Interference Cancellation at Receivers in Cache-Enabled Wireless Networks
In this paper, we propose to exploit the limited cache packets as side information to cancel incoming interference at the receiver side. We consider a stochastic network where the random locations of base stations and users are modeled using Poisson point processes. Caching schemes to reap both the local caching gain and the interference cancellation gain for the users are developed based on two factors: the density of different user subsets and the packets cached in the corresponding subsets. The packet loss rate (PLR) is analyzed, which depends on both the cached packets and the channel state information (CSI) available at the receiver. Theoretical results reveal the tradeoff between caching resource and wireless resource. The performance for different caching schemes are analyzed and the minimum achievable PLR for the distributed caching is derived.
Caching, interference cancellation, packet loss rate, caching scheme, Poisson point process.
Both the wireless network topology and the information transmission mode are changing with the advancement of information and communication technologies. In regard to the wireless network topology, nodes are densely and randomly located, yielding serious interference [SINR]. Interference is a key limitation on future networks. In regard to information transmission, content-centric services (e.g., multimedia transmission) instead of connection-centric services (e.g., voice communication) account for most of mobile traffic [5G2],[lau5G]. Caching exploiting content-centric traffic has been proposed to unleash the ultimate potential of the network [femto2, caching1].
There are some works on interference management in cache-enabled networks, which are in terms of the degrees of freedom (DoF) from the information-theoretic point of view. In [aided], an interference channel with three transmitters and three receivers is considered. It is shown that caching split files at transmitters can increase the throughput via interference management. In [IA], the DoF gain is proved to be achievable via caching parts of files at the transmitters for a three-user interference channel. Caching at base stations (BSs) for opportunistic multiple-input multiple-output cooperation is proposed in [Anliu] to achieve the DoF gain without requiring high-speed fronthaul links. In [lau5G], physical layer (PHY)-caching at BSs is proposed to mitigate interference and improve the number of DoF in wireless networks. The storage-latency tradeoff is analyzed in [sengupta] for the network with cache-enabled transmitters, and the transmission rate is specified by the DoF. The standard DoF is adopted in [tranrecei] as the performance metric for the network with interference channels. Transmitters and receivers are with caching strategy of equal file splitting. [hachem] studies the benefit of caching for the system with two cache-enabled transmitters and two cache-enabled receivers in the interference channel. The layered architecture is proposed and the DoF for the optimal strategy is computed. The concept of fractional delivery time (FDT) is proposed in [TMM] to reflect the DoF enhancement due to transmitter caching and the load reduction due to receiver caching. A complete constant-factor approximation of the DoF is proposed in [hachem2] for the network with caching at both transmitters and receivers.
However, previous works with information-theoretic framework assume that the global channel state information (CSI) is available. The performance for the network with only partial CSI available should be investigated. The randomness and complexity of node locations due to the stochastic topology of the network need to be addressed. And interference management is performed based on the caching at the transmitter side in previous works, where extra payload of fronthaul/backhaul is needed for the cooperation among transmitters. Moreover, caching schemes for cache-enabled networks to exploit both the local caching gain and the interference cancellation gain at the receiver side need to be elaborated further. Different from the information-theoretic framework, in this paper, we focus on the stochastic network where random numbers of BSs and users are spatially located in the two-dimensional plane. The effects of CSI are addressed and the caching schemes are analyzed. Our main contributions are summarized as follows,
We propose to cancel the incoming interference with partial CSI and cached packets at users. Random numbers of BSs and users are considered in the stochastic network.
The effects of the CSI are analyzed on the network performance in terms of packet loss rate (PLR), specifically, when partial, global and none of CSI are available.
The effects of the caching scheme on the PLR are further elaborated. And the optimal caching scheme for the users with distributed caching are provided to reap both the local caching gain and the interference cancellation gain.
Ii System model and Protocol description
Ii-a Network Architecture
Consider the wireless network where BSs and users are independently located according to Poisson Point Processes (PPPs) and . The intensities of and are and , respectively. The system is slotted and the duration of each slot is seconds. Each user is assumed to randomly request a packet of the fixed length Mb in a slot from the packet library [TMM]. The packet is requested by the user with the probability in the slot. Define as the packet access probability set. Note that and without loss of generality (w.l.o.g.), .
Each user has a limited caching storage with size of Mb, and of the packets in the packet library are pre-cached at the user. Therefore, there are totally kinds of caching schemes for different users. Classify all the users into subsets according to their caching schemes. Denote the density of the users in the -th subset as for , and . W.l.o.g., assume . Let denote whether users in the -th subset has cached packet (), where indicates that packet has been cached in the users of the -th subset, and otherwise. Then the caching scheme for the network depends on matrices and . Denote the set of the cached packets in the users of the -th subsect as . When the requested packet has been cached at the user, the user reads it out immediately from its local caching; otherwise, the user should obtain the requested packet from its nearest BS. Requests are waiting to be served in the infinite buffer of the BS, and each BS is assumed to transmit a packet in each slot on the FIFO-basis (first-in, first-out). Consider the service discipline that a request is dropped out of the buffer at the end of the slot assigned to it, no matter whether the BS has transmitted the requested packet successfully or not. The packet loss rate will be elaborated in Section III.
Ii-B Interference Cancellation with Cached Packets
All BSs share the same wireless channel with bandwidth of MHz to transmit packets to users in the downlink. Consider the CSI in the downlink is available at the user, if the distance from the BS to the user is smaller than . As a simplified prototype of the network, Fig. 1 illustrates two BSs ( and ) and two cache-enabled users. The first cache-enabled user has stored packets and the second cache-enabled user has stored packets . The two users are covered by and , respectively. When and transmit packet and , respectively, to the first and second users at the same slot, the received signal of the -th user is
for . is the transmit power, and are respectively the distance from the serving and the interfering to the -th user, and are the corresponding channel fading, denotes the path-loss exponent, and are the transmit signal with unit power, is the zero-mean additive white Gaussian noise (AWGN) with power . When the distance from to the -th user is smaller than , the CSI is known to the -th user. Consider there is a specific index table of the packets and it is known to all BSs and users. Before the interfering transmits a packet (e.g., packet ) which has been cached by the users around, broadcasts the packet index via extra interactive signals to let the users around know the incoming interference signal in the slot. Therefore, based on the CSI knowledge (i.e., ) and the side information (i.e., the cached packet : ), the -th user can cancel the interference (i.e., the term “” in equation (1)). Accordingly, the signal-to-interference-plus-noise ratio (SINR) of the -th user is .
Iii The packet loss rate
In each slot, of users in the -th subset sent their requests to BSs to obtain packet . Therefore, in the plane, totally of users sent their requests to the BSs to obtain packet . Then based on the aforementioned transmission scheme, in each slot the fraction of BSs transmitting packet is , which can be calculated by
where for . It is the average caching probability of packet over the whole network.
Based on Slivnyak’s theorem, we conduct the analysis with considering that there is a typical user at the origin of the Euclidean area [SINR]. Denote as the distance between the typical user and its serving BS. Due to the randomness of the BSs and users, the distance between the typical user and its serving BS is variable. The probability density function (PDF) of is [SINR]. When the typical user is in the -th subset and it requests packet which has not been cached in the local caching, the received signal of the typical user from its serving BS is given by
where is the desired signal of the typical user for packet . and are interfering signals. is the distance between the typical user and its serving BS. and are the distances from interfering BSs to the typical user. , and are the corresponding channel fading. Consider Rayleigh fading channel with average unit power in this paper. and are independently thinning PPPs with parameter and , respectively. is the distribution of interfering BSs transmitting packets included in the cached packet set , and is that of interfering BSs transmitting packets included in the complementary set . Note that the interference from the interfering BSs (distributed with ) inside the circle (centered at the origin with radius ) can be cancelled by the typical user with the knowledge of the CSI and the cached packets. Therefore, the residual interference of the typical user comes from i): the BSs distributed with outside the circle centered at the origin with radius (denoted by ), and ii): the BSs distributed with outside the circle centered at the origin with radius (denoted by ). It can be observed that , if all the users are with the same caching scheme (i.e., ). It implies the network cannot reap any interference cancellation gain when all users are with the same caching scheme. The impacts of caching schemes on the network performance will be investigated in Section LABEL:sec:schemes.
Therefore, the SINR of the typical user is given by
where are the residual interference after the interference cancellation. A packet will be lost if it cannot be transmitted completely over the slot assigned to it. The PLR can be calculated by
Denote . The average is taken over both the channel fading distribution and the spatial PPP. We then have,
The PLR for users in the -th subset to obtain the un-cached packets with partial CSI can be calculated with equation (1) at the bottom of the next page.
Please refer to the Appendix.
The PLR for the un-cached packet deceases with the increase of . It can be proved that when . Increasing (more CSI) is helpful to reap the interference cancellation gain and to reduce the PLR.
Moreover, the PLR of cached packets is zero because cached packets can be read out immediately from local caching. Accordingly, when the user in the -th subset requests packet which has or not been cached, the PLR is