Capacity of Cellular Wireless Networks

Capacity of Cellular Wireless Networks

Abstract: In this paper, a tractable model of cellular wireless networks is considered, where both the base station (BS) and mobile user (MU) locations are distributed as independent Poisson point processes, and each MU connects to its nearest BS. Each packet from the BS is transmitted using an automatic repeat- request strategy until the signal-to-interference-plus-noise ratio (SINR) is larger than a threshold, and the packet delay is equal to the expected number of retransmissions required for successful reception. We define the network capacity as the product of the BS density and the reciprocal of the packet delay, maximized over all BS strategies.

This definition of capacity, while being natural, is non-trivial to analyses because of the temporal correlations of SINRs and arbitrary BS strategies. An exact characterization (non-asymptotic) of this natural capacity metric is derived, which shows that the capacity increases polynomially with the BS density in the low BS density regime and then scales inverse exponentially with the increasing BS density.

Existing system:

Cell densification, the number of base stations is increased to decrease the individual cell-sizes in the hope of improving connectivity and communication rate. Single-shot performance metrics such as connection probability or average rate have been considered in past for analyzing the effects of cell densification , that typically conclude that there is a phase transition; initially performance improves as the BS density increases, then it saturates, and eventually it starts to degrade, but explicit dependence was not identified. Taking a more comprehensive view via including retransmissions, where the effects of temporal correlations of SINRs are fully incorporated, we show that in the low-BS density regime, cell densification increases the capacity polynomially, while in the high-BS density regime, BS densification leads to a exponential fall in the capacity. Thus, cell densification needs to be undertaken judiciously.

Proposed system: The proposed strategy to achieve the lower bound on the min-local-delay only depends on the distance between the BS and the MU, and does not require channel state information (CSI) that changes at a much faster time scale than the distance.

In particular, if the BS-MU distance is d and the path-loss function is _(d), then the strategy transmits with power _(d)−1 with probability min{1,M_(d)−1} in any slot dedicated for the MU, where M is the average power constraint. Note that the strategy is not adaptive, making it suitable for practical implementation with low complexity. The basic idea behind the strategy is to transmit infrequently, but whenever an attempt is made, sufficient power is used to compensate the path-loss completely.

Advantages: Large BS densities, Theorem 2 is essentially a negative result that shows that even when each BS has all the local information, that can be used adaptively, the expected local delay increases at least exponentially with the density of BSs. Consequently, the network wide capacity decreases exponentially with the increase in the density of BSs in the high-BS density regime. We briefly discuss the key ideas used to derive the lower bounds on the expected local delay. To derive, we focus on the low-BS density regime, where interference is weak and the analysis is relatively easier.

Disadvantages: The difficulty arises because of arbitrary base station (BS) and mobile user (MU) locations and implementation of complicated scheduling protocols and signal processing algorithms. One approach to quantify the capacity is to run extensive simulations, however, that is computationally expensive.

An alternative approach that has been successful in past is to make some assumptions on node locations and approach the problem theoretically. With this motivation, in this paper, we consider the tractable model of a cellular wireless network, where BS locations are assumed to be distributed as a homogenous Poisson point process (PPP).

Modules: Mobile user: FINDING the capacity of a cellular wireless network is an important and challenging problem. The difficulty arises because of arbitrary base station (BS) and mobile user (MU) locations and implementation of complicated scheduling protocols and signal processing algorithms. One approach to quantify the capacity is to run extensive simulations, however, that is computationally expensive. An alternative approach that has been successful in past is to make some assumptions on node locations and approach the problem theoretically. With this motivation, in this paper, we consider the tractable model of a cellular wireless network, where BS locations are assumed to be distributed as a homogenous Poisson point process (PPP). The tractable model is a reasonable abstraction in the modern scenario, where multiple layers of BSs (macro, micro, femto) are overlaid over each other.

Moreover, we consider the widely used BS-MU (mobile user) association rule, where each MU connects to its nearest BS, i.e., all MUs lying in a Voronoi cell connect to the representative.

Single – to – interference – plus – noise ratio: We consider the signal-to-interference-plus-noise ratio (SINR) model of transmission for each BS-MU communication, where communication is deemed successful at the MU if the SINR is larger than a threshold that depends on the rate of transmission. In particular, following Shannon formula, if the rate of

transmission is log, then SINR greater than _ is sufficient for successful reception.

To model practical implementations, we also consider that each BS implements automatic-repeat-request (ARQ) for retransmitting packets until the SINR seen at the MU is above the specified threshold. For simplicity, only the basic ARQ is considered where each retransmission is decoded independently of previous rounds at the receiver, without any chase-combining or incremental redundancy (called hybrid-ARQ (HARQ). Most modern cellular networks use HARQ; however, presently it remains intractable for the problem considered in this paper, and is an object of future work.

Local Delay: In prior work, local delay has been considered in and several follow-up papers, for which either the analysis assumes that the SINRs are independent across time slots, or an ALOHA strategy is used by the BSs. With SINR independence assumption across time, the expected local delay is the reciprocal of the success probability in any one slot. While with the ALOHA strategy, conditioned on the location of the BSs, the SINRs are independent across time, and the expected local delay can be found by averaging over the location of the BSs. In this paper, since we are considering general BS strategies that can be both spatially and temporally correlated, such a direct analysis is not possible.

Channel state information: The proposed strategy to achieve the lower bound on the min-local-delay only depends on the distance between the BS and the MU, and does not require channel state information (CSI) that changes at a much faster time scale than the distance.

In particular, if the BS-MU distance is d and the path-loss function is _(d), then the strategy transmits with power _(d)−1 with probability min{1,M_(d)−1} in any slot dedicated for the MU, where M is the average power constraint. Note that the strategy is not adaptive, making it suitable for practical implementation with low complexity. The basic idea behind the strategy is to transmit infrequently, but whenever an attempt is made, sufficient power is used to compensate the path-loss completely.