Masoud Sharif

On the capacity of MIMO broadcast channels with partial side information

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.

On the capacity of MIMO broadcast channel with partial side information

Since having full channel state information in the transmitter is not reasonable in many applications and lack of channel knowledge does not lead to linear growth of the sum rate capacity as the number transmit antennas increases, it is therefore of interest to investigate transmission schemes that employ only partial CSI. In this paper, we propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the sum-rate capacity of our scheme scales as M log log n, which is precisely the same scaling obtained with perfect channel information. We furthermore show that linear increase in capacity can be obtained provided that M does not grow faster than O(log n). We also study the fairness of our scheduling scheme and show that, when M is large enough, the system becomes interference-dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path-loss. In fact, using M = /spl alpha/ log n transmit antennas emerges as a desirable operating point, both in terms of providing linear increase in capacity as well as in guaranteeing fairness.

A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users

In this letter, we derive the scaling laws of the sum rate for fading multiple-input multiple-output Gaussian broadcast channels using time sharing to the strongest user, dirty-paper coding (DPC), and beamforming, when the number of users (receivers) n is large. Throughout the letter, we assume a fix average transmit power and consider a block-fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like MloglognN for DPC, and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of time sharing to the strongest user scales like min(M,N)loglogn. Therefore, the asymptotic gain of DPC over time sharing for the sum rate is (M/min(M,N)) when M and N are fixed. It is also shown that if M grows as logn, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum-rate capacity of time -sharing scales like Nloglogn

On the peak-to-average power of OFDM signals based on oversampling

Orthogonal frequency-division multiplexing (OFDM) introduces large amplitude variations in time, which can result in significant signal distortion in the presence of nonlinear amplifiers. We introduce a new bound for the peak of the continuous envelope of an OFDM signal, based on the maximum of its corresponding oversampled sequence; it is shown to be very tight as the oversampling rate increases. The bound is then used to derive a closed-form probability upper bound for the complementary cumulative distribution function of the peak-to-mean envelope power ratio of uncoded OFDM signals for sufficiently large numbers of subcarriers. As another application of the bound for oversampled sequences, we propose tight relative error bounds for computation of the peak power using two main methods: the oversampled inverse fast Fourier transform and the method introduced for coded systems based on minimum distance decoding of the code.

Clipping noise cancellation in OFDM systems using oversampled signal reconstruction

Clipping the OFDM signals in the digital part of the transmitter is one of the simplest methods to reduce the peak factor. However, it suffers from additional clipping distortion, peak regrowth after digital to analog conversion, and out-of-band radiation in the case of oversampled sequence clipping. We use oversampled sequence clipping to combat the effect of peak regrowth and propose a method to reconstruct the clipped samples and mitigate the clipping distortion in the presence of channel noise at the expense of bandwidth expansion. We show through extensive simulations that by slightly increasing the bandwidth of the system, we can significantly improve the performance while limiting the maximum amplitude of the analog signal.

Scaling Laws of Cognitive Networks

Opportunistic secondary spectrum usage has the potential to dramatically increase spectral efficiency and rates of a network of secondary cognitive users. In this work we consider a cognitive network: n pairs of cognitive transmitter and receiver wish to communicate simultaneously in the presence of a single primary transmitter-receiver link. We assume each cognitive transmitter-receiver pair communicates in a realistic single-hop fashion, as cognitive links are likely to be highly localized in space. We first show that under an outage constraint on the primary links capacity, provided that the density of the cognitive users is constant, the sum-rate of the n cognitive links scales linearly with n as n ¿ ¿. This scaling is in contrast to the sum-rate scaling of ¿n seen in multi-hop ad-hoc networks. We then explore the optimal radius of the primary exclusive region: the region in which no secondary cognitive users may transmit, such that the outage constraint on the primary user is satisfied. We obtain bounds that help the design of this primary exclusive region, outside of which cognitive radios may freely transmit.

The Effect of Channel Estimation Error on the Throughput of Broadcast Channels

In a broadcast channel in which one transmitter serves n receivers, the capacity region highly depends on the amount of channel state information (CSI) at the transmitter. Assuming that the transmitter knows the SNR of all the receivers, opportunistic strategy maximizes the throughput (sum-rate) of the system. It is usually assumed that CSI is accurate, however, evaluating the SNR is basically an estimation problem in the receiver which cannot be done without error. In this paper, we analyze the effect of the noisy estimation of SNR on the throughput of a broadcast channel. We propose a generalization of the opportunistic transmission in which the transmitter still sends to the user with the highest estimated SNR, but backs off on the transmit rate based on the variance of the estimation error. We obtain the optimum amount of back off and compute the throughput for our scheduling scheme. Clearly, the estimation can be improved by using a longer training phase; however, longer training would deteriorate the throughput. In the final part of the paper, we address this trade off and obtain the optimum training strategy that maximizes the throughput of the system

Existence of codes with constant PMEPR and related design

Recently, several coding methods have been proposed to reduce the high peak-to-mean envelope ratio (PMEPR) of multicarrier signals. It has also been shown that with probability one, the PMEPR of any random codeword chosen from a symmetric quadrature amplitude modulation/phase shift keying (QAM/PSK) constellation is logn for large n, where n is the number of subcarriers. Therefore, the question is how much reduction beyond logn can one asymptotically achieve with coding, and what is the price in terms of the rate loss? In this paper, by optimally choosing the sign of each subcarrier, we prove the existence of q-ary codes of constant PMEPR for sufficiently large n and with a rate loss of at most log/sub q/2. We also obtain a Varsharmov-Gilbert-type upper bound on the rate of a code, given its minimum Hamming distance with constant PMEPR, for large n. Since ours is an existence result, we also study the problem of designing signs for PMEPR reduction. Motivated by a derandomization algorithm suggested by Spencer, we propose a deterministic and efficient algorithm to design signs such that the PMEPR of the resulting codeword is less than clogn for any n, where c is a constant independent of n. For symmetric q-ary constellations, this algorithm constructs a code with rate 1-log/sub q/2 and with PMEPR of clogn with simple encoding and decoding. Simulation results for our algorithm are presented.

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system parameters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.

Scaling laws of sum rate using time-sharing, DPC, and beamforming for MIMO broadcast channels

This paper derives scaling laws of the sum rate throughput for MIMO Gaussian broadcast channels using time-sharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Assuming a fixed total average transmit power, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like M log log nTV for DPC and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and TV are fixed, the sum rate of time-sharing to the strongest user scales like min(M,N) log log n. It is also shown that if M grows as logn, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum rate capacity of time-sharing scales like N log log n.