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Consider a wireless communication system where the base station has multiple antennas and users have a single antenna. For both the multiple access and broadcast channels, the sum capacity scales at best linearly with the number of antennas at the base station and double logarithmically with the number of users as the user pool grows asymptotically...
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... authors proposed a scheduling algorithm for downlink space division multiple access (SDMA) with quantized CSI feedback. Since the upper-bound of P out decreases exponentially with the feedback load ¯ K, P out can be made arbitrarily close to zero by increasing ¯ K or equivalently the average feedback rate B(U ), since ¯ K = B(U )/ log(N T ). Fig. 3 shows that the upper bound of P out , namely N N/N t t e − ¯ K/Nt , decreases rapidly with ¯ K. The decreasing rate is lower for a larger number of antennas N t and vice ...
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... proof is given in Appendix B. To achieve the multi-user diversity gain, the probability P out in Theorem 1 must be close to zero [6]. As shown in Fig. 3, P out converges to zero rapidly by increasing the feedback load, namely the average number of feedback users. Consequently, from (26), the asymptotic capacity scaling can be made arbitrarily close to the optimal one N t log log U by increasing the feedback load. In summary, a wireless multi-antenna system using multi-user aware ...
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Citations
... One can also categorize limited feedback approaches according to whether all [4][5][6] or only an appropriate subset [30][31][32] of the users feed back their CSI. In the latter case, for a given maximum feedback rate, criteria are established so that the number of users that feed back their quantized channel is kept limited. ...
... In [31], multiuser aware limited feedback is proposed so that the optimal sum rate scaling is obtained in the large number of users limit. The authors design codebooks for channel norm and channel direction quantization based on orthonormal vector sets for the latter. ...
Multi-antenna schemes have been shown to provide remarkable gains in terms of spectral efficiency and extensive research has been dedicated to studying those in detail, discovering new setups in which multi-input multi-output (MIMO) schemes can be used and making them practical. This thesis is concerned with certain aspects of two particular setups in which MIMO techniques may be implemented, which we summarize below. - Limited feedback in the MIMO broadcast channel: We consider the downlink of a single cell where the base station (BS) has multiple antennas. A particular issue when dealing with such a system is that of channel state information at the transmitter (CSIT): this has been shown to play a cardinal role, particularly in the case when users are equipped with single antennas. Given the importance of acquiring that CSIT, and the fact that this acquisition comes at the cost of using resources on the uplink direction and introducing delays, a large body of literature has been concerned with limited feedback schemes for this setup. In this thesis, we contribute two ideas to try to make the most of the available feedback resource. - Coordination and Cooperation in multicell systems: The above model of a single cell corresponds roughly to current cellular designs where frequency planning is used to separate cells that use the same frequency resources so that inter-cell interference is limited. This is however not very efficient and MIMO techniques may be used to allow for increased performance at full reuse. Thus incorporating more antennas at a given BS gives it the possibility to mitigate the interference it causes at users in other cells. This is one of the topics we deal with in this thesis and propose a scheme which, while requiring local CSI only, is shown to perform quite well. MIMO techniques in a multicell environment can moreover extend to multicell processing (MCP), whereby several BSs pool their antennas to essentially act as a giant MIMO transmitter. % and jointly serve their users. This, however, has significant costs in terms of backhaul for data and CSI sharing, which threatens the scalability of MCP. We start investigating how to deal with limitations related to both these aspects.
... The set T1 is determined by the incomplete gamma distribution Gamma(Nt, 1) which can be bounded by [6][7]: ...
