Cellular wireless network architectures employing a tiered structure, consisting of traditional macro-cells and small-cells, have attracted much attention recently because of their potential to dramatically increase network capacity. These architectures can reduce the distances of transmit-receiver pairs, thus enhancing radio link qualities. However, a tiered cell deployment could incur severe cochannel interference. Prior work for single-tier networks has proposed coordinated multi-point (CoMP) transmission, which includes joint transmission, as a possible solution for overcoming the rate limitations induced by cochannel interference. Because users in each cell experience various interference conditions, each cell needs to support single transmission (in which only one cell transmits to a single user) and joint transmission. In a conventional implementation, a particular combination of transmissions over the entire network is fixed in advance for each time slot and opportunistic scheduling chooses one of the users supported by each transmission. However, when the number of users to be scheduled is small, the throughput improvement from opportunistic scheduling becomes limited. To overcome this problem, we propose a cumulative distribution function-based scheduling scheme which jointly chooses the transmitter set and the corresponding scheduled users in a two-tier network. It is shown that the throughput performance can be improved compared to those of the fixed slot resource allocation scheme because more users "compete" for slot resources.

The above paper mistakenly employs the incorrect in- equalities of and in Appendix B, and as a result, it leads to incorrect derivation procedures of the lower and the upper-bounds on the average mutual information.

In this study, the authors present a resource allocation scheme that determines both a set of multicast basestations and a transmission scheme minimising the aggregate number of multicast resources in all of the multicast basestations while satisfying the multicast coverage requirement in an orthogonal frequency division multiple access-based single frequency networks (SFNs). In particular, the proposed scheme consists of two phases. In the first phase, a multicast basestation set and a transmission scheme are initially found to minimise the aggregate number of multicast resources. Then, in the second phase, the transmission scheme is adjusted according to the multicast users' performance reports. In addition, the multicast basestation set is adaptively updated if the aggregate number of multicast resources significantly changes as compared to that after the set was most recently updated. Using computer simulations, the authors demonstrate that the proposed scheme can efficiently utilise the radio resources for multicast transmission.

In modern wireless communications, systems that send a common information stream (called multicasting systems) are widely needed for distributing content such as television or radio. In this paper, the multiple antenna physical layer multicasting channel is considered, in which a common message is simultaneously transmitted to multiple single-antenna users. To achieve the capacity of this multicasting set-up, the covariance matrix of the transmit signal vector needs to be determined to maximize the smallest maximum achievable rate among all the users. In this paper, we develop a simple successive algorithm to determine the covariance matrix of the signal vector under the assumption that channel state information (CSI) is perfectly available at the transmitter. We first characterize properties of the capacity achieving covariance matrix and derive a closed-form expression for the matrix in the two-user case. We then derive a closed-form expression for the rate maximizing beamformer in the case of two users and propose a successive beamforming algorithm that generates the beamforming vector with low computational complexity. In the proposed precoding design scheme, the covariance matrix is successively constructed by orthogonalizing the subspace spanned by each user's channel vector until the maximum number of recursions (which is the same as the minimum of the number of transmit antennas and the number of users) is reached. The achievable rate of the proposed scheme is compared with the capacity of optimal transmission, transmit beamforming, antenna subset selection, and open-loop transmission which does not require CSI at the transmitter. As the number of users and/or antennas grows large, it is shown that the average achievable rate of the proposed scheme achieves the same average achievable rate scaling as the true capacity while reducing the computational complexity.

