^{1}

^{*}

^{2}

^{*}

Continuous increase in demand of wireless services such as voice, data and multimedia is fueling the need of spectrally efficient techniques in communication networks. The MCCDMA-MIMO, a system of Multi Carrier Code Division Multiple Access (MCCDMA) technique with multiple antennas at both the transmitter and receiver gets benefits of ability to adopt multiple access capability from MCCDMA technique, achieves high data rate from MIMO concepts and becomes a very attractive multiple access technique for the future wireless communication systems. But, the wireless channels in MCCDMA-MIMO networks are known to display significant variations across active users’ subcarriers as well as among subcarriers of the same user due to simultaneous spectrum utilization. This leads to the undesirable Multiple-Access Interference (MAI) and Inters Carrier Interference (ICI), accordingly degrades the performance of the system. So, the interference mitigation methodology in the MCDMA-MIMO system has received a lot of attention in next generation mobile environment. The power control and sub carrier grouping methods have been long standing open solutions for capacity enhancement. The strategic choice of assigning the transmission power to each individual subcarrier in the MCCDMA-MIMO system is subjected to the knowledge of Channel State Information (CSI), which usually becomes imperfect due to the time varying nature of the channels. The goal of this paper is to allocate proper power to sub-carriers of MCCDMA-MIMO system by playing water filling game theory against the CSI errors to improve the performance of the system.

The Multi Carrier Code Division Multiple Access (MCCDMA) is becoming a very attractive multiple access technique for high-rate data transmission in the future wireless communication because of its multiple access capability, robustness against fading, and ISI mitigations [

In this paper, the MCCDMA-MIMO system subdivides subcarriers into a set of non-overlapping subcarrier groups. A user in the system is assigned to the subcarrier group that holds the best CSI and transmits the whole data of the user through the selected group of sub-carriers or varying the number of sub-carriers according to user’s requirement. The power control and group assignment methods processed with the knowledge of CSI as an objective function that is received from receiver. Power control and group assignment in MCCDMA give optimal solution only if the CSI is actual and valid. However, such performance gain comes at the expense of significant signaling overhead due to the sharing of CSI and transmission data. So, the CSI is subjected to the errors because of the imperfect channel estimation/measurement due to the time varying nature of the channels and does not provide the optimal solution for the mutual-information maximization problem. This paper considered the Signal Interference/Noise Ratio (SINR) of the given user assigned on the subcarrier group as an objective function to distribute power along the sub carrier groups to restrict the interference noise.

The game theory is an effective tool used to allocate power for each user with the independent knowledge of actual channel realization and gives solution for overall capacity maximization problem [

The organization of this paper is as follows. Section 2 deals with the system architecture of MCCDMA- MIMO system considered in this paper, formation of game model and strategy of the game for power control algorithm in MCCDMA-MIMO system. Section 3 describes solution for the problem and to maximize the pay- off using water filling game theory. The results are depicted in section 4 and the conclusions are given in section 5.

A multi cellular MCCDMA network constituted of

bandwidth “W” is subdivided into “N_{C}” subcarriers. Bandwidth of subcarriers is selected such that they approx-

imately exhibit flat fading channel characteristics (i.e., _{C}” is the coherence band-

width). Each “G” subcarriers constitute a group over which individual streams will be spread. As a result of subcarrier grouping, system bandwidth could be described in terms of a set of subcarrier groups,

Î B, is effectively supporting “U” active data users. Each base station operates under the constraint that it has at its disposal a maximum amount of power to share among all active sessions [

where

The time domain data stream for each user is divided into multiple parallel streams and each stream is spread using a spreading sequence as shown in _{t}” transmit antennas and “N_{r}” receive antennas and is illustrated in

The game model in the MCCDMA transmitter plays against the behavior of a wireless channel and assigns power level to the respective sub carriers. The game model also considered that the CSI errors are uncorrelated across subcarriers. The strategies of this game are the possible power level which can be assigned on the sub carriers subject to the constraint of total power at the transmitter and total sub carriers. The objective function in the strategy of the game is the SINR value received from the receiver [

where

This SINR value is considered as an objective function for the power control game to allocate the optimal power to each user. The channel capacity of the individual user “u” in the base station “b” is considered as utility function of the game and expressed as

The total system capacity of the base station “b” that constitutes “U” active users [

Then the MCCDMA symbols are transmitted through MIMO system of N_{t}, N_{r} antenna with channel matrix H(t, t) [

The water filling game theory concept is modeled with selfish users and each user is interested in maximizing their own normalized effective capacity, or achievable throughput (rate), subject to an average power constraint [

where

The water filling (WF) algorithm results in optimal solution only if the CSI is actual and valid. This, however, is not usually the case in realistic systems and environments due to the CSI estimation error. Due to the channel variation during the unavoidable delay, the noisy channel estimation and the limited feedback, perfect channel knowledge is not reachable by the transmitter in practice. The Clark’s correlation function of the fading process is defined as

where α_{m} is defined by the Bessel function of 0^{th} order J_{0}(2πf_{D}mT), and f_{D} is the Doppler frequency.

are the channel gain of the l^{th} and (l + m)^{th} frame of the n^{th} carrier.

