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

On the existence of codes with constant bounded PMEPR for multicarrier signals

It has been shown that with probability one the peak to mean envelope power ratio (PMEPR) of any random codeword chosen from a symmetric QAM/PSK constellation is log n where n is the number of subcarriers [1]. In this paper, the existence of codes with nonzero rate and PMEPR bounded by a constant is established

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

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

We derive the 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 nN 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) log log n. It is also shown that if M grows as log n, 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

A deterministic algorithm that achieves the PMEPR of c log n for multicarrier signals

Multicarrier signals often exhibit large peak to mean envelope power ratios (PMEPR) which can be problematic in practice. In this paper, we study adjusting the sign of each subcarrier in order to reduce the PMEPR of a multicarrier signal with n subcarriers. Considering that any randomly chosen codeword has PMEPR of log n with probability one and for large values of n [1], randomly choosing signs should lead to the PMEPR of log n in the probability sense. Based on the derandomization algorithm suggested in [2], we propose a deterministic and efficient algorithm to design signs such that the PMEPR of the resulting codeword is less than c log n for any n where c is a constant independent of n. By using a symmetric q-ary constellation, this algorithm in fact constructs a code with rate 1 - logq 2, PMEPR of c log n, and with simple encoding and decoding. We then present simulation results for our algorithm

Delay guarantee versus throughput in broadcast fading channels

We consider a single-antenna broadcast fading channel with n backlogged users. Assuming the transmission is packet-based, we define the delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. A delay optimal strategy such as round-robin achieves the delay of mn. For the optimal throughput strategy (i.e. transmitting to the user with the best channel condition at each channel use), we derive the mean and variance of the delay for any m and n. For large n, it is proved that the expected delay in receiving the first packet in all users scales like n log n as opposed to n for the round-robin scheduling

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=αlogn 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