Random Access Game in Fading Channels with Capture: Equilibria and Braess-like Paradoxes

The Nash equilibrium point of the transmission probabilities in a slotted ALOHA system with selfish nodes is analyzed. The system consists of a finite number of heterogeneous nodes, each trying to minimize its average transmission probability (or power investment) selfishly while meeting its average throughput demand over the shared wireless channel to a common base station (BS). We use a game-theoretic approach to analyze the network under two reception models: one is called power capture, the other is called signal to interference plus noise ratio (SINR) capture. It is shown that, in some situations, Braess-like paradoxes may occur. That is, the performance of the system may become worse instead of better when channel state information (CSI) is available at the selfish nodes. In particular, for homogeneous nodes, we analytically present that Braess-like paradoxes occur in the power capture model, and in the SINR capture model with the capture ratio larger than one and the noise to signal ratio sufficiently small.Comment: 30 pages, 5 figure

On Modeling Coverage and Rate of Random Cellular Networks under Generic Channel Fading

In this paper we provide an analytic framework for computing the expected downlink coverage probability, and the associated data rate of cellular networks, where base stations are distributed in a random manner. The provided expressions are in computable integral forms that accommodate generic channel fading conditions. We develop these expressions by modelling the cellular interference using stochastic geometry analysis, then we employ them for comparing the coverage resulting from various channel fading conditions namely Rayleigh and Rician fading, in addition to the fading-less channel. Furthermore, we expand the work to accommodate the effects of random frequency reuse on the cellular coverage and rate. Monte-Carlo simulations are conducted to validate the theoretical analysis, where the results show a very close match

A delay analysis for opportunistic transmission in fading broadcast channels

We consider a single-antenna broadcast block fading channel (downlink scheduling) with n users where the transmission is packet-based and all users are backlogged. We define the delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. This is a more stringent notion of delay than average delay and is the worst case delay among the users. A delay optimal scheduling scheme, such as round-robin, achieves the delay of mn. In a heterogeneous network and for the optimal throughput strategy where the transmitter sends the packet to the user with the best channel conditions, we derive the moment generating function of the delay for any m and n. For large n and in a homogeneous network, the expected delay in receiving one packet by all the receivers scales as n log n, as opposed to n for the round-robin scheduling. We also show that when m grows faster than (log n)^r, for some r > 1, then the expected value of delay scales like mn. This roughly determines the time-scale required for the system to behave fairly in a homogeneous network. We then propose a scheme to significantly reduce the delay at the expense of a small throughput hit. We further look into two generalizations of our work: i) the effect of temporal channel correlation and ii) the advantage of multiple transmit antennas on the delay. For a channel with memory of two, we prove that the delay scales again like n log n no matter how severe the correlation is. For a system with M transmit antennas, we prove that the expected delay in receiving one packet by all the users scales like (n log n)/(M +O((M^2)/n) for large n and when M is not growing faster than log n. Thus, when the temporal channel correlation is zero, multiple transmit antenna systems do not reduce the delay significantly. However, when channel correlation is present, they can lead to significant gains by “decorrelating” the effective channel through means such as random beamforming

Joint collision resolution and transmit‐power adjustment for Aloha‐type random access

We consider uplink random access for which slotted Aloha has usually been employed with unknown channel conditions. Upon failure of a transmission attempt, a user cannot tell whether the failure was caused by collision with other simultaneously transmitting users or by his use of insufficient transmit power. If a transmission attempt failed due to collision which could have been resolved by retransmission, increasing transmit power would just waste power and, moreover, reduce the other users' chance of successful access. To handle this lack of information on the cause of failure, we propose a novel Cause‐of‐Failure resolution, where the transmit power is increased after a given number of consecutive unsuccessful access attempts when the probability that a given failure is caused by collision becomes sufficiently low. To exploit the thus‐obtained transmit power for the next random access attempt, we also determine the Cause‐of‐Success based on the number of consecutive successful attempts, i.e., whether to (probabilistically) decrease or maintain the current transmit power. This way, users can adjust their transmit power for random access, which we call Auto Power Fallback (APF), considered as an advanced version of the power ramping algorithm. We evaluate APF by modeling analysis and numerical computation based on the slotted Aloha, showing that APF determines a suitable transmit power for uplink random accesses while achieving good performance. Copyright © 2011 John Wiley & Sons, Ltd. We consider uplink random access for which slotted Aloha has usually been employed with unknown channel conditions. To handle this lack of information on the cause of failure , we propose a novel Cause‐of‐Failure resolution, where the transmit power is increased after a given number of consecutive unsuccessful access attempts when the probability that a given failure is caused by collision becomes sufficiently low. Users can adjust their transmit power for random access, which we call Auto Power Fallback (APF), considered as an advanced version of the power ramping algorithm.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96361/1/wcm1105.pd

Delay Considerations for Opportunistic Scheduling in Broadcast Fading Channels

We consider a single-antenna broadcast block fading channel with n users where the transmission is packetbased. We define the (packet) delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. This is a more stringent notion of delay than average delay and is the worst case (access) delay among the users. A delay optimal scheduling scheme, such as round-robin, achieves the delay of mn. For the opportunistic scheduling (which is throughput optimal) where the transmitter sends the packet to the user with the best channel conditions at each channel use, we derive the mean and variance of the delay for any m and n. For large n and in a homogeneous network, it is proved that the expected delay in receiving one packet by all the receivers scales as n log n, as opposed to n for the round-robin scheduling. We also show that when m grows faster than (log n)^r, for some r > 1, then the delay scales as mn. This roughly determines the timescale required for the system to behave fairly in a homogeneous network. We then propose a scheme to significantly reduce the delay at the expense of a small throughput hit. We further look into the advantage of multiple transmit antennas on the delay. For a system with M antennas in the transmitter where at each channel use packets are sent to M different users, we obtain the expected delay in receiving one packet by all the users