In MISO multiuser downlink wireless communication systems with precoding at the transmission, the capacity depends on the channel state information at the transmitter. Since the feedback data rate increases with the number of users in the cell it is important to perform a selection of the users at the receiver. In this paper, we evaluate the performance of different user selection algorithms at the receiver side through the noisy uplink channel. We evaluate the effect of the noisy channel on the classical norm criterion and on a criterion based on the orthogonality between the user channels. Without cooperation between the users, we only allow users that are semi-orthogonal to feedback their channel information as analog and quantized information to the base station through the noisy uplink channel. We propose an algorithm to reduce the noise effect on the analog feedback for semi-orthogonal user selection algorithm. We show that the semi-orthogonal criterion with quantized feedback gives better performance compared to the norm criterion for perfect and noisy uplink channels.
... In that work, feedback reduction is realized by silencing users for which the SINR estimate is below a certain threshold, while a constant feedback rate is used for users which pass the threshold. Extensions to the MIMO case were given in [14], [15] whereby not only the channel quality but also the accuracy of the quantized channel direction is considered in the feedback decision process. This contrasts with our approach where the adaptive process tweaks the quantization accuracy according to the channel quality seen by the user and, importantly, according to the probability of selection that the user estimates for itself. ...
We consider a MIMO broadcast channel where the channel state information at the transmitter (CSIT), to be used for user scheduling and beamforming, is gained through a limited-rate feedback channel. In view of optimizing the overall spectral efficiency of the system, we propose an adaptive scheme in which the feedback rate is no longer constant but rather optimized as a function of the time-dependent channel quality seen at the user side. One key idea is that, under an average feedback rate constraint, a user ought to provide more feedback at moments when it is more likely to be scheduled.We provide the theoretical grounds for our approach then derive quasi-optimal feedback resource allocation schemes, the performance of which is illustrated through Monte Carlo simulations.
... The set T 1 is determined by the incomplete gamma distribution Gamma(N t , 1) which can be bounded by [4][5]: ...
For MISO multi-user downlink wireless communication system with precoding at the transmission, the channel state information at the transmitter can provide tremendous capacity gains. However, the amount of feedback data increases with the number of users in the cell and the number of transmit antennas. In this paper, we study on different algorithms and criteria in order to significantly reduce the amount of feedback data. We associate the classical norm criterion with a criterion based on the orthogonality between the user channels. Without cooperation between the users, we only allow users that are semi-orthogonal to feedback their channel information (CQI and CDI) to the base station. The feedback CDI is quantized using a local grassmanian packing. We show that the proposed combined criterion with a finite feedback rate gives better performance compared to the norm criterion. Furthermore we show that the performance is not affected by CQI quantization.
... In a subset of the former (e.g. [5], [6]), randomly designed beams are launched from the base station, then the users reply with a simple SINR feedback to allow the assignment of the best set of users to the pre-launched beams, while in another (e.g. [12], [13], [14]) only an appropriate subset of the users feed back their channel and a subgroup of these users is selected for transmission. In the second category, the beamforming matrix is designed after receiving CSIT from all users in the form of their quantized channel information (see among others [8], [9], [10]). ...
An adaptive scheme was introduced in view of optimizing the overall spectral efficiency of a multiuser MIMO wireless broadcast channel where the channel state information at the transmitting base station (CSIT), to be used for user scheduling and beamforming, is acquired over a limited-rate feedback channel. In this scheme, the feedback rate is no longer constant per scheduling period but rather optimized as a function of the time-dependent channel quality seen at the user side. The present paper further refines this idea and elaborates on some of the associated practical concerns.
... However, when the feedback rate is fixed, the scaling is only maintained if the feedback rate is linearly scaled with SNR in dB [5, 6, 7]. One can also categorize limited feedback approaches according to whether all [6, 7, 8] or only a subset [9, 10, 11] of the users feed back their CSI. In the latter case, for a given maximum feedback rate, criteria are established so that the number of users that feedback their quantized channel is kept limited. ...
