How much feedback is required in MIMO Broadcast Channels?

In this paper, a downlink communication system, in which a Base Station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas ($K \leq M$), is considered. It is assumed that the receivers have perfect Channel State Information (CSI), while the BS only knows the partial CSI, provided by the receivers via feedback. The minimum amount of feedback required at the BS, to achieve the maximum sum-rate capacity in the asymptotic case of $N \to \infty$ and different ranges of SNR is studied. In the fixed and low SNR regimes, it is demonstrated that to achieve the maximum sum-rate, an infinite amount of feedback is required. Moreover, in order to reduce the gap to the optimum sum-rate to zero, in the fixed SNR regime, the minimum amount of feedback scales as $\theta(\ln \ln \ln N)$, which is achievable by the Random Beam-Forming scheme proposed in [14]. In the high SNR regime, two cases are considered; in the case of $K < M$, it is proved that the minimum amount of feedback bits to reduce the gap between the achievable sum-rate and the maximum sum-rate to zero grows logaritmically with SNR, which is achievable by the "Generalized Random Beam-Forming" scheme, proposed in [18]. In the case of $K = M$, it is shown that by using the Random Beam-Forming scheme and the total amount of feedback not growing with SNR, the maximum sum-rate capacity is achieved.Comment: Submitted to IEEE Trans. on Inform. Theor

On the Delay-Throughput Tradeoff in Distributed Wireless Networks

This paper deals with the delay-throughput analysis of a single-hop wireless network with $n$ transmitter/receiver pairs. All channels are assumed to be block Rayleigh fading with shadowing, described by parameters $(\alpha,\varpi)$, where $\alpha$ denotes the probability of shadowing and $\varpi$ represents the average cross-link gains. The analysis relies on the distributed on-off power allocation strategy (i.e., links with a direct channel gain above a certain threshold transmit at full power and the rest remain silent) for the deterministic and stochastic packet arrival processes. It is also assumed that each transmitter has a buffer size of one packet and dropping occurs once a packet arrives in the buffer while the previous packet has not been served. In the first part of the paper, we define a new notion of performance in the network, called effective throughput, which captures the effect of arrival process in the network throughput, and maximize it for different cases of packet arrival process. It is proved that the effective throughput of the network asymptotically scales as $\frac{\log n}{\hat{\alpha}}$, with $\hat{\alpha} \triangleq \alpha \varpi$, regardless of the packet arrival process. In the second part of the paper, we present the delay characteristics of the underlying network in terms of the packet dropping probability. We derive the sufficient conditions in the asymptotic case of $n \to \infty$ such that the packet dropping probability tend to zero, while achieving the maximum effective throughput of the network. Finally, we study the trade-off between the effective throughput, delay, and packet dropping probability of the network for different packet arrival processes.Comment: Submitted to IEEE Transactions on Information Theory (34 pages

Asymptotic Analysis of Amplify and Forward Relaying in a Parallel MIMO Relay Network

This paper considers the setup of a parallel MIMO relay network in which $K$ relays, each equipped with $N$ antennas, assist the transmitter and the receiver, each equipped with $M$ antennas, in the half-duplex mode, under the assumption that $N\geq{M}$. This setup has been studied in the literature like in \cite{nabar}, \cite{nabar2}, and \cite{qr}. In this paper, a simple scheme, the so-called Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of $K\to{\infty}$ with a gap no more than $O(\frac{1}{\log(K)})$. This result is shown to hold, as long as the power of the relays scales as $\omega(\frac{\log^9(K)}{K})$. Finally, the asymptotic SNR behavior is studied and it is proved that the proposed scheme achieves the full multiplexing gain, regardless of the number of relays

Scheduling and Codeword Length Optimization in Time Varying Wireless Networks

In this paper, a downlink scenario in which a single-antenna base station communicates with K single antenna users, over a time-correlated fading channel, is considered. It is assumed that channel state information is perfectly known at each receiver, while the statistical characteristics of the fading process and the fading gain at the beginning of each frame are known to the transmitter. By evaluating the random coding error exponent of the time-correlated fading channel, it is shown that there is an optimal codeword length which maximizes the throughput. The throughput of the conventional scheduling that transmits to the user with the maximum signal to noise ratio is examined using both fixed length codewords and variable length codewords. Although optimizing the codeword length improves the performance, it is shown that using the conventional scheduling, the gap between the achievable throughput and the maximum possible throughput of the system tends to infinity as K goes to infinity. A simple scheduling that considers both the signal to noise ratio and the channel time variation is proposed. It is shown that by using this scheduling, the gap between the achievable throughput and the maximum throughput of the system approaches zero

On the Throughput Maximization in Dencentralized Wireless Networks

A distributed single-hop wireless network with $K$ links is considered, where the links are partitioned into a fixed number ($M$) of clusters each operating in a subchannel with bandwidth $\frac{W}{M}$. The subchannels are assumed to be orthogonal to each other. A general shadow-fading model, described by parameters $(\alpha,\varpi)$, is considered where $\alpha$ denotes the probability of shadowing and $\varpi$ ($\varpi \leq 1$) represents the average cross-link gains. The main goal of this paper is to find the maximum network throughput in the asymptotic regime of $K \to \infty$, which is achieved by: i) proposing a distributed and non-iterative power allocation strategy, where the objective of each user is to maximize its best estimate (based on its local information, i.e., direct channel gain) of the average network throughput, and ii) choosing the optimum value for $M$. In the first part of the paper, the network hroughput is defined as the \textit{average sum-rate} of the network, which is shown to scale as $\Theta (\log K)$. Moreover, it is proved that in the strong interference scenario, the optimum power allocation strategy for each user is a threshold-based on-off scheme. In the second part, the network throughput is defined as the \textit{guaranteed sum-rate}, when the outage probability approaches zero. In this scenario, it is demonstrated that the on-off power allocation scheme maximizes the throughput, which scales as $\frac{W}{\alpha \varpi} \log K$. Moreover, the optimum spectrum sharing for maximizing the average sum-rate and the guaranteed sum-rate is achieved at M=1.Comment: Submitted to IEEE Transactions on Information Theor

SCMA Codebook Design

Multicarrier CDMA is a multiple access scheme in which modulated QAM symbols are spread over OFDMA tones by using a generally complex spreading sequence. Effectively, a QAM symbol is repeated over multiple tones. Low density signature (LDS) is a version of CDMA with low density spreading sequences allowing us to take advantage of a near optimal message passing algorithm (MPA) receiver with practically feasible complexity. Sparse code multiple access (SCMA) is a multi-dimensional codebook-based non-orthogonal spreading technique. In SCMA, the procedure of bit to QAM symbol mapping and spreading are combined together and incoming bits are directly mapped to multi-dimensional codewords of SCMA codebook sets. Each layer has its dedicated codebook. Shaping gain of a multi-dimensional constellation is one of the main sources of the performance improvement in comparison to the simple repetition of QAM symbols in LDS. Meanwhile, like LDS, SCMA enjoys the low complexity reception techniques due to the sparsity of SCMA codewords. In this paper a systematic approach is proposed to design SCMA codebooks mainly based on the design principles of lattice constellations. Simulation results are presented to show the performance gain of SCMA compared to LDS and OFDMA.Comment: Accepted for IEEE VTC-fall 201