The use of multiple-input multiple-output (MIMO) systems with multiple antenna elements provides an efficient solution for future wireless communication. In recent times, wireless communication has been characterized by high speed, higher data throughput, and high Bit Error Rate (BER) in a limited bandwidth. Low data speed handover, low Signal Noise Ratio (SNR), and hardware power drainage are common channel problems with wireless systems. The objective of this research seeks a way to optimize channel capacity and enhance system performance. The paper presents a comprehensive performance analysis of channel capacity under the Rayleigh fading channel using water water-filling technique. MATLAB was used to analyze and simulate the process. Simulation results revealed that the water-filling algorithm can effectively optimize channel capacity in the wireless communication system.

Today wireless communication system is faced with several channel impairments including but not limited to low bit error rates, drop calls, high power consumption such as those experienced in the third generation (3G), Long Term Evolution (LTE), worldwide interoperability for microwave access (WiMAX), and wireless fidelity (WIFI). To overcome these challenges, the MIMO communication technique was introduced to provide high quality of service, increase the data rate, improve coverage, reduce outage probabilities, and carry out another performance matrix of data communications. MIMO guaranteed spatial diversity gains to overcome small-scale fading effects by using diversity. It reduces path loss, by using array gain in the distribution of the antennas. It increases capacity by spatial multiplexing using parallel stream transmission and Spatial Division Multiple Access (SDMA); by focusing on a narrow transmission beam using a smart antenna. MIMO uses beamforming to enhance interference reduction and spatial multiplexing, and special MIMO for close-loop spatial multiplexing [

The transmission energy can be managed and minimized with an optimum resource allocation technique. This resource allocation is fundamentally based on the convex optimization problem which uses the water-filling algorithms principle [

The main objective of this work is to optimize the channel capacity of wireless communication systems. To achieve this, an iterative Water-filling algorithm is used for the MIMO system. The performance analysis is recorded based on the simulation results of ergodic capacity, Bit-Error-Rate (BER), outage probability, and channel gains using Binary phase shift keying (BPSK) modulation techniques. MATLAB simulation was used during the simulation process.

The rest of the paper is organized as follows: related literatures were discussed in Section 2. The research methodologies and system model were defined in Section 3. In Section 4, results and a discussion of simulation were presented. Finally, the summary and conclusion are presented in Section 5.

A MIMO system was inspired by papers presented by two renowned engineer scientists; Telatar and Foschini. They inferred that there is a dramatic linear increase in channel capacity with some antennas [

Spatial Diversity is employed to make the transmission more robust, though it does not increase data rate as inferred by studies carried out by [

In [

Power allocation is an optimization problem to maximize capacity. Depending on the closed or opened loop mode, allocation is based on CSI. Intuitively we will allocate more power to channels based on performance quality.

Ideally, channels are expected to be naturally very turbulent due to physical and logical phenomena along and within which they are composed. The question of whether all the approaches that were studied in the literature as means of optimizing the channel affect its performances in resolving data distortion/contamination in wireless communication has to be addressed. In this research, we therefore analyzed the water-filling algorithm by means of considering the channel SNR and making an assumption that

The system model of a wireless communication system is, to consider a transmitter with N transmits antennas, and a receiver with M receives antennas. The channel can be modeled by the

where x is the M × 1 transmitted vector and n is the N × 1 Additive White Guassian Noise (AWGN) vector, normalized so that its covariance matrix is an identity matrix.

_{N}, the identity matrix of N. In the formula, the H can be defined as

The capacity of a random MIMO channel with power constraint P_{T} can be presented as an expected value of

where Φ = E_{T.}

Estimating the capacity of a MIMO system the channel state information (CSI) is a critical parameter that must be determined.

When the transmitter does not know the channel; In this case, it is optimal to use a uniform power distribution [

Uncorrelated noise can also be assumed in each receiver branch which is described by the covariance matrix given by

The mean capacity for a MIMO channel can therefore be presented as:

where ρ =

MIMO channel ‘H’ can further be analyzed by taking diagonal the product matrix

where E is the eigenvector matrix with orthogonal column and ∧ is the diagonal matrix with the eigenvalue on the main diagonal. Using this notation, the mean channel capacity will be represented as:

By using the Singular value decomposition the product

U and V are unitary matrices of left and right singular vectors respectively and Σ a diagonal matrix with singular values on the main diagonal. Capacity will be presented as:

With the diagonalization of the product matrix, the channel capacity of MIMO is seen to include unitary and diagonal matrices only. Thus, total capacity of a MIMO channel consists of the sum of parallel AWGN SISO sub-channels. The number of parallel sub-channels is determined using the rank of the channel matrix. This rank of the channel matrix is given as:

Applying the rank (H) recalling that the determinant of a unitary matrix is equal to unity, the channel capacity can be represented respectively as:

where _{T} is received by an equal number of n_{R} antennas without interferences occurring, or where each transmitted signal is received by a separate set of receive antennas.

