Effect of Variable Cyclic Prefix Length on OFDM System Performance over Different Wireless Channel Models

A Cyclic Prefix (CP) is a significant feature of an OFDM waveform. It is used to completely eliminate both Inter-Symbol Interference (ISI) and Inter-Carrier Interference (ICI) as long as the CP length is greater than the channel delay spread. By eliminating both ISI and ICI, the CP compensates for the effect of the multipath dispersion; but it consumes a considerable amount of the scarce spectrum and the power. Conventional OFDM uses a fixed and large CP length to overcome the ISI caused by channel delay spread under wireless mobile environment. This approach may degrade the overall spectral efficiency as well as consumes relatively more transmitter energy. Therefore, there is a need to adopt the CP length according to instantaneous channel parameters. In this paper, we presented a method for investigating the effect of varying the CP length on OFDM system performance over different multipath channel models. We estimated the variable CP length based on the RMS delay spread of the channels' power delay profile (PDP). According to this method, the estimated CP length optimizes the system capacity and improves the overall system performance. We showed that this approach could lead to a mathematical formula presenting the relationship between the CP length and the RMS delay spread of the channels.


I. INTRODUCTION
There is an ever increasing demand to increase the data throughput and to make more efficient use of the available spectrum in wireless data communication systems. The Orthogonal Frequency Division Multiplexing (OFDM) modulation technique is one of the methods used to achieve these goals. Due to its robustness against multi-path fading the OFDM is becoming a modulation technique of choice for most commercial high-speed broadband wireless communication systems. The OFDM is a special form of multi-carrier modulation schemes that is capable of overcoming the frequency selectivity of the radio channels and providing high data rates without the ISI [1][2][3]. However, in multipath fading channels, the time variation of a fading channel over an OFDM symbol period destroys the orthogonality between the sub-channel and leads to the ICI [4,5].
A circular extension known as the CP is added at the head of OFDM symbols in order to eliminate both ISI and ICI. To achieve this goal, the CP length must be greater than the delay spread of the multipath channel [6]. However the introduction of the CP reduces the bandwidth efficiency and decreases the data rate (capacity of the system) because it conveys no information.It also disperses the transmitter energy(the amount of consumed power relies on how large CP length), where the signal-to-noise (SNR) lost due to the CP introduction indicates the loss of transmission energy. Because of the loss of SNR and the bandwidth efficiency, the CP needs to be chosen optimally. Typically, it is chosen based on the multipath channel duration in a given operating environment [7,8].
The CP is always appended to the head of the OFDM symbols. This result in loss of spectral efficiency of the system. For example, in IEEE 802.11a/g standard about 25% of the useful signal is utilized by the CP [9,10]. Therefore, it is essential to understand the CP adaptation scheme. The conventional OFDM uses a large and fixed CP length, which is selected to be several times more than the RMS delay spread of the operating environment. This CP selection mandates devices which experience smaller RMS delay spread to use an excessively longer CP. In this situation the scarce network resource is misused and the limited battery power is wasted from the device perspective [9,10]. This fact motivates the research into ways for making the CP length shorter and even adaptive. An adaptive CP length could introduce a significant enhancement in spectral efficiency. In 2004, Zhang [11] proposed a method to adopt the CP length based on the variation of the channel delay spread. His method suggested selection of the CP length which is twice the channel RMS delay spread. In 2005, Chiwoo, Youngbin,Panyuh, Hyeonwoo and Jaeweon [12] proposed another method to adopt the CP length via adjusting the sampling rate. The drawback of this method is that it requires a wide OFDM spectrum; since the CP is extended by sampling up, the occupied bandwidth will also increase. In [11,12], the Power Delay Profile (PDP) of the channels is fitted into a Negative Exponentially Decaying Profile (NEDP). Based on the NEDP a mathematical formula is derived to estimate the variable CP length for the different channel models.
The evaluation of the CP length requirements for different mobile environments is the problem addressed in this research. In this paper, the variable CP length is estimated based on the RMS delay spread of the channel and the PDPs are not fitted into NEDP but it is scaled by a weighting function to ensure the synchronicity assumption. Furthermore, an analytical method for evaluating Signal to Interference and Noise Ratio (SINR)in OFDM system is utilized in this paper for the evaluation of the CP length over different channel model. Fig.1 shows a basic model of an OFDM system. First the input binary data are generated and converted to the data symbols by using different modulation schemes. Once the sequence of binary values is mapped to a data symbol form, the next step is to generate an OFDM waveform by converting the serial data symbol sequence into a number of shorter parallel symbol sequences. These modulated signals are processed by the IFFT block. Then, the CP is added to the signals. The CP extends the OFDM symbol by copying the last samples of the OFDM symbol and appending it in front of the transmitted OFDM symbol. The reason for that is to preserve the orthogonality between the sub-carriers. Also, the CP allows receiver to integrate over an integer number of sinusoid cycles for each of the multi-paths when it performs OFDM demodulation with the FFT. After adding the CP, the signals are converted to serial form and transmitted through the channel [13].At the receiver side, a reverse process is performed. The serial data is received and converted to the parallel form. Then cyclic prefix is removed. After removal of cyclic prefix, Fast Fourier Transform is performed. Then the signals are demodulated using different modulation schemes to get the original binary data [13].  2 shows the proposed OFDM system model. According to this model, at the transmitter end the signal is modulated and subsequently the CP controller attaches the CP length adaptively to mitigate both ISI and ICI introduced due to the channel. At the receiver end, the CP controller detaches the CP length before demodulator in order to recover the transmitted signal. An analytical method for evaluating SINR in OFDM system is taken from [14]. The SINR can be defined as:

II. SYSTEM MODEL DESCRIPTION
Where is the useful signal power, is the interference signal power and 2 is the variance of the additive white noise. The useful and the interference signal powers are both obtained from the PDP scaled by a weighting function called "bias function" given as: Where is the CP length, is the useful OFDM symbol length and is total OFDM symbol length. The channel PDP is assumed to have taps with power | | 2 and ℎ tap at delay . The channel is normalized such that ∑ =1 = 1. So, the useful signal power is given by: While the interference signals power is given by: IV. WIRELESS STANDARD AND CHANNEL MODELS Several wireless channel models are used to simulate the radio wave propagation. These channels are currently utilized in industry where each model is convenient for a specific type of environment. Uses of standardized models allow researchers to provide 'apple to apple' comparisons of the obtained results. The considered channel models that are used for the performance evaluation tasks in this paper work are: A. ITU CHANNEL MODELS The ITU channel models consist of two types of the channels. Table.1 and Table.2 show the PDPs and the characteristic of these channels. Theses Tables indicate the relative delay, the average power for the taps of the multi-path channel and the RMS delay spread based on the ITU recommendation.

B. EITU CHANNEL MODELS
The Extended ITU channel model for LTE was called Extended Pedestrian-A (EPA), Extended Vehicular-A (EVA), and Extended Typical Urban (ETU). Table.3 represents the PDPs of this channel. This Table shows the channel models parameters such as the excess delay, the average power and the RMS delay spread.

C. 3GPP CHANNEL MODELS
The 3GPP channel model consists of urban micro-cell and urban macro-cell channel model. Table.4 shows the tap delay, the average power and the RMS delay spread for these channel models.

B. Effect of CP Length on OFDM System Spectral Efficiency
In this sub-section, a conducted study giving insight on the impact of the CP length on the capacity of a base-band synchronized OFDM system. The capacity is used to evaluate the system and it is measured in bits per second per hertz. This study indicates how the CP length affects Spectral Efficiency Loss (SEL) and Signal to Interference and Noise Ratio (SINR) where SINR is mapped to capacity through Shannon's formula [14]. The optimum CP length maximizes the capacity for a given set of system parameters. The system parameter that considered in this section is the PDPs for the different channel models such as ITU-A, ITU-B, EITU and 3GPP.
As seen previously, maximizing SINR causes high BER at the receiver side, which requires a larger CP length, but utilizing a larger CP length extends the transmission time required. Therefore, an optimization of the SINR is required and can be obtained from Shannon's capacity theorem. In [14] system capacity modeling is proposed with adaptive modulation scheme and degradation factor (a link adaptation loss from the Shannon limit). It follows that capacity model is given by: Where SELis the Spectral Efficiency Loss (CP length / Total OFDM symbol length) and∝ is the degradation factorwhich has a value of 0.4 for this study as it is used in [14]. also indicate that the CP length increases as the RMS delay spread is increased. One of the methods used to estimate the CP length is based on the RMS delay spread; according to this method the CP length is estimated and it is given as: (CP=α*RMS) where α is the constant in the range between (2.5to3.5). This conforms the findings of a previous study by Arslan who found that the (CP=β*RMS)) where β is the constant in the range between (2to4) [15]. It can also be observed that the estimated CP maximizes the system capacity, but increasing the CP length beyond this optimum CP results in decreasing the system capacity.

C. Mathematical Relationship Between the CP &the RMS
Delay Spread of the Channel. As mentioned in one of the previous sections the CP can be estimated based on the RMS delay spread of the channel. In this study the SINR is applied to the PDP and the CP is calculated based on the RMS delay spread. It is found that CP=α*RMS where αis the constant in the range between (2.5to3.5) optimizes the system's performance. Fig 10, 11 and  12 show the mathematical relationship between the CP and the RMS delay spread. It can be seen clearly from these figures that the CP length increases as the RMS delay spread of the channel is increased which indicates a linear relationship exists between them. Obviously the RMS delay spread is not fixed in the mobile wireless communication and its value changes depending on the terrain, clutter, antenna directivity and other factors related to propagation environment. The conventional OFDM system uses a fixed and large CP length which increases the overhead, but if one estimates the CP length based on the RMS delay spread the overhead will be reduced. Therefore; the CP length needs to be adjusted to the environment so that the mobile battery power and scarce spectrum can be conserved when the delay spread is small. Furthermore the system performance will be maintained by  The optimal parameters associated with above analysis can be summarized in the Table 5: An adaptive OFDM system with variable CP length over different channel models with different PDPs was described in this paper. It presented a method that is used to estimate the CP length based on the RMS delay spread of the channel. According to this method, the CP length is chosen to improve the system performance and to optimize the system capacity by mitigating both ISI and ICI. The results showed thatthe optimal CP length correlates very well with the RMS delay spread of thechannