Upon receiving y (t), node checks whether it can correctly decode the packet. If not, it assumes that this is due to the unknown multi-hop interference caused by node, in which case it waits for signals received in additional slots. In slot t +, node receives y (t + ) = h x (t + ) + h x (t) + z (t + ), which contains a strong signal h x (t) and a weak signal h x (t + ). Node can use the strong signal in y (t + ) that contains x(t) to eliminate the interference signal h x (t) in y (t). 6 Obviously, if h x (t) is strong enough, node can receive the packet x(t) sent by node directly without needing node as relay. However, we assume here that h x (t) is not strong enough for correct reception, because otherwise the underlying routing mechanism will not choose node as relay, but h x (t) may cause a remarkable level of interference that affects the correct reception of x (t ) from h x (t ). Explicitly, node calculates the following: g, (t) = y (t) h h y (t + ) = h x (t ) + z (t) h h (h x (t + ) + z (t + )). The resulting signal now contains the useful signal h x (t ) and the interference-plus-noise signal z (t) h h (h x (t + ) + z (t + )). We expect that the remaining interference-plus-noise signal in g, (t) is much smaller than h x (t) + z (t) in y (t), because h h and the additional noise signal z (t + ) is usually much weaker than the data-carrying signal. A rigorous analysis on the remaining interference-plus-noise power will be given later in this paper. If the remaining interference-plus-noise is still too strong, node can wait for one more slot to receive y (t + ) = h x (t + ) + h x (t + ) + z (t + ) and perform another round of cancellation to cancel out the term involving x (t + ) in g, (t), yielding g, (t) = g, (t) + h h y (t + ) = h x (t ) + z (t) h h z (t + ) + h h (h x (t + ) + z (t + )). Now, the remaining interference-plus-noise term is further smaller. Suppose node can now decode x(t) from g, (t), it can then send out x(t ) in the next slot t +, so that node receives the following signal for t 5: y (t) = h x (t) + h x (t ) + h x (t ) + z (t). Using the definition of t j and j in Section II, we have = t t =, because node transmits packet x(t ) in slot t. The operation is similar for node and all remaining nodes. From y (t), node intends to receive x (t ) transmitted by node, and has to cancel out the signals h x (t) and h x (t ) from nodes and, respectively. Node waits for four additional slots until it has received the following signals: y (t+) = h x(t+) + h x(t+) + h x(t) + z (t+) y (t+) = h x (t+) + h x (t+) + h x (t) + z (t+). It then computes g, (t) = y (t) h h y (t + ) h h y (t + ) to cancel out h x (t) and h x (t ) from y (t), which introduces additional interference terms (of much lower strength) involving x(t + ), x(t + ), and x(t + ). If needed, these can be cancelled out again using y (t + 6), y (t + 7), and y (t + 8) received in subsequent slots. Assuming the SINR is then sufficiently large for decoding x (t ), node can send

4 g i,m (t) g i,m (t) ± j = j = = h (i),i x(t i ) ± ± + j = j = j = j = j m= h jih ji h (i),i j = j = j m= j m= j m+= h jih ji h jmi h m y i (t + δ j + δ j δ jm ) () (i),i h jih ji h jm+i h m x(t i + δ j + δ j δ jm+ ) (i),i h jih ji h jmi h m z i (t + δ j + δ j δ jm )... (i),i z i (t + δ j + δ j ) j = h ji h (i),i z i (t + δ j ) + z i (t) () out x (t ) in slot t + 9, and we have =. In slots t, the destination node (indexed 5) receives y 5 (t)=h 5 x(t)+h 5 x(t)+h 5 x(t)+h 5 x(t)+z 5 (t). It intends to decode packet x(t ) which is carried in the strongest signal component of y 5 (t). The remaining interference terms can be cancelled using a similar approach as above. A Note on Time Shifting: Because we consider fixed values of h ji and SINR threshold, the number of additional signals (received after slot t) a node requires for successful interference cancellation remains unchanged, thus the values of j are also fixed 7. Therefore, from (), we have i y i (t + τ) = h ji x (t j + τ) + z i (t + τ) () j= for integer values of τ. This expression has also been used while discussing the above example. Also