This paper proposes an efficient two-stage channel quantization and feedback scheme for the downlink limited-feedback network multiple-input multiple-output (MIMO) system. In the first stage, the users report their best set of base-station antenna and physical resource block combinations, and the base-stations schedule the best user for each antenna in each resource block. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. This paper proposes an analytical framework to show that, under a total feedback budget of B bits, the number of bits assigned to the second feedback stage should scale as log B, and in quantizing channel vectors from different base-stations, each user should allocate feedback bits in proportion to the channel magnitudes in dB scale. Under these optimized bit allocations, the overall sum rate of the system is shown to scale double-logarithmically with B, linearly with the total number of antennas, and logarithmically with transmit power, thus achieving both multiuser diversity and spatial multiplexing gains under limited feedback. Finally, realistic wireless propagation model of an urban small-cell deployment is used to show that the proposed scheme can approach the performance of a network MIMO system with full channel state information with only modest amount of channel feedback.

This paper proposes an efficient two-stage beamforming and scheduling algorithm for the limited-feedback cooperative multi-point (CoMP) systems. The system includes multiple base-stations cooperatively transmitting data to a pool of users, which share a rate-limited feedback channel for sending back the channel state information (CSI). The feedback mechanism is divided into two stages that are used separately for scheduling and beamforming. In the first stage, the users report their best channel gain from all the base-station antennas and the basestations schedule the best user for each of their antennas. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. The paper proposes an analytical framework to derive the bit allocation between the two feedback stages and the bit allocation for quantizing each user's CSI. For a total number of feedback bits B, it is shown that the number of bits assigned to the second feedback stage should scale as log B. Furthermore, in quantizing channel vectors from different base-stations, each user should allocate its feedback budget in proportion to the logarithm of the corresponding channel gains. These bit allocation are then used to show that the overall system performance scales double-logarithmically with B and logarithmically with the transmit SNR. The paper further presents several numerical results to show that, in comparison with other beamforming-scheduling algorithms in the literature, the proposed scheme provides a consistent improvement in downlink sum rate and network utility. Such improvements, in particular, are achieved in spite of a significant reduction in the beamforming-scheduling computational complexity, which makes the proposed scheme an attractive solution for practical system implementations.

This paper proposes an efficient two-stage limited feedback beamforming and scheduling scheme for multiple antenna cellular communication systems. The system model includes a base-station with M antennas and a large pool of users with a total feedback rate of B bits per fading block. The feedback process is divided into two stages. In the first stage, the users measure their channel gains from each antenna and feedback the index of the antenna with the highest channel gain along with the gain itself. Based on this information, the base station schedules M users with the highest channel gains from its M antennas and polls those users for explicit quantization of their vector channels in the second stage. Based on these quantized channels, the base-station then forms zero-forcing beamforming vectors for downlink transmission. This paper presents an approximate analysis for the proposed scheme which is used to optimize the bit allocation between the two feedback stages. It is shown that for a total number of feedback bits B, the number of feedback bits assigned to the second stage, B2, should scale as M(M-1) log(SNR × B). In particular, the fraction B2/B behaves as logB/B in the asymptotic regime where B → ∞. Further, the approximate downlink sum rate is shown to scale as M log SNR + M log log B, suggesting that both multiuser multiplexing and multiuser diversity gains are realized. As the numerical results verify, the proposed feedback scheme, in spite of its low complexity, performs very close to the more complicated beamforming and scheduling schemes in the literature and in fact outperforms such schemes in the high-SNR regime.

This paper studies the structure of the channel quantization codebook for multiuser MISO systems with limited channel state information at the base-station. The problem is cast in the form of minimizing the sum power subject to the worst-case SINR constraints over spherical channel uncertainty regions. This paper adopts a zero-forcing approach for beamforming vectors design, and uses a robust optimization technique via semideflnite programming (SDP) for power control as the benchmark performance measure. We then present an alternative less complex and practically feasible method for computing the power values and present sufficient conditions on the uncertainty radius so that the resulting sum power remains close to the SDP solution. The proposed conditions guarantee that the interference caused by the channel uncertainties can be effectively controlled. Based on these conditions, we study the structure of the channel quantization codebooks and show that the quantization codebook has a product form that involves spatially uniform quantization of the channel direction, and independent channel magnitude quantization which is uniform in dB scale. The structural insight obtained by our analysis also gives a bit-sharing law for dividing the quantization bits between the two codebooks. We finally show that the total number of quantization bits should increase as log(SINRtarget) as the target SINR increases.