The capacity of the MIMO channel when channel information is unknown at the transmitter is maximized when all the eigenvalues

This means that the capacity of an orthogonal MIMO channel is M times the capacity of a SISO channel.

When the channel matrix is understood at the transmitter; Here, the maximum capacity of the MIMO channel may be achieved by employing a technique of distributing power to a channel of lesser noise [

where

With a reduced range of non-zero singular values in the data rate equations, the capability of the MIMO channel is guaranteed to be reduced owing to a rank-deficient channel matrix. This situation occurs when the signals arriving at the receivers are correlated. Low correlation is not a guarantee of high capacity even though a high channel rank is necessary to obtain a high spectral efficiency in MIMO [

The study adopted the water-filling model. This model is comparable to gushing water into a vessel. In communication systems, it’s accustomed to denote an inspiration in system design style and observe for exploit methods on communications channels. In analogous, Pascal law, the amplifies system in communications network repeaters or receivers amplifies every channel to the desired power level to compensate the channel impairments [

The water-filing algorithm rule proves its optimality for channels having Additive White Gaussian Noise (AWGN) and inter-symbol interference (ISI). It is a customary baseline algorithmic rule for numerous digital communications systems. The entire quantity of water filled symbolizes the power allocated (Pt) to the system. See illustration in

where Pt is the power budget of MIMO system which is allocated among the different channels and H is the channel matrix of the system. Channel capability is given as:

For the ergodic channel capacity, considering the two case situations, the

The algorithms follow as below:

1. Re-order the MIMO sub-channel gain realization in an ascending order

2. Take the inverse of the channel gains.

3. Water filling has a non-uniform step structure due to the inverse of the channel gain.

4. ab initio, take the sum of the Total Power (Pt) and the Inverse of the channel gain. It provides the whole space in the water-filling and inverse power gain.

5. Decide the initial water level by the formula given below by taking the average power allocated (average water level)

6. The power values of each sub-channel are calculated by subtracting the inverse channel gain of each channel.

7. Discontinue the iteration process at any level where the Power allocated value becomes negative.

Here Pt = total level of power provide,

Another index of system performances of the data rate (channel capacity) is the outage probability. Capacity on the channel instant response is supposed to remain constant throughout the transmission of a finite-length coded block of data. If it falls below the outage capacity, there is a chance that the transmit block of data may be decoded with error, whichever committal to the writing theme (coding scheme) is utilized. The chance that the capacity is a smaller amount than the outage capability is denoted by the letter q. This is expressed by

In a finite probability (1 − q) where the channel capacity is higher than

During this section, the results are presented and discussed based on the outcome.

This study deploys several parameters to simulate the channel capacity (data rate) of wireless communication. These parameters were used to support the areas of consideration within the MATlab codes.

S/N | Parameter | Values |
---|---|---|

1 | Transmitted power | [3], [2], [1], [4], [0] |

2 | Transmitted power | 10 |

3 | Capacity | 4.7027 |

4 | Total power | 5 |

5 | Input power | [4], [3], [2], [1], [0] |

6 | Noise power | [2], [3], [4], [1], [5] |

7 | Numbers of channels | 5 |

8 | Frequency | Rayliegh |

9 | Modulation | BPSK |

In

The MIMO channel capacity has so far been optimized based on the assumption that all transmit and receive antennas are used simultaneously. From the simulation results, there is a far difference in channel capacity when different arrays of antennas are used. In _{T} and N_{R}. The reason for the variation is that under a close loop, the transmit power is shared to a channel with less noise. This shows that a key part of the Eigen beamforming technique is choosing appropriate powers for each of the transmitted symbols. As SNR increases, there seems to be a convergence in capacity. However, the differences between the two conditions were slight. But there occurs a level shift ward in the graph showing lateral improvement in the channel. This correlate with several researches carried out by the majority referred [_{b}N_{o.}

MIMO presents the best option in an outage condition. The SNR within the channel coverage areas is an optimum determinant for an outage. At reduced channel capacity, outage probability is extremely high (

The performance of the wireless communication system is better when water water-filling algorithm is applied to MIMO. This technique allocates optimum power to sub-channels with less noise. These power allocation principles provide energy efficiency with respect to the corresponding average channel capacity by providing a high energy rate. The results of the simulations show that channel capacity is optimized by deploying the water-filling technique. The simulation indicates a linear increment in capacity when the system SNR increases. There was a significant performance of about 50% performance indication between conventional MIMO and MIMO with water-filling technique.

Authors wish to thank Prof. Eko James Akpama, postgraduate coordinator of the Electrical Electronics Engineering department CRUTECH, Mrs Patience Ngobi, for her typesetting work. This work was supported by contributions from families and friends too many to mention here. But we appreciate them greatly for their unalloyed contribution both in kind and in cash.