due to fixed j, each node is able to keep decoding and sending new packets every slot after it has successfully received its first packet, as shown in Fig.. This also holds for the general case presented next. B. General Case In general, when an arbitrary node i receives y i (t) (see ()), we aim to cancel out all the interference signals from nodes,,..., i, so that only h (i),i x (t i ) remains, from which we can decode x (t i ). We define δ j = t j t i for j < i. According to (), we have i y i (t + δ j ) = h ji x (t j + δ j ) + z i (t + δ j ) j= = h (i),i x (t j )+ h ji x (t j +δ j )+z i (t+δ j ), j= 7 For more general cases with variable h ji and, our scheme is still applicable. The only difference is that j may increase over time (or alternatively, we can fix it at a large value at the beginning), and there may be additional idle slots at certain nodes after packet transmission has started. We leave detailed studies on this aspect for future work, and assume fixed j values in this paper. where we note that t j = t i + δ j. This expression shows that node i transmits x (t j ) in slot t + δ j, so we can use y i (t + δ j ) to cancel h ji x (t j ) in y i (t). After waiting for max j<i δ j = i slots, node i can cancel all the interferences from y i (t) by calculating g i, (t) = y i (t) j = = h (i),i x(t i ) j = h ji h (i),i y i (t + δ j ) (5) j = j = h jih ji h (i),i x(t i +δ j +δ j ) h ji h (i),i z i (t + δ j ) + z i (t). (6) If another round of cancellation is needed to further reduce the remaining interference term i i h j ih j i j = j = h (i),i x(t i + δ j +δ j ), node i waits for additional i slots and calculates g i, (t) = g i, (t) + j = j = = h (i),i x(t i ) + + j = j = j = j = j = j = h jih ji h y i (t + δ j + δ j ) (7) (i),i h jih jih ji h x(t i +δ j +δ j +δ j ) (i),i h jih ji h z i (t + δ j + δ j ) (i),i h ji h (i),i z i (t + δ j ) + z i (t). (8) Considering the general case, the m-th round of cancellation is performed according to (), which can be expanded as (), where we denote g i,0 (t) = y i (t) for simplicity. These expressions are obtained by iteratively applying the following cancellation principle: Cancel all interference terms from g i,m (t) in the m- th cancellation round, without considering any additional interference terms that are brought in by the cancellation process (these additional interferences are cancelled in the next cancellation round if needed).

5 We note that the sign of interference signals inverses in every cancellation round, thus the ± sign in () takes + when m is even and when m is odd. In () and (), i j = i j m= j m= i j = stands for the concatenation of m sums with their respective iteration variables j,..., j m. It can be verified that (5) (8) are special cases of () and (). After m rounds of cancellation, m i slots have elapsed since slot t. If node i can successfully decode x (t i ) now, it sends out x (t i ) in slot t + m i +. End-to-End Delay: Assume that m is the same for different nodes i, we have i i = t i t i = m i +, yielding i = (m + ) i +, (9) which is a difference equation with respect to i. Noting that = 0, we can solve the difference equation (9) as { i if m = 0 i = (m+) i m, if m > 0. (0) We note that i is the end-to-end delay (expressed in the number of timeslots) of packet transmission from node to node i. Therefore, (0) is an expression for calculating the delay. The total delay from node to node N is N. IV. WHEN DOES IT WORK? In the following, we discuss insights behind the aforementioned interference cancellation scheme, and derive conditions under which the proposed scheme works. A. Upper Bound of Interference-Plus-Noise Power We note that in (), all the signal components starting from the second term (i.e., excluding h (i),i x(t i )) are either interference or noise. Let P I,m denote the total power of these interference-plus-noise signals in g i,m (t). We have an upper bound of P I,m. Proposition. For i, P I,m has the following upper bound: P I,m h(i),i (i )ρ m P T + σ ρm+ ρ, () where we recall that P T denotes the transmission power and σ denotes the noise power, ρ is