Wireless multicasting (also called common information broadcasting) is a technique where a common information message is transmitted to multiple users. This is typically accomplished by having the basestation broadcast out a signal representing this message. In this paper, we consider a multicasting scheme where the basestation transmits the multicasting signal without any a-priori knowledge of the users' channel state information. In this set-up, a hybrid automatic repeat request (ARQ) control is employed to improve the reliability of multicasting communication. In most hybrid ARQ set-ups, each user is usually allocated a dedicated feedback channel to tell the basestation if the previously transmitted signal was correctly decoded. However, dedicated feedback channels waste significant uplink resources, especially when the number of users is large. To mitigate this problem, we consider a negative acknowledgement (NACK) based hybrid ARQ control where the failed users are allowed to transmit the NACK signal (which is assumed to be the same for all users) through a common channel while the other users remain silent. We consider the effect of feedback error and multicasting signal decoding error on our hybrid ARQ system performance as the number of users grows large. Specifically, it is shown that the throughput performance of the proposed hybrid ARQ scheme using repetition retransmission is not severely degraded relative to the throughput performance of the noiseless feedback case. In addition, we show that the performance improvement obtained by replacing repetition encoding with incremental redundancy becomes insignificant for the large number of users asymptote. On the other hand, it is shown that the improvement provided by incremental redundancy is significant when some of the users are allowed to fail to decode the message.

Physical layer multicasting in wireless networks has been proposed to efficiently send an identical message to multiple users simultaneously. In this paper, we consider multiple antenna multicasting where the transmitter is equipped with Mtantennas and data is transmitted to K single-antenna users. When the downlink channels are assumed to follow an uncorrelated Rayleigh distribution, the multicasting capacity scaling for the large K asymptote is known. On the other hand, the effect of channel spatial correlation on the capacity performance has not been well addressed. Therefore, we investigate the effect of correlation using the channel correlation information at the transmitter. Using extreme value theory, it is shown that signaling using uniformly allocated transmit powers on the spatial channel correlation matrix's eigenvectors with non-zero eigenvalues approaches the multicasting capacity for the large K asymptote. Compared to the performance of uncorrelated fading channels with a constraint on the trace of the spatial correlation matrix, it is shown that the channel correlation degrades the performance. Specifically, if the correlation matrix is full rank the asymptotic outage (average) capacity ratio, which is defined as the ratio of the outage (average) capacities of the correlated fading channel and the uncorrelated fading channel as K goes to infinity, is equivalent to the geometric mean of the eigenvalues of the transmit channel correlation matrix of the correlated channel. On the other hand, if the correlation matrix is not full rank, the capacity ratios become zero. To assess the value of knowledge of the channel correlation information at the transmitter, we compare the asymptotic performances with and without knowledge of the channel correlation information. Specifically, the asymptotic performance improvement due to this correlation knowledge becomes (Mt/M)1/Mfor the large K asymptote, where M is the rank of the transmit channel correlation matrix. In addition, we discuss the issues of nonidentical transmit channel correlations among the users and correlation between users' channels.

In this paper, we present a hybrid automatic repeat request (ARQ) scheme for wireless multicast with incremental redundancy channel coding and packet retransmission. With this scheme, we can reliably deliver the same copy of information to different users with mild delay. In addition, the design of the feedback channel for this scheme can be greatly simplified as no effort must be expended to combat cross user interference. We assume that there is always a packet for the transmitter to send whenever the channel is available. The transmitter is assumed to have a buffer of infinite length so that there is no packet-dropping. Three specific schemes are studied, including generalized slotted ALOHA (GSA), repetition time diversity (RTD), and general incremental redundancy (IR). The scaling laws of the average delay and average throughput with respect of the number of users are derived. In addition, we also derive a condition to obtain a linear scaling for both the throughput and the delay with respect to the number of users. Since every user can achieve no more than the ergodic capacity, we actually achieve the optimal scaling law in this case. Simulation results confirm our findings.

Generally limited feedback systems that multiplex multiple user signals are noise power limited in the low signal-tonoise- ratio (SNR) regime and interference power limited in the high SNR regime. If the amount of feedback does not grow with SNR, then there is a sum rate ceiling that increasing the transmit power alone cannot surpass. This paper proposes a simple dual mode system where the base station serves either one user or as many users as the number of transmit antennas. The switching mechanism is smooth and is based on instantaneous system conditions. The mobile determines its preferred transmission mode by using a very simple signal-to-interference-and-noiseratio (SINR) threshold. Based on the mobiles' feedback, the base station chooses the method of signalling accordingly. With a finite number of feedback bits per mobile, it is shown that the proposed system achieves close to the maximum of the sum-rate for single user and multiuser modes. We identify the preferrable mode for an asymptotically large number of users and/or SNR. This proposed architecture is suitable for systems with moderate coherence time, a moderate to large number of users, and a moderate SNR that cannot afford complex processing at the base station or at the mobile.

