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In this paper the system performance of an MC-CDMA (multi-carrier coded-division multiple-access) system operating over single-cell with two-tier femtocell environment is analyzed. Consider two-tier scenario is deployed with a macrocell site in which is being surrounded several femtocells, which are designed to serve a group of subscribers locate in a small coverage area such as small office, home office or a house. The coverage area is typically up to 100 meters in radius. Mostly, the femtocell is applied to serve indoor subscribers, thus, the Rayleigh fading is adopted to characterize the propagation channel. The technique of TH-MC- CDMA (time-hopped multi-carrier coded-division multiple-access) technique is supposed to transmit each symbol alternatively with fair time (slotting)/frequency (coding) for each user in the hotspots (the area around 0th femtocell). The intensity of signals estimated at a mobile unit located in the second tie, i.e., the femtocell coverage area, is an important issue. The contribution of the paper is mainly to evaluate the system performance with both the BER (bit error rate) and OP (outage probability) according to the most important parameters, for example, the activating user number, the hopping number provided by TH-MC-CDMA system and the subcarrier number. Furthermore, the discussion of interference avoidance is also discussed with non-analytically.

Recently, the last mile transmission has attracted a huge of attention due to the fact that cell phones have become indispensable in people’s life, especially, in indoor wireless transmission. In order to go through the full path that provides enough intensity of signal to arrive at the mobile unit of a subscriber located at indoor site where is a small coverage area, such as a building, home office, small firm or even in a mobile vehicle. The femtocell with two-tier network is being installed to improve the cellular capacity. The reasons for a significant interest has focused in recent on the supplication of femtocells are: it is defined widely in the telecommunications industry as easily installed, low-cost, and low power cellular BS (base station) that works in licensed spectrum to link traditionally to a mobile operation network without modifying mobile terminals. In general, the co-sited users (i.e., the mobile users located under the same coverage of a femtocell) are limited due to the coverage is smaller than other kinds of base station (BS). On contrast, the less interference caused by the other subscribes can serve higher reuse of spectrum. Moreover, decentralized strategies for interference management may be much suitable for femtocells, because of femtocells are mainly costing in traffic, installation fee, and without any operator influence [

Specifically, it is known that there are two alternate technologies for deploying femtocells coverage, i.e., relay and WiFi (IEEE802.16j). The coverage of radius for a femtocell is in tens of meters, and it is much smaller than that of the macrocells radius range about in hundreds of meters. Except the advantages mentioned before, the others are including prolong handset battery life and obtain a higher SINR (signal-to-interference-plus-noise ratio) [

Seriously speaking, in order to obtain the most completely analytical results of the system performance for mobile unit operating in such an deployed environment with short-term fading, at least three terms of the RF (radio frequency) interferences should be involved, for instance, (A) macrocell-to-femtocell interference, (B) femtocell-to-femtocell interference, (C) femtocell-tomacrocell interference, arising from a femtocell-based cellular should be included in the analysis of system performance for an MC-CDMA system. Apart from, the three terms pointed out previously, the really involved interferences which are necessary for the evaluation of system performance should be depending on the propagation channel models and the multiple access techniques, e.g., TH-CDMA, TH-MC-CDMA, or TH-OFDMA, etc.. Such that the fast time scale fading channel is not appropriate for indoor wireless communications, nevertheless the multipath effects needs to take into account an indoor propagation model. This report is organized as follows. In Section 2, the channel environments of an two-tier femtocell network are analyzed first; then the statistical analysis of the MC-CDMA system is derived in Section 3, following the analytical results reported in Section 4, a brief conclusion is drawn in Section 5.

Under the condition which assumes that a two-tier femtocell structure is shown in

at same assigned space within space.

Lemma 1. As a Poisson process with expectation value, , happened in the sizable space, the process is a random subset in, thus the following facts are satisfied,

1) The random subset acts as a femtocell with radius and a sizable point pattern.

2) denotes the number of points, see it as the number of mobile users within a femtocell, located in that lies in area, where for.

3) and are generally considered independent each other for all non-contiguous subset,.

Thus, the determination of the total mean and variance of the interference, , where, in the case of assuming that the femtocell BS and users are randomly distributed in a microcell, i.e., in a SPPP area, they can adopt that the expression given as [

and

respectively, where is the intensity of, i.e., the mean number of points per unit space. Finally, the different kinds of moment of interference exist in a two tier femtocell channel environment can be obtained by using of the aforementioned procedures.