defined as h (i),i (i ) ρ = h(i),i. () Proof: Because h ji h (i),i for j [, i ], by finding the power of g i,m (t) from its expression (), replacing the coefficients h ji at the numerators with the upper bound h(i),i, and noting that the noise-related terms constitute a geometric series, we have P I,m j = j = j m+= h(i),i (m+) h(i),i m P T m h + σ (i),i θ (i )θ θ=0 h (i),i θ = ( ) h(i),i h (i),i m (i ) (i ) h(i),i P T ( m ) h(i),i θ (i ) + σ h(i),i θ=0 = h(i),i (i )ρ m P T + σ ρm+ ρ. B. Sufficient Condition for Successful Packet Reception Proposition. Node i can successfully decode x(t i ) from g i,m (t) when the following conditions hold: h(i),i i < h (i),i σ h (i),i + () P T σ h (i),i h (i),i (i) m log ρ σ. () P T h (i),i h (i),i (i) Proof: We note that node i can successfully decode x(t i ) when the following condition holds: h(i),i P I,m. (5) Combining (5) with (), we obtain a stricter condition for successful reception: h (i),i h(i),i, (6) (i )ρm P T + σ ρ m+ ρ which is equivalent to h(i),i σ ρ ( ) h (i),i (i)p T σ ρ ρ m. ρ Substituting () into the above inequality, we know that (6) is equivalent to h(i),i σ ρ ( h (i),i P T ) σ ρ m+. ρ (7) Using elementary algebra, we can easily verify that when the following conditions are satisfied: h(i),i (thus h(i),i σ m log ρ ρ ρ <, (8) σ ρ > 0 (9) > 0 because ), h (i),i P T σ ρ h(i),i σ ρ, (0)

6 then (7) is satisfied, thus (5) and (6) are also satisfied. Substituting () into (8) (0), we can show that (8) is equivalent to i < h (i),i h (i),i +, and (9) is equivalent to (). Hence, when () holds, (8) and (9) also hold. The righthand side (RHS) of (0) is equal to the RHS of (), thus (0) holds when () holds. Proposition, which gives a set of sufficient conditions, provides a possibly conservative value on the number of required cancellation rounds m, governed by the lower bound in (). If () is satisfied, packet x(t i ) can be successfully received by node i when m satisfies (). We note that the minimum value of m satisfying () is always finite if () (thus (8) and (9) in the proof) holds. Therefore, we can say that multi-hop interference can be effectively cancelled within a finite number of rounds when () holds. C. How Many Nodes Are Allowed? Condition () imposes an upper bound on i, implying that i (thus N) cannot be too large. Assume that h ji d, where α ji d ji is the geographical distance between nodes j and i, and α is the path-loss exponent related to the wireless environment. Suppose we have equally spaced nodes, such that d (i),i = d (i),i. Define a quantity B > 0 such that h (i),i σ = B, () σ thus = B. When B = ɛ for an arbitrarily h (i),i P T small ɛ > 0, condition () becomes i < α + ɛ. () In practical environments, we normally have < α < 6, which means that the proposed approach always works for chain networks with N = nodes. Whether it works with more nodes depends on the value of α in the environment. For example when α =, we can have N = 6. Also note that we are using the sufficient condition given by Proposition, so our results here may be conservative (as we will see in the numerical results next section), and the proposed approach may work well with much larger values of N. The value of B in () is related to the placement of nodes. A smaller value of B implies a larger h (i),i. We should normally have B > because otherwise nodes i and i can communicate directly (when there is no interference) and node i may be ignored by common routing protocols. Aspects related to optimal node placement is open for future research. Because we fix the ratio h (i),i / h (i),i = α here, a smaller B also yields a larger h(i),i. V. NUMERICAL RESULTS We now present some numerical results of the proposed interference cancellation scheme based on the above analysis. We first evaluate the SINR after interference cancellation, at different nodes and with different number of cancellation rounds m. The same static channel model as in Section IV-C is SINR (db) SINR (db) SINR (db) m= m= m= m= (LB) (actual) m= m= m= m= (LB) (actual) (a) m= m= m= m= (LB) (actual) (b) (c) Figure. SINR at node i, under different values of m, where (a) α =., (b) α =, (c) α =. The solid lines denote the theoretical lower bound (LB) and the dashed lines denote the actual values. used in the evaluation. More realistic cases involving random channel coefficients is left for future work. We set the signalto-noise (SNR) ratio of single-hop transmission (without interference) to 0 db, based on which we can calculate the SINR of g i,m (t). We use two different methods to calculate the SINR. One is based on the theoretical interference-plus-