After the l^{th} frame arrives the receiver, power and rate allocation can be effectively performed for the (l + m)^{th} frame at the transmitter, where the delay “m” is caused by the distance between the transmitter and the receiver. With the correlation function (7), the channel coefficient of the nth subcarrier in frequency domain for the (l + m)^{th} frame can be written

where V_{n}_{,k }is complex Gaussian distributed with zero mean and variance given by

If the transmitted data is known or correctly decided by the receiver, the estimated channel coefficient of the n^{th} subcarrier in frequency domain h_{n}_{,k} can be derived with the least squares channel estimation, shown as

The channel estimation error E_{n}_{,k} is a zero-mean complex Gaussian random variable with variance

The additive channel noise has almost identical characteristics over time. Thus, the reliability of the channel prediction can be available at the transmitter, and the receiver only needs to feed the estimated channel coefficients back. Before that, they must be quantized, i.e., represented by a limited number of bits, denoted by “B”. The quantized channel estimate of an arbitrary subcarrier “n” is referred to as

The quantization error can be generally expressed as a complex Gaussian distributed random variable with zero mean and variance

From the previous analysis, the channel estimation error E_{n}_{,k}, the quantization error Z_{n}_{,k} and the channel time-variation V_{n}_{,k} can be treated as stochastically independent. Therefore, the integrated CSI error η_{n}_{,k} is complex Gaussian distributed with zero mean and variance

With these imperfect CSI, the capacity maximization of overall MCCDMA-MIMO system is given by

which includes the CSI imperfection due to the channel variation during the feedback delay, the limited feedback.

To show the advantage of the sub carrier grouping with power distribution using IWFA algorithms under imperfect CSI, computer simulations are performed in multi-path propagation. The uncertainty of the CSI is

achieved through error variance in noise _{D} = 50 Hz, 100 Hz

and 150 Hz). The performance improvements of mean capacity of the system and BER reduction are analyzed with the numerical conditions shown

The group assignment strategy to maximize the overall mean capacity and minimize the BER using IWFA is followed by the algorithm mentioned in section 3. The capacity improvement of MCCDMA in SISO using IWFA is compared with power allocation without water filling algorithm. The Further capacity enhancement of MCCDMA through MIMO multiplexing (2 × 2, 4 × 4) is also analyzed with and without IWFA. _{D} = 50, f_{D} = 100 and f_{D} = 150 respectively. The power control and sub carrier group assignment strategy in the MCCDMA system improves the BER performance by eliminating transmission on poor subcarrier. Since majority of bit errors occur on severely de-graded subcarriers. The BER performances of the MCCDMA-MIMO system are shown in _{D} = 50, f_{D} = 100 and f_{D} = 150 respectively.

The MCCDMA-MIMO system with water filling has a greater performance enhancement as compared to the system without water filling even under the imperfect CSI. The capacity enhancement of the system is due to the proper power allocation to all users by IWFA with sub carrier group assignment strategy. The algorithm limits the interference noise among all users by avoiding excess power to any particular user and assigns the favorable

Simulation parameters | |
---|---|

Parameters | Specifications |

MCCDMA system | Multi cellular structure with three cell |

No of carriers (N_{C}) | 256 |

Number of groups | 16 |

Spreading factors | 16 |

Multipath channel model | Rayleigh fading |

Channel condition | AWGN channel |

MIMO sizes | 2 × 2 and 4 × 4 |

Monte Carlo Channel realization | 10,000 |

Number of iterations | 1000 |

SINR range | −10 dB to 30 dB |

Detector | MMSE |

sub carrier group according to data rate demands. The signal transmission of the system through MIMO gives an additional improvement of the system capacity.

The effect of CSI impairment caused by the channel variation during the unavoidable delay, the noisy channel estimation and the limited feedback in MCCDMA-MIMO system is considered in this paper. With this uncertainty conditions, the capacity enhancement and BER reduction in MCDMA-MIMO are achieved by IWFA based power control and sub carrier group assignment method. The power distribution to each user using IWFA is modeled based on the SINR value as an objective function which is received from receiver in the presence of imperfect CSI. The distribution of users across subcarrier groups as well as their transmission powers by IWFA method has a significant effect on how users and power are accordingly distributed elsewhere in the network to maximize the capacity and minimize the BER of the system.