Resource allocation and OFDM system transmission for 5G cellular communications

Cellular communication technology has been developed for over a hundred years and has reached its fifth generation in mobile. 5G, as a new generation of communication technology, has comprehensively changed the mobile network application model with its ability of high-speed transmission, low network latency, and large-scale connectivity. It has brought a new impetus to the development of various industries. Cellular communication uses cellular wireless networking to connect terminals and network devices through wireless channels so that users can communicate with each other during their activities, with the main feature being the mobility of the terminals and the automatic roaming process across local networks. The use of OFDM in 5G communications can significantly improve the efficiency and capacity of wireless signal transmission. This paper provides a detailed introduction to the use of OFDM in cellular communications through frequency division multiplexing and OFDM.


Introduction
Integer frequency multiplexing (IFR) is a frequency planning technique that efficiently uses the limited spectrum resources available in wireless networks.However, limited spectrum resources and the high demand for wireless communications pose significant challenges for designing and optimizing 5G wireless networks.Integer Frequency Reuse (IFR) is a frequency planning technique that efficiently uses the limited spectrum resources in wireless networks by dividing the network into multiple regions and assigning different frequencies to each region.The advantage of IFR is that it can increase the capacity and coverage of the network by reducing co-channel interference and reducing the coverage of channels.Still, IFR can lead to a waste of spectrum resources as the frequency resources in some regions may be wasted.
In addition, IFR technology can also lead to channel imbalance, which means that channel fading can occur, as different channel states are affected by spatial propagation, emission and scattering.And the receiver may not be able to decode the signal correctly, leading to an increase in BER and a decrease in communication quality.Optimisation is therefore required, according to formula (1) : One can obtain the relationship between received power and transmitted power.By appropriately adjusting the transmit power, the impact of channel fading on communication quality can be reduced.Using fractional frequency multiplexing (FFR) technology, frequency resources can be divided into different sub-carriers, each using different transmission frequencies.This maximizes spectrum efficiency and reduces same-frequency interference between trade-offs.To achieve this, the Waterfilling Power Allocation method is used in this paper.This method is a common power allocation strategy in wireless communication systems that maximizes the system's information transmission rate while satisfying the power constraint.The limited total transmit power is allocated to different channel resources to ensure that each channel resource's signal-to-noise ratio (SNR) is equal.In water-filled power allocation, channel resources are allocated based on channel quality (SNR), the better the channel quality the higher the power allocated to the channel resource.With water-filled power allocation, the signal-to-noise ratio on each channel resource can be made equal, thus maximising the information transmission rate of the system.In addition, water-filled power allocation can also allocate power according to different channel qualities, thus achieving optimal use of resources and improving the system's energy efficiency.
As the number of users and devices increases, the need for efficient resource allocation and interference management becomes more important.Here, orthogonal frequency division multiplexing (OFDM) can be used in the face of channel fading.OFDM reduces intra-cell interference and improves system performance and is a modulation technique in which a large number of orthogonal subcarriers can be used by the transmitter to send blocks of symbols in parallel to the receiver.OFDM actually increases the symbol period but reduces the delay due to the diffusion effect, and uses FFT and IFFT function to ensure that the sub-carriers are orthogonal to each other in the presence of additional interference causing ground fading.In a multi-user scenario, spectrum resources can be allocated to different user groups via IFR, and then power can be allocated within each user using Water-filling Power Allocation, and data can be transmitted using OFDM, resulting in lower BER.