7 Figure 5. of m. Delay, i (timeslots) m= m= m= m= End-to-end delay from node to node i, under different values noise upper bound in (), which gives an SINR lower bound (LB); the other is based on the actual signal expression in (). Obviously, the second method gives the actual SINR, but it is also more complex than the first method. Fig. shows the results with different path-loss exponents α. Note that m = 0 corresponds to the existing EE-KIC approach without cancelling unknown multi-hop interferences. We can see from Fig. that the proposed approach (with m > 0) provides a significant gain in SINR. Even when m =, the gain compared to m = 0 is over db (based on the actual SINR values) in all cases we evaluate here. The gain goes higher when α is larger because the multihop interference is more attenuated with a larger α. This SINR gain is important for EE-KIC to work in scenarios with multi-hop interference. For example, consider α = and = 0 db, EE-KIC would not work without the proposed approach (i.e., m = 0) when N, because the SINR is below the = 0 db threshold; using a single round of cancellation with the proposed approach (i.e., m = ), the SINR becomes significantly above = 0 db and EE-KIC works (at least for N {,, 5, 6}). At node i =, the SINR is equal to the single-hop SNR (0 db), because there is no unknown multi-hop interference at this node. For nodes i, the SINR is below 0 db and depends on the value of m. As expected, a larger m yields a higher SINR. When m is large enough, the SINR becomes very close to the single-hop SNR. The theoretical LB is equal to the actual SINR when i =. At i >, the LB tends to significantly underestimate the SINR and thus the performance of the proposed approach. This is because the interference-plus-noise upper bound in () replaces all h ji for j < i with h(i),i, which remarkably enlarges the interferences from nodes that are three or more hops away. This validates that the results presented in Section IV-C are quite conservative, and the proposed approach should actually perform much better. Since it is hard to obtain meaningful analytical results directly from (), an interesting direction for future work is to find tighter theoretical bounds for the interference-plus-noise power. Fig. 5 shows the end-to-end delay from node to node i, i.e., the i values computed from (0). When i = N, this corresponds to the total delay from the source node (node ) to the destination node (node N). We see that the delay increases with the number of cancellation rounds m and the node index i. However, a good news is that m usually does not need to be too large to obtain a reasonably high SINR gain, as seen in Fig.. Also note that the packets in this paper do not need to be full data packets on the network layer. In fact, they can be as short as a single symbol if a proper scheduling and synchronization scheme is available. Furthermore, the delay is due to the idling time before each node receives its first packet. Once the first packet has been received, there is no additional delay for receiving subsequent packets. A large chain network does not necessarily have all nodes waiting for the first packet to arrive (or waiting for the whole transmission to complete). It can schedule some other transmissions in those idling slots instead. With such a properly designed scheduling mechanism, the throughput benefit of EE-KIC can still be maintained although the transmission delay may be large. VI. CONCLUSION In this paper, we have studied EE-KIC with multi-hop interference. 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