This paper investigates the joint design and optimization of the power control and beamforming codebooks for the single-user multiple-input single-output (MISO) wireless systems with a rate-limited feedback link. The problem is cast in the form of minimizing the outage probability subject to the transmit power constraint and cardinality constraints on the beamforming and power codebooks. We show that by appropriately choosing and fixing the beamforming codebook and optimizing the power codebook for that beamforming codebook, it is possible to achieve a performance very close to the optimal joint optimization. Further, this paper investigates the optimal tradeoffs between beamforming and power codebook sizes for different number of feedback bits and transmit antennas. Given a target outage probability, our results provide the optimal codebook sizes independent of the target rate. As the outage probability decreases, we show that the optimal joint design should use fewer feedback bits for beamforming and more feedback bits for power control. The jointly optimized beamforming and power control modules combine the power gain of beamforming and diversity gain of power control, which enable it to approach the performance of the system with perfect channel state information as the feedback link capacity increases to infinity - something that is not possible with beamforming or power control alone.

We consider the problem of beamforming codebook design for limited feedback half-duplex multiple-input multiple output (MIMO) amplify-and-forward (AF) relay system. In the first part of the paper, the direct link between the source and the destination is ignored. Assuming perfect channel state information (CSI), we show that the source and the relay should map their signals to the dominant right singular vectors of the source-relay and relay-destination channels. For the limited feedback scenario, we prove the appropriateness of Grassmannian codebooks as the source and relay beamforming codebooks based on the distributions of the optimal source and relay beamforming vectors. In the second part of the paper, the direct link is considered in the problem model. Assuming perfect CSI, we derive the optimization problem that identifies the optimal source beamforming vector and show that the solution to this problem is uniformly distributed on the unit sphere for independent and identically distributed (i.i.d) Rayleigh channels. For the limited feedback scenario, we justify the appropriateness of Grassmannian codebooks for quantizing the optimal source beamforming vector based on its distribution. Finally, a modified quantization scheme is presented, which introduces a negligible penalty in the system performance but significantly reduces the required number of feedback bits.

In this paper, we discuss the optimum random and deterministic power selection algorithms in Aloha networks, where nodes run Exponential Backoff (EB) for contention resolution. In random case, the transmission power of a packet is selected from the available power levels, based on a predetermined probability mass function, while with the deterministic algorithms the transmission power of a packet is a deterministic function of the number of collisions the packet has experienced. Most of the related works in the literature have not addressed the power-throughput characteristics of the power selection algorithms for use in practical system designs and, therefore, this subject has been the major motivation of this paper. For the random case, we will derive optimum random power selection algorithms for unconstrained and constrained power budget scenarios and the corresponding optimum power-throughput characteristics will be presented for the latter case based on perfect capture model. Next, we will introduce a method to extend these results to SIR-based capture model, which will result in sub- optimum power steps and the sub-optimum power-throughput characteristics for the random case. This characteristic will reveal power budget requirements for the target throughput values. In the next step, deterministic power selection algorithms will be introduced and discussed with unconstrained and constrained power budget scenarios and sub-optimum power-throughput characteristic will be derived based on the perfect model. Similar methods, introduced for the random case, may be used to adapt the results to SIR-based model. Finally, by comparing the presented power-throughput characteristics, it will be demonstrated that optimum random and sub-optimum deterministic power selection algorithms have very similar behaviors. Therefore, noting that deterministic algorithms do not require any random power generator block, they may be preferred to random algorithms in similar scenarios.

In this paper, we will analyze a decentralized transmission power level selection algorithm in conjunction with Binary Exponential Back-off retransmission scheme, in large slotted-Aloha networks under saturation condition. In this algorithm, the transmission power is steadily increased by an amount called power step, until the packet is successfully transmitted. We will use SIR-based capture model to study the performance of this algorithm with small and large power steps. Our analysis proves that, although small power steps may seem favorable for power saving purposes, these power steps face throughput collapse under high load conditions (large number of nodes), while properly chosen large power steps guarantee higher throughputs and require approximately the same average powers.