Integer frequency multiplexing (IFR)
With the need to use frequency division techniques in this paper, it is necessary to introduce the signal interference ratio to explain the communication between users, the signal interference ratio of the user by the degree of intra-cellular and inter-cellular interference, in fact, the ratio of received power and transmitted power to determine the reception effect, the same channel cell separation far enough to reduce inter-cellular interference, but in order to maximize the number of users that can be accommodated in the system, but also as much as possible to However, in order to maximize the number of users, it is necessary to increase the number of frequency multiplexes and reduce the cellular radius, which can increase the number of users in all aspects of the system can be scaled down to ensure a constant SINR per user, as shown by the Shannon channel capacity [1].
A good cellular system design is interference-limited, i. e. the interference power in the system far exceeds the noise power, i. e. the noise is negligible, and is therefore defined as SIR, the SIR is calculated according to the following formula (2): For the use of frequency division multiplexing then, it is necessary to introduce the multiplexing distance D, which is an important factor in determining the average interference between multiplexed clusters, let the cellular radius be R, then the relationship between the two can be seen in Figure 1.Let the coordinates of the center of a cellular cluster be (0, 0), the coordinates of the neighboring upper left cell are (-1, 0), and the coordinates of the lower left spanning a multiplexed cluster are (-2, 2).The distance between the center of neighboring cells is √3R, so Q in the formula can be expressed as the ratio of D to R. N. represents the number of cells defined within a group Assign the first channel set C1 to any The number of cells defined within a group is represented by N. The first channel set C1 is assigned to any cell, and using this cell as a reference, i cells are moved along the x-axis and then j cells are moved along the y-axis, assigning channel set C1 to the cell with coordinates (i, j).Return to the original cellular and repeat in a different direction, with an angle of 60° between the different directions, until all directions from the original cellular have been changed.In order to allocate C1 to the entire coverage area, the above process is repeated from any cell that has just been allocated C1, until there are no unallocated cells from any cell allocated C1.Then the next allocation of C2 can be made, and so on.Then i and j determine the size of the cellular cluster, and the calculation of N can be based on equation (3)： N = i 2 + ij + j 2 (3) So let's say that there are 19 cells in the whole network to form a 19-cell network IFR3 system, the multiplexing factor is 3, the total number of channels is expressed as Nc, which is 18, then Nc/(multiplexing factor) is 6 and the number of sub-channels within a cell is 6.Because there is no interference between different sub-channels, the corresponding is the same sub-channel because the frequency is the same will produce interference between users.Still, this interference will increase with the increase in distance and reduce the situation, so try not to arrange the same channel near a cellular channel.The same color indicates the same sub-channel, which can be seen in Figure 2： Figure 2. Allocation of sub-channels.The quality of communication according to Shannon's theorem can then be expressed in terms of channel capacity is defined by formula (4): When initially calculating the channel capacity of each cell, there will be interference in the same frequency band, so it will be necessary to add the corresponding interference to the denominator below, except for the central cell [2].The figure shows interference exists between multiplexed clusters 2, 4 and 6.When adding interference, it is important to note that each cell has a different number of users, so the corresponding user interference will be equal to the number of users in that cell, and cannot be repeatedly added up.

Water-filling power allocation
If there are not six users in a cell without equal allocation, then more users are allocated when there are more users in the cell and less when there are fewer.The same channel capacity can be applied to express the quality of communication with the following formula (5): The equation reveals that the channel capacity is influenced by the gain (H[f]), the transmit power Pf, and the noise power.In the case of Gaussian white noise, with a fixed signal gain value, the impact of the transmit power on the channel capacity is examined.To address this issue, this study presents the water-filling power allocation technique, which involves distributing more power to subcarriers with higher channel quality and less power to subcarriers with lower channel quality.The fundamental concept of water-filling is discussed in [3].The water level represents the total power available for transmission, while the different subcarriers represent different channels.The water level is allocated between the subcarriers according to their channel quality.More water is allocated to the deeper part of the tub (i.e. the better channel) and less water to the shallower part (i.e. the poorer channel).This ensures that the total power is allocated in such a way as to maximise the overall data rate.For the constraint that the sum of the transmit power values for each sub-channel must be less than the maximum transmit power value, it is sufficient to find the value of the constraint coefficient using the Lagrange multiplier method to construct the Lagrange function.The construction method can be seen in the equation ( 6): The derivation results can be seen in the equation ( 7 Letting β = λln2, the result of the multiplication is the following equation ( 8): The equation ( 9) is possible to introduce: where [x]+ denotes a value of x when x > 0 and a value of 0 when x ≤ 0. However, the optimal power allocation cannot be derived directly at this point, and an appropriate water injection level β needs to be obtained using an iterative method.A fast iterative algorithm is proposed in the literature [4], giving a visible formula (10) for the calculation of the initial value of β and a correction for each β, visible in formula (11) : where 0<μ<1 is the adjustment step and NON denotes the total number of subcarriers for this actual power allocation.This fast water injection algorithm mainly provides a method for fast convergence of β values, but the number of operations per iteration does not decrease.One iteration requires 2N additions and N+2 multiplications, which is O(N), and the whole algorithm is O(kN), where N is the number of subcarriers and k is the number of iterations.

Formatting author affiliations
The operation of the definition of noise requires noise power and variance according to equation ( 12) : Then the expression for the probability density according to the Gaussian distribution is shown in formula (13)： The equation σω 2 is the variance, then an expression for complex Gaussian noise can be defined.It is used to model the various types of interference received within the channel during reception or transmission.

