Investigation of Intra-cellular Toriodal Sectorisation in a DS-CDMA Cellular System

David Bozward, Tonda Priyanto and Ron Brewster

Department of Electronic Engineering and Applied Physics

Aston University, Birmingham, U.K.

ABSTRACT

The splitting of bandwidth resources in a cellular system incurs wastage of this premium limited commodity, but is necessary in order to manage the multiplexing and frequency reuse in the system. In FDMA and TDMA systems this normally involves the use of guard bands and with Direct Sequence Code Division Multiple Access (DS-CDMA) systems it may result from dividing the overall frequency allocation into smaller spread spectrum bandwidths. Splitting the resources in a DS-CDMA system reduces the overall system capacity and its flexibility to handle a variety of data rates, but enables a higher degree of spectrum utilisation as users within the system can now be managed more efficiently rather than all generating noise contributions in the same part of the spectrum.

This paper investigates the optimum allocation and usage of the spectrum in a DS-CDMA cellular environment. This is gauged by the number of users per cell and the overall spectrum efficiency. The paper proposes the use of in-cell toroidal frequency sectorisation to increase the capacity of a DS-CDMA system and therefore the frequency reuse factor, when combined with power control, to determine the coverage radius of the mobile transmitter.

1. INTRODUCTION

In both the first and second generations of cellular mobile communications, frequency planning is by far the biggest continuing problem, with a large amount of man-power being expended on it. In a DS-CDMA system the capacity is limited by the ability to reject unwanted users' transmissions that are received. One of the main advantages of a DS-CDMA system is that frequency planning would not be required and the addition of an extra base station to the system would thus be simplified.

In a DS-CDMA system, all users communicate over the same bandwidth using an individual Pseudorandom Noise (PN) sequence to spread the modulated data signal over a wider bandwidth. The users' transmissions are therefore stacked upon one another in the frequency domain causing interference to one another, yet due to the knowledge held in the coding, a receiver may demodulate the required signal once the codes are synchronised. The capacity of a cellular CDMA system is bounded due to the base station having to communicate with every active mobile user in its cell. The basic equation [1,2] for the capacity of a cellular DS-CDMA system in terms of the number of users in it can be written as:-

  (1)

where is the bit energy-to-noise spectral density ratio required for adequate performance and Pg is the processing gain, is voice activity ratio, F is Frequency Reuse and G is the Sectorisation gain. This equation assumes perfect power control and that the codes have no cross-correlation between the users' transmissions so as not to significantly degrade the Bit Error Rate (BER). In a multi cell system user generated interference will be contributed from other cells and this will degrade the system performance, this element is known as the frequency reuse factor.

2. FREQUENCY REUSE

The received user generated interference is determined by the inverse fourth-power law relationship between signal strength and distance. This approximation becomes valid at some distance from the transmitter rather than near to it, and in turn this means that in small cells the carrier-to-interference ratio deteriorates, as does the frequency reuse factor F.

The concept of frequency reuse in the first generation of analogue mobile telephones was used to control the amount of co-channel interference to an acceptable limit using spatial separation, whilst also increasing system capacity. In a CDMA system the frequency reuse factor F is defined [3] as the amount of interference received in a cell from stations operating in neighbouring cells and is given by the following equation:-

  (2)

where is the power due to transmissions in the desired cell and is the noise generated from the C cells adjacent to the desired cell. This may be interpreted as follows:-

  (3)

where are the noise interference contributions from individual cells in rings 1,2,3,.. etc. which is shown in figure 1. This contribution to noise from all neighbouring cells has been calculated [4] to be equal to approximately 0.65 of the interference which is due to the mobile stations operating within the cell. This produces a total interference of 1.65 (equivalent to the denominator in equation 3) and a frequency reuse factor of around 0.61.

3. SPECTRUM ALLOCATION

In a DS-CDMA system there are many ways in which to split the spectrum so that the required user density and spectrum usage are achieved. The systems ability to reject unwanted noise can be used to provide a variation in transmission bandwidth, data rate and error performance.

Figure 2 shows the variety of ways in which the combination of spreading bandwidth, system data rate and the required signal-to-noise ratios can be used. A shows the straight case in which all users are allocated the entire bandwidth and use the same spreading code rate. B shows the case where the entire bandwidth is split into sub-bands, which we will call user-stacks, here three user-stacks are shown. This case has been proposed by [4] for the second generation in the USA. C and D provide a mix of the first two allocations depending upon the required signal-to-noise ratio.

4. IN-CELL FREQUENCY ALLOCATION

In a simplified DS-CDMA system all users communicate within the same frequency bandwidth on the same stack. For additional capacity a number of these stacks may be used and it is envisaged that these will be placed side by side [4,5] just as in the FDMA case, (see figure 2B) except they contain many users' signals stacked upon one another. Each cell will use all the frequency bands allocated to it and as such no frequency planning will be required as the neighbouring cell interference will be constant throughout the system.

One feature in a DS-CDMA cellular system is that if the distribution of users is not equal from one cell to another and, say, one cell has a greater load compared to its neighbouring cells, then this may be carried as long as the loading in the surrounding cells is reduced. It has been reported [3] that this reduction in the surrounding cells may increase the capacity by around 10% to 50% depending on the distribution of mobile stations in the wanted cell. This is mainly due to the frequency reuse factor defined above because the neighbouring cells contribute smaller interference coefficients k1,k2,k3,...etc to the higher loaded cell.