Multiple-input multiple-output (MIMO) systems can be leveraged to increase capacity in fading channels. Especially in multiuser downlink communication systems, it has been shown that knowledge of channel state information at the transmitter (CSIT) is critical to leverage the capacity gain available from multiple antennas. When duplexing is performed using time division, CSIT can often be successfully obtained when channel reciprocity is available. CSIT acquisition, however, is much more difficult in frequency division duplexing. Sending feedback on the uplink has been shown to be a powerful technique to improve downlink performance in single user MIMO systems. The basic idea is to restrict the CSIT to a B bit codebook so that the mobiles can easily transmit these bits on the uplink. In this paper, we consider the multiuser downlink model with unitary precoding when there is a codebook consisting of 2Bunitary matrices that the precoder is restricted to lie in. This codebook is designed offline and known to both the base-station and all users. Each user sends back signal-to-interference plus noise ratio (SINR) information along with binary feedback about the unitary precoder. Based on the CSIT received on the uplink, the base-station selects one of the unitary matrices in the codebook to maximize the sum-rate. For this set-up, we first analyze the sum-rate performance of the unitary precoding scheme. We then show that the codebook of unitary pre-coders represents a collection of points in a special kind of manifold and show how the achievable sum-rate performance relates to the minimum distance of the codebook points in this space. Finally, we present a framework for constructing the codebook to maximize this minimum distance. Monte Carlo simulation results are presented to show the sum-rate performance of the proposed codebook design.

Wireless cellular networks often need to convey the same data to multiple users simultaneously. This kind of transmission is known as physical layer multicasting. Unfortunately, when any user fails to receive the data correctly, the information must be retransmitted to all the users, resulting in a waste of radio resources. Thus, it is important to investigate the outage probability of multicast channels, which is defined as the probability that the smallest maximum achievable rate among all of the users is smaller than a specified transmission rate. In this paper, we consider the use of multiple antenna multicast channels where the transmitter is equipped with Mtantennas and independent data is transmitted on each antenna to K users. Using extreme value theory, we derive a closed form limiting distribution that the exact distribution of the multicasting channel converges to when the number of users K is taken to infinity. From this result, we find upper and lower-bounds on the outage probability. It is shown that for a given outage probability the upper-bound becomes sufficiently tight to approximate the exact outage probability with K such that it converges to the exact one with a speed faster than Theta (K-1/Mt). Using this upper-bound, we identify conditions on the transmission rate and the transmit power necessary to maintain constant outage performance as K increases. Specifically, the transmission rate should be decreased as Theta (K-1/Mt) or the transmit power should be increased as Theta (K1/Mt). This means that the outage performance improves as the number of transmit antennas increases, because spatial diversity can be well exploited. However, this increase in the number of transmit antennas requires a significant cost. To improve the performance without requiring additional cost, we consider a multiple-slot multicasting that transmits the same data over multiple slots and an antenna subset selection scheme that transmits the data over some subset of the transmit antennas. It is shown that the transmission rate of multiple-slot scheme can be increased when the number of slots is carefully chosen and the diversity-multiplexing trade-off is the same as that of K = 1. Also, the gain in the transmission rate from selecting some subset of the transmit antennas is derived.

In this paper, we investigate the effect of spatial correlation on throughput performance of downlink multi-antenna transmission schemes exploiting multiuser diversity, in which partial channel information such as signal-to-interference plus noise power ratio (SINR) is available at the transmitter. The asymptotic analysis is performed based on the extreme value theory. From this analysis, we demonstrate that the throughput optimal transmission scheme depends on the degree of the antenna correlation and the operating SNR. Especially, the multiuser spatial multiplexing known as the asymptotically optimal transmission scheme is no longer optimal in highly correlated multiple antenna channels.