The general process of OFDM transmission
By allocating N sub-carriers by IFR, the entire channel is divided into N sub-channels by IFR, and the N sub-channels are transmitted in parallel, which can be achieved relatively easily.The 16-QAM modulation method is chosen for its fast data transmission rate, strong anti-interference capability and spectrum saving.16-QAM works with the IFFT for modulation and the FFT for demodulation, without the need for multiple oscillation sources or the use of bandpass filtering for signal separation [4].It is crucial to utilize the cyclic prefix (CP) method throughout the OFDM transmission system to mitigate inter-code interference caused by signal multipath propagation under certain conditions.Once the output is separated from the CP, it undergoes linear interpolation method estimation in the frequency domain, followed by MMSE and forced zero equalizers, and ultimately the computation of BER, which is the general process for OFDM transmissions.

16-QAM modulation
Regarding the 16-QAM modulation, this method maps the bits of transmitted symbols onto the complex plane and constellation diagram, using Gray Code.The two adjacent constellation points in both the horizontal axis (I) and vertical axis (Q) directions of the complex plane differ by only one bit.This results in the higher 2 bits of symbols on the I-direction axis from negative to positive being 00, 01, 11, 10, 11, 10, which is a 2-bit Gray code.Similarly, the lower 2 bits of the symbol on the Qdirection axis from positive to negative are 00, 01, 11, 10, forming another 2-bit Gray code.The constellation diagram can be seen in Figure 3.In the process of implementing 16QAM modulation using Gray code mapping, a complex modulation symbol is formed.The I and Q components of this symbol correspond to the real and imaginary parts of the complex plane, respectively, and are then amplitude modulated onto two orthogonal carriers.The resulting signals are combined to produce the modulated signal [5], where each sample point represents a vector state.With 16 states in 16-QAM, each 4-bit binary number specifies one of the 16 possible states.The 16-QAM modulation scheme specifies 16 combinations of carriers and phases, with 4 bits being transmitted per symbol cycle.The number of constellation points in 16-QAM directly correlates to the amount of data bits that can be transmitted in a cycle and the overall spectrum utilization.Therefore, having more constellation points in 16-QAM results in higher data transmission rates and better spectral efficiency.

CP role in the transmission process
In an OFDM system, the cyclic prefix (CP) is used to copy the tail of the initial incoming signal to the head of the signal.This insertion of a protected interval eliminates interference between OFDM symbols.Additionally, the CP ensures that the time delay extension received at the receiver end is a trailing signal that is still a complete signal generated within the FFT window.This ensures orthogonality between subcarriers, as the inner product is zero as long as the last signal to appear is complete, as per the circular convolution property of the FFT [6].To ensure no inter-code crosstalk, a guard period (GP) is added between symbols, while the inclusion of the CP within the GP ensures subcarrier orthogonality and completely eliminates the destruction of inter-carrier orthogonality caused by multipath propagation.Therefore, OFDM systems exhibit good resistance to multipath interference [7].The OFDM modulation is the signal multiplied by each subcarrier for transmission, and it is equivalent to sending a frequency domain response using an FFT for each impulse response.The loop length after passing through the convolution sequence is the number of subcarriers plus the length of the CP.By adding the length of the impulse response and subtracting the part of the sequence header that overlaps with the last transmitted signal, the final length of the loop can be determined.The process of inserting the lead signal before mapping to the gray code is the inverse of adding the CP.After converting the signal to the frequency domain for demodulation using the FFT [8][9], it is mapped back to the gray code during decoding, as if it were in the frequency domain.Finally, the pilot signal is removed, and the number of erroneous bits is divided by the total number of transmitted signals to calculate the BER.

Spectrum resource allocation for integer frequency multiplexing (IFR)
With the IFR3 assignment model, the sub-channel assignments within each cell are as shown in Figure 4, one to the other [10].

FFR (water-filling power allocation) for power distribution
An optimal value of β can be obtained from the previous equation and shown in Figure 5: It can be seen that the highest value in red after the iterative operation is the best β value, and then the brown part below this value is assigned power according to the noise level.The results of the signal processing in terms of channel capacity can be seen in Figures 6 and 7   The comparison shows that as the SNR takes on a larger range of values, the closer the two curves are to each other, and the larger the average capacity will be taken to be.The channel capacity obtained by the power injection algorithm will converge to the average power allocated channel capacity when the SNR increases to a certain level.Therefore adaptive resource allocation and modulation techniques are used, whereby a different number of bits of information is allocated to each sub-channel in each channel symbol period according to the instantaneous characteristics of the channel, allowing the system to achieve the maximum bit rate.

Transmission of OFDM
After the modulation process of 16-QAM in OFDM, the modulated constellation diagram is obtained as shown in Figure 8:   Therefore, the greater the signal-to-noise ratio, the smaller the BER will be and the effect of OFDM transmission through the equaliser after a certain transmit power has been obtained.