Accordingly, for the purpose of calculating the BER performance for a referenced subscriber operating in an two-tier femtocell system, the MRC (maximal ratio combining) diversity scheme is assumed to implement for receiving the signal. Thus, to determine the SINR (signal-to-interference-plus-noise) at the output of the MRC for the referenced user is necessary, and it is written as

where is the average value of the received signal for the referenced user, it can be obtained as

where denotes the received power of a user within a femtocell, N is the number of subcarrier, indicates the channel fading fraction of the 0th received path at a femtocell site. The total interferences, , shown in the denominator of (3) can be expressed as

, where, the first term, , denotes as all the components of interference caused from the sources of same tier around the femtocell, and it is named as co-tier interference. The second term, , is designated as all the components of interferences come from the sources of different tier around the femtocell, and it is called as cross-tier interference. These two kinds of interference would be analyzed later. While the last term, , expresses the AWGN component with a double-sided power spectral density of, which is able to be calculated as

where bit interval is expressed as which is assumed smaller than the TH-MC-CDMA period, that is, , where denotes the processing gain, and is the chip-time of the PN (pseudo-noise) sequence for a TH-MC-CDMA system.

Furthermore, interferences belong to co-tier and crosstier interference can be explained by the diagram shown in

first tier is indexed as. Similarly,

are used to express the active subscribers number located on the second femtocell. The figure says that the subscriber, , in macrocell occupies the first time slot is communicating with the macrocell. The femtocell holds on the second time slot, and femtocell is within the third time slot, and so on. Moreover, the interferences structure can be described by the

To obtain the BER and OP of the system, the calculation of SINR for the signal at the output of decision maker is necessary. It is not only for determining the system average BER but for obtaining the outage probability experienced by macrocell and femtocell as subcarrier is below a threshold, i.e., the femtocel/macrocell outage probability is used to defined as the probability that the SINR, and, of the corresponding system is lower than a pre-defined value. Generally, small coverage size of a femtocell is considered since the tier of femtocell is installed in indoor application. Based on such assumption, the variance of is able to be written as [

where

and

The same second moment for and is represented as, and is a log-normal distribution with variance. The and are two empirical parameters designated as and, respectively, where and are correspon-ding to the referenced distance for indoor loss of femtocell and macrocell, and m/s, is the Doppler frequency. By substituting (7) and (8) into (2), the variance of can be obtained easily as

Next, consider there are activating users are working in the femtocell, the variance of can be determined as

Finally, the variance of is able to be evaluated as

where has been defined in (8), and is the received power of a macrocell user.

It is easy to obtain the SINR expression of the system after substituting all of the second moment results from the statistically evaluated equations into the specified SINR formula, and which is obtained as (see Appendix)

where.

Once the SINR is obtained the evaluation of system performance with the BER, consequently, with coherent demodulation technique the BER conditioned on the instantaneous SINR for an MC-CDMA system working in an two-tier femtocell cellular network is given as [

where, , present the mean value of the desired signal, and is the well-known Macuamm Q-function, which can be alternate expressed as [

The desired signal and the total interference are determined completely. Next, the average error probability for an MC-CDMA system in correlated-Nakagami-m fading channels can be accomplished by averaging over L variates with the jpdf shown in (13), and denoted as

The previous equation involving L-fold integration can be evaluated by the detailed means given in [

Moreover, another criterion for evaluating the system performance is to evaluate the OP at some cell site where the events of femtocell BSs and the users deployed in the designated environment are assumed as Poisson random. It is defined the uplink capacity of a two tier network as the maximum number of including femtocell BS and macrocell subscribers can supply to cause the OP of the total users experience within a two tier system is going to down below a threshold value and that is determined as

where represents a preset threshold value of SNR, and the equation illustrated previously conditioning on the number can be advanced obtained as

where is a expect operator, N indicts the processing gain, denotes the complementary error function, and is the BER of the corresponding BS, that is,

.

It seems natural to make sense that the hopping numbers of a TH-CDMA system generated to serves different femtocells surrounding around a macrocell definitely dominates the performance of a two-tier femtocell networks. On the basis of derived formulas the results for proving the facts aforementioned are illustrated in

exists in

In the paper the evaluation of system performance for an MC-CDMA (multi-carrier coded-division multiple-access) system operating over single-cell with two-tier femtocell environment is derived and analyzed with the numerical results. The scenario is assumed that there are several femtocells arbitrarily distributed around a macrocell, and the Rayleigh fading environment is considered. Under the consideration of TH-CDMA scheme in alternatively spreading the data to each user with fair opportunity, the results show that the system performance is definitely dominated by the parameter of the hopping number. In addition, the number of subcarrier is still one of the important factors to affect the system performance of the MC-CDMA system operating in multi-user transmission systems.

The results of SINR for a referenced user working in an MC-CDMA system located at femtocell within two-tier system can be obtained by substituting the average desired signal and the summation of all the interferences shown previous, and calculated as

where the received average bit power of the users within macrocell, , is assumed as ten multiplied by the power of the users within femtocell, , i.e., , represents the chosen macrocelland let. Thus, the becomes as

By cancelling the parameter s, and substituting into the previous equation, it becomes as