Before an analysis of the various benefits of band splitting in a DS-CDMA system are considered, let us consider the reduction in the overall system capacity when the total bandwidth is split. The first consideration is the guard bands used in such a system and how these affect the overall system capacity. The guard band is used to reduce the adjacent stack interference, which provides a better signal-to-noise ratio and therefore better system capacity. The size of the guard band is a trade off between these two factors. Figure 3 shows the effect of varying the size of the guard band for a fixed number of stacks.

The capacity degradation is proportional to the number of transmitter users in the adjacent stacks along with their interference powers. Therefore the number of users in the ith stack is given by:-

  (4)

and the total capacity in users for the system, is therefore given by:-

  (5)

(6)

Figure 4 shows how the capacity is affected when the splitting bandwidths are varied while maintaining the required . The total capacity decreases as a function of the number of splitting bandwidths. This decrease is at first rapid, between 1 and 3 splits, while, after 10 splits, it is almost constant, the 1 becoming the dominant value in the equation.

This indicates that having only one user stack provides the greatest utilisation of the bandwidth resources available. Having a very large number of bandwidths provides a slightly better capacity than having in the region of 10 to 30 stacks. The maximum loss is approximately 2.5% of the total capacity.

Taking the system features of power control, multiple user stacks and the cellular structure of the network into account, additional system capacity may be achieved through spatial separation of each user stack within the cellular system. If these stacks were used for mobiles at a particular radius or signal power within the cell, the system could now reduce interference transmissions into neighbouring cells on these frequencies. This is shown in figure 5A where the cell is split into rings of three radii each with a separate allocated frequency stack. It can be seen from figures 5A and 5B that spatial separation may be achieved either by using banding, where it is achieved within the cell, or using clustering, where large network size is required.

In the banding system, the inner stack will produce a significantly reduced interference into the neighbouring cells as the power used within it will be small in comparison to the other stacks and the distance to the next cell, which utilises the same frequencies, is much larger in comparison to the simplified case. This enables greater capacity in these inner stacks than in the outer radius stacks, which are nearer to the neighbouring cells. Two methods of banding were investigated. Firstly, where one bandwidth is used from the centre up to a particular radius which was named Disk sectorisation and, secondly, where a bandwidth is only used within a range of radii which was named Toroid sectorisation. These are shown in figure 6. In the cluster system, an increase in the frequency reuse factor is accomplished by having a greater distance (multiple of cells) between adjacent frequencies.

These methods of cell sectorisation have been analysed for clusters of between two and four, and for bands of two and four frequency stacks. A constant bandwidth is used and is split according to the differing requirements. The cell model used assumes all the cells to be circles, which is near the practical case. Two situations are therefore considered, firstly, where all the circles only touch and do not overlap and, secondly, where all the area is covered and therefore cell areas are overlapping.

Figure 7 shows the results using the clustering frequency management with 1 to 4 frequency bands. Figure 8 shows the same information but for the banding case. The one frequency band capacity is the same for both systems and thus a direct comparison may be made. These results show the diminishing increasing gain when a larger number of frequencies are used in the system. It is interesting to note that the overlapping banding results are better than the non-overlapping clustering results which indicates that there is a region where the system parameters will need to be analysed to find the correct usage of the bandwidth allocated.

5. CONCLUSION

This paper has shown through a simple analysis that splitting the bandwidth of a DS-CDMA system provides a decrease in the capacity of the system of around 2.5%. When bandwidth splitting is used, a increase in capacity may be achieved through either frequency clustering or banding of the cells. This gain, which levels off at around three user stacks varies depending upon the method and the terrain under consideration. There is an increase in capacity of between 50% to 70%. The use of bandwidth splitting in a CDMA system therefore allows efficient usage of the spectrum when clustering or banding frequency allocation techniques are used.

6. REFERENCES

[1] Dixon R.C., 1976 Spread Spectrum Systems John Wiley & Sons

[2] Gilhousen K.S., Jacobs I.M., Padovani R., Viterbi A.J., Weaver L. A., Wheatley C. E. 1991 "On the Capacity of a Cellular CDMA System" IEEE Transactions on Vehicular Technology Vol.40 No.2 pp303-312

[3] Rapparot T.S., Milstein L.B., 1990 "Effects of path Loss and Fringe User Distribution on CDMA Cellular Frequency Reuse Efficiency" IEEE Global Telecommunications Conference pp500-566

[4] Qualcomm 1992 "An Overview of the Application of Code Division Multiple Access (CDMA) to Digital Cellular Systems and Personal Cellular Networks"

[5]Schilling D.L., Apelewicz T., 1992 "Broadband-CDMA: A PCS Wireless technology to Achieve Wireline Quality and maximize Spectral Efficiency" Symposium on Wireless Personal Communications pp4/1-10

Figure 1

Neighbouring Cell Interference

Figure 2

Various DS-CDMA Bandwidth Allocations

Figure 3

Total capacity and Processing gain against.

the width of the Guardband

Figure 4

Capacity of the Total System as a Function

of the Number of Spliting Bandwidths

Figure 5A.

Banding System

Figure 5B.

Cell Clustering

Figure 6

Two types of banding systems.

Figure 7

Cluster frequency Management Techniques

Figure 8

Banding frequency Management Techniques