Conclusion
This article investigates the application of FFR and OFDM in 5G cellular communications.We propose an IFR-FFR and OFDM scheme that can effectively reduce inter-and intra-cellular interference and improve system performance and user experience.The study results indicate that the sub-channel assignment of IFR is effective.This involves transmitting power through FFR, ultimately enabling the OFDM system to transmit.The study found that the channel capacity improves as the signal-to-noise ratio increases and the bit error rate decreases.This leads to a higher quality communication process, and the proposed scheme can achieve better system performance.The proposed IFR-FFR and OFDM schemes have great potential for practical application in 5G cellular networks and can provide better quality of service to users.

Figure 1 .
Figure 1.Schematic diagram of the network.Let the coordinates of the center of a cellular cluster be (0, 0), the coordinates of the neighboring upper left cell are (-1, 0), and the coordinates of the lower left spanning a multiplexed cluster are (-2, 2).The distance between the center of neighboring cells is √3R, so Q in the formula can be expressed as the ratio of D to R. N. represents the number of cells defined within a group Assign the first channel set C1 to any The number of cells defined within a group is represented by N. The first channel set C1 is assigned to any cell, and using this cell as a reference, i cells are moved along the x-axis and then j cells are moved along the y-axis, assigning channel set C1 to the cell with coordinates (i, j).Return to the original cellular and repeat in a different direction, with an angle of 60° between the different directions, until all directions from the original cellular have been changed.In order to allocate C1 to the entire coverage area, the above process is repeated from any cell that has just been allocated C1, until there are no unallocated cells from any cell allocated C1.Then the next allocation of C2 can be made, and so on.Then i and j determine the size of the cellular cluster, and the calculation of N can be based on equation (3)： N = i 2 + ij + j 2(3) So let's say that there are 19 cells in the whole network to form a 19-cell network IFR3 system, the multiplexing factor is 3, the total number of channels is expressed as Nc, which is 18, then Nc/(multiplexing factor) is 6 and the number of sub-channels within a cell is 6.Because there is no interference between different sub-channels, the corresponding is the same sub-channel because the frequency is the same will produce interference between users.Still, this interference will increase with the increase in distance and reduce the situation, so try not to arrange the same channel near a cellular channel.The same color indicates the same sub-channel, which can be seen in Figure2：

Figure 3 .
Figure 3. Constellation chart mapping gray code.In the process of implementing 16QAM modulation using Gray code mapping, a complex modulation symbol is formed.The I and Q components of this symbol correspond to the real and imaginary parts of the complex plane, respectively, and are then amplitude modulated onto two orthogonal carriers.The resulting signals are combined to produce the modulated signal[5], where each sample point represents a vector state.With 16 states in 16-QAM, each 4-bit binary number specifies one of the 16 possible states.The 16-QAM modulation scheme specifies 16 combinations of carriers and phases, with 4 bits being transmitted per symbol cycle.The number of constellation points in 16-QAM directly correlates to the amount of data bits that can be transmitted in a cycle and the overall spectrum utilization.Therefore, having more constellation points in 16-QAM results in higher data transmission rates and better spectral efficiency.

Figure 5 .
Figure 5. Water Injection distribution chart.It can be seen that the highest value in red after the iterative operation is the best β value, and then the brown part below this value is assigned power according to the noise level.The results of the signal processing in terms of channel capacity can be seen in Figures6 and 7: Figure 5. Water Injection distribution chart.It can be seen that the highest value in red after the iterative operation is the best β value, and then the brown part below this value is assigned power according to the noise level.The results of the signal processing in terms of channel capacity can be seen in Figures6 and 7:

Figure 7 .
Figure 7. Changing the SNR value.The comparison shows that as the SNR takes on a larger range of values, the closer the two curves are to each other, and the larger the average capacity will be taken to be.The channel capacity obtained by the power injection algorithm will converge to the average power allocated channel capacity when the SNR increases to a certain level.Therefore adaptive resource allocation and modulation techniques are used, whereby a different number of bits of information is allocated to each sub-channel in each channel symbol period according to the instantaneous characteristics of the channel, allowing the system to achieve the maximum bit rate.

Figure 8 .
Figure 8. Constellation diagram after modulation.The frequencies of the signal at the receiving end and the transmitted signal are shown in Figure 9:

Figure 9 .
Figure 9. Receive and transmit frequency.whenthe CP length is 64.Since 16-QAM transmits 4 bits per cycle, it needs to be multiplied by 4 for 106 cycles and the number of times the overrun signal is removed.Four BER are obtained with different equalizers and with or without the leading signal acting on the system, then the BER results are shown in Figure10:

Figure 10 .
Figure 10.Bit error rate.Therefore, the greater the signal-to-noise ratio, the smaller the BER will be and the effect of OFDM transmission through the equaliser after a certain transmit power has been obtained.