When a spread spectrum contention-based feedback channel is employed, it has been shown that most of the multiuser diversity gain can be maintained without any delay constraint. To address the delay in sending packets, we investigate how a spread spectrum contention-based feedback channel affects the delay and throughput performance. Using large deviations techniques, we show that most of the multiuser diversity gain can be maintained while satisfying a delay constraint in which the probability that the maximum delay of any bits in any users' queues is less than a specified value. In addition, we show that the spectral efficiency improves as the number of users increases while maintaining a fixed normalized maximum delay (which is defined as the ratio of the maximum delay and the number of users) as the number of users increases.

Limited feedback systems that simultaneously transmit to multiple users are noise power limited at low SNR and interference power limited at high SNR. Specifically, there is a sum rate upper bound such that increasing the transmit power alone cannot surpass. In this paper, we propose a dual-mode system that selects between single user mode and multiuser mode. The mobile determines its preferred transmission mode by a simple threshold rule of its SINR. Judiciously combining mobiles' feedback, the base station with MTtransmit antennas chooses the better communication mode. It is shown that this proposed system asymptotically achieves unbounded capacity growth when increasing the number of mobiles or when increasing the SNR, without requiring extra feedback bits. We show the asymptotically preferable mode as the number of users and/or SNR increases. Lastly, we use computer simulations to verify our findings.

In downlink multiuser systems, multiple-input multiple-output (MIMO) technology can be leveraged to increase capacity in fading channels. Knowledge of channel state information at the transmitter (CSIT) is important to obtaining this capacity gain. It is unrealistic to obtain perfect CSIT, but partial CSIT can often be made available by using some practical feedback method. Based on partial CSIT, codebook techniques have been shown to improve performance of MIMO multiuser systems. Unfortunately, the codebook design problem has not been fully investigated. In this paper, we consider a multiuser multiple antenna downlink model with unitary precoding using a codebook consisting of 2B unitary matrices. The appropriate precoding matrix is chosen from this codebook, which is known to both the basestation and the receivers. By defining and using a carefully chosen distance function, the minimum distance of the codebook is shown to relate to the average sum-rate of the unitary precoded system. From our analysis, a codebook design criterion is developed based on maximizing the minimum distance of the codebook. Then, a framework for constructing the codebook is presented to maximize this minimum distance. Monte Carlo simulation results are given to show the average sum-rate capacity performance of the proposed codebook design.

Multiuser diversity gain is an effective technique for improving the performance of wireless networks. This gain can be exploited by scheduling the users with the best current channel conditions. However, this kind of scheduling requires that the base station (or access point) knows some kind of channel quality indicator (CQI) information for every user in the system. When the wireless link lacks channel reciprocity, each user must feed back this CQI information to the base station. The required feedback load makes exploiting multiuser diversity extremely difficult when the number of users becomes large. To alleviate this problem, this paper considers a contention-based CQI feedback where only users whose channel gains are larger than a threshold are allowed to transmit their CQI information through a spread-spectrum based contention channel. Considering the capture effect in this contention channel, it is shown that i) the multiuser diversity gain can be exploited regardless of the number of transmit antennas at the base station and ii) the total system throughput exponentially approaches that of the full feedback scheme as the spreading code length of the contention channel linearly increases. In addition, it is also shown that multiuser diversity can be maintained with the feedback delay of time-variant channels. We also consider the issue of differentiated rate scheduling, in which the base station gives different rates to different subsets of mobiles. In this scenario, mobiles feed back their CQI with some access probability, and we show this technique causes only a negligible throughput loss compared to the case without supporting differentiated rate.

In this paper, we investigate throughput performance of downlink multi-antenna transmission schemes exploiting multiuser diversity. The asymptotic analysis is performed based on the extreme value theory. From this analysis, it is demonstrated that the multiuser spatial multiplexing known as the asymptotically optimal transmission scheme is no longer optimal in highly correlated multiple antenna channels