We consider the downlink of a multiuser MIMO channel, corresponding to a single cell with an N<sub>t</sub>-antenna base station and K single-antenna mobile terminals (MTs). It is known that when full channel state information (CSI) is available at the transmitter (full CSIT) the capacity of the system scales as N<sub>t</sub> log(P/N<sub>t</sub>- log K), under a total power constraint P [1], While, when the transmitter has no CSI, scaling reduces to that of a TDMA system. This paper examines the more realistic case of having an intermediate state of CSI. The key idea is based on a split of the allotted feedback between two stages: A first stage devoted to scheduling followed by a second stage for precoder design for the selected users. Based on an approximation of the achievable sum rate, we introduce a method for determining the splitting of the feedback rate so as to maximize performance and provide intuitions. We illustrate the gains of the 2-stage approach via Monte Carlo simulations.
We investigate a limited feedback precoder based on symbol pairwise error probability (PEP) for a block-faded K×n
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downlink multiple-input multiple-output (MIMO) channel. In the considered system, K = ⌊n
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⌋ single-antenna users feedback quantized channel state information to the n
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-antenna transmitter using B bits per-transmit-antenna per user. We analytically show that for α <; (1/2), B ≥ 1 and n
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→ ∞, both symbol PEP and achievable rate of each of the K downlink users almost surely converge to the symbol PEP and achievable rate of K parallel additive white Gaussian noise (AWGN) channels, respectively. We show that the encoding complexity of the precoder is O(n
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K). We also show that if channel coefficients estimated by the user are corrupted by AWGN noise, the symbol PEP and achievable rate of each user almost surely converge to the symbol PEP and achievable rate in a scaled AWGN channel with B > 1 and n
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→ ∞. For correlated channels, we derive a condition, which enables the proposed precoder almost surely to cancel multi-user interference for large n
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values. Finally, we numerically compare the bit error rate, encoding complexity, and per-user achievable rate of the proposed scheme with the existing designs.
In this chapter, we focus on the different feedback strategies for the case of a multiuser wireless communication system with multiple transmitter and receiver antennas. Firstly, we analyze the capacity of the multiuser MIMO system with single receive antenna for uplink and downlink by assuming that the full channel state information (CSI) is available at the transmitter. Secondly, we examine the precoding and user selection algorithms for MIMO multiuser systems with one and multiple receive antennas in flat fading and frequency selective wireless channels. Since optimal precoding using dirty paper coding has a prohibitively high computational complexity due to the associated encoding process, it is a great practical interest to design MIMO multiuser systems with low complexity and a minimum CSI requirement at the transmitter side. One suboptimal approach is to apply linear precoding schemes, such as zero forcing beamforming (ZF-BF) or minimum mean square error criterion. Multiuser MIMO wireless communication with ZF-BF requires a brute-force exhaustive search over all possible user sets and the complexity of an exhaustive search is prohibitive when the number of users is large. In order to decrease the complexity of this search, several suboptimal user scheduling algorithms have been designed. Generally, these algorithms fall into two categories: Capacity-based and Frobenius norm-based algorithm. Lastly, we show the effect of reduced and limited feedback information including user selection at the receiver side and quantization for both single carrier and multicarrier transmissions. We perform user selection at the user side since the users having a poor channel (low norm or/and interference) should not take part in the user selection algorithm, nor feedback their channel information. By using a self-discrimination criterion at the receiver side, it is possible to reduce the feedback load and the complexity of the user selection algorithm at base station. We show different user selection criteria and quantization strategies to reduce feedback load for both single and multicarrier communication systems.
In this paper, we propose a joint successive pre-coding and user selection algorithm in multi-user multiple-input multiple-output (MIMO) broadcast channel with limited feedback. The proposed scheme recalculates each user's best precoding vector by projecting the original precoding vector, which is obtained by limited feedback, onto the orthogonal complement space of the precoding vectors of the selected users. The base station (BS) then calculates the estimated signal-to-interference-plus-noise ratio (SINR) for each unselected user using the best precoding vector, and choose the one with the largest SINR. Numerical results illustrate the performance of the scheme.
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 2<sup>B</sup> unitary 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.
