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We study the important problem of resource allocation for the downlink of Multiple-Input Multiple output (MIMO) Multicast Wireless Systems operating over frequency-selective channels and we propose a low-complexity but efficient resource allocation algorithm for MIMO-enabled OFDMA systems. The proposed solution guarantees a minimum spectrum share for each user while also takes advantage of the multicast transmission mode. The presence of multiple antennas in both transmitter and receiver offers spatial diversity to the system along with the frequency diversity added by the OFDMA access scheme. The computational complexity is reduced from exponential to linear and validation of the proposed solution is achieved through various simulation scenarios in comparison with other multicast and unicast reference schemes used in MIMO-OFDMA systems. Numerical results and complexity analysis demonstrate the feasibility of the proposed algorithm.

Future wireless systems along with voice are envisioned to provide plethora of rich multimedia services like mobile TV, video conferencing, and so forth, with various bandwidth requirements [

Works [

OFDMA is based on Orthogonal Frequency Modulation (OFDM) scheme and helps exploit multiuser diversity in frequency-selective channels, since it is very likely that some subcarriers that are in deep fade for some users are in good channel state for at least one of the other users [

Dynamic resource allocation algorithms have been developed in order to exploit the multiuser diversity that OFDMA offers and improve system capacity. More specifically, in [

On the other hand, when multiple users demand the same multimedia content (Figure

Multiple users demand the same data content.

To that end, authors in [

In fading environments, MIMO technology offers significant increase in link range and improvement in spectrum efficiency without additional spectrum and power requirements. Due to these properties, MIMO systems have received much attention by researchers and manufacturers. The block diagram of a MIMO system is given in Figure

Block diagram of MIMO-OFDM multicast system.

The high computational complexity of optimally allocating subcarriers in MIMO systems [

In this paper, motivated by works in [

The rest of the paper is organized as follows. Section

The block diagram of the considered MIMO-OFDM-based wireless multicast system is given in Figure

Each user’s bits are modulated into

The great advantage of the multicast transmission is that data can be delivered to multiple receivers through a single transmission. However, each member user (MU) of a multicast group (MG) experiences a different Signal-to-Noise Ratio (SNR) on a specific subcarrier from other users in the same group. In other words, achievable data rates by individual users in a group are not equal on a particular subcarrier, and a widely adopted approach is to transmit at the data rate determined by the MU with the worst channel condition in an MG [

In this paper, the following assumptions are used.

The BS has perfect knowledge of channel state information (CSI) of all users in the system via dedicated feedback channels, and it is able to determine the maximum rate a user can receive data, as well as on which subcarrier the transmission takes place.

The transmitted signals experience slowly time varying fading, so the channel coefficients can be regarded as constants during the resource allocation process.

The transmission power is equally distributed among subcarriers; that is,

We assume the subcarrier allocation matrix

Considering the assumptions previous, the optimization problem in order to maximize the aggregate data rate while a minimum spectrum share is ensured for each MG is formulated as follows:

subject to

In the problem formulation, the binary variable

It is very hard to determine the optimal solution of the problem (

This section provides and analyzes the proposed low complexity resource allocation (LCRA) algorithm. The pseudocode of the LCRA algorithm is given in Algorithm

Find

Set

Find

Set

Update (

Inputs of the LCRA algorithm are the sets of the total available subcarriers

Find

Set

In step 2, the BS seeks the matching of MG

Find

Set

Update (

In step 3, if unallocated subcarriers exist, those are allocated according to the criterion of maximizing the aggregate data rate by allocating a subcarrier to the group with the best channel condition among all MGs. Then the selected subcarrier is excluded from the set

The problem described by (

In step 1, the algorithm requires constant time in order to form the involved sets and the power portion for each subcarrier.

In the second step, the pair of group and subcarrier which gives the highest

Step 3 searches for the best MG

The overall LCRA complexity is upper bounded by

It is worth mentioning that the design assumptions that only users of the same MG are capable of sharing a subcarrier and the spatial multiplexing MIMO mode we adopted, reduce significantly the system complexity. Exhaustive search for the optimal user selection for MIMO systems requires

Algorithm complexity.

Exhaustive search | LCRA | [ | Optimal user selection [ | Subcarrier allocation in [ |
---|---|---|---|---|

We consider an OFDMA system with

Simulation parameters.

Parameters | Values |
---|---|

Bandwidth | |

Number of subcarriers | 128 |

Number of transmit antennas | 2 |

Number of receive antennas | 2 |

Fast fading | Jakes Model |

Number of multipath components (taps) | 6 |

AWGN spectral density (single-sided) | −80 dBW/Hz |

Number of users | 16 |

Maximum doppler shift |

In all scenarios, the proposed LCRA algorithm is compared for different values of

Each variant is determined by the value of

It is important to highlight that as the number of MUs in an MG tends to infinity, the ergodic system capacity becomes independent of the MG size [

We validate the proposed scheme based on:

Fairness pointer is given in (

In this section, we give the performance of the LCRA in comparison with the reference multicast and unicast schemes described in the previous section. We launch simulations for various scenarios and those are outlined in the following.

In Figures

System data rate versus average SNR.

Fairness versus average SNR.

From Figure

This simulation scenario investigates spectral efficiency and fairness of the LCRA algorithm along with the other reference schemes against the average BER. Average BER varies from 10^{−7} to 10^{−3} with average SNR being set to 20 dB. Figure

Spectral efficiency versus average BER.

Fairness versus average BER.

In this simulation case, various numbers of multicast groups are considered from 2 to 8, whereby SNR

Spectral efficiency versus number of MGs.

Fairness pointer versus number of MGs.

From Figure

We consider two different multicast services which are provided to the available users. Thus, users are divided into two MGs, namely, MG-1 and MG-2 and we also consider that we have

Spectral efficiency versus SNR-no pathloss difference between MGs.

Fairness pointer versus SNR—no pathloss difference between MGs.

Spectral efficiency versus SNR—pathloss difference between MGs.

Fairness pointer versus SNR—pathloss difference between MGs.

Individual MG spectral efficiency versus SNR—no pathloss difference between MGs.

Individual MG spectral efficiency versus SNR—pathloss difference between MGs.

Channel distribution—no pathloss difference between MGs.

Channel distribution—pathloss difference between MGs.

From Figures

When there is no pathloss difference between the groups, individual MG rates seem to be very close as well as their assigned spectrum. More specifically, the average channel distribution is 64.6 and 63.4 subcarriers for MG-1 and MG-2, respectively. The proposed LCRA gives 64.4 subcarriers to MG-1 and 63.6 to MG-2 on average, while with TDMA, strict fairness exists with 64 subcarriers to each group.

On the other hand, when pathloss is considered in simulations, we see that the group with less pathloss (MG-2) gives better performance than multicast group MG-1 in all schemes. The gap between the achievable bit rates of MG-1 and MG-2 is wider with the scheme in [

In this paper, a resource allocation algorithm for the MIMO multicast systems over frequency-selective channels has been introduced. Multicasting enables multiple users to share a subcarrier and results have shown that this enhances significantly the total throughput. The capacity can become even higher by the presence of multiple MGs which bring more diversity into the system.

The proposed algorithm proved also to be very useful in systems wherein multiple MGs coexist, particularly in case their wireless link conditions are very different. LCRA is capable of providing bandwidth access guarantees to MGs in a flexible and controllable way that other reference schemes are unable to provide.

In parallel the proposed solution achieves low-complexity implementation by reducing the computational complexity from exponential to linear. Additionally, its computational complexity is independent of the presence of multiple antennas in both BS and users and as it is analyzed proved to be comparable with other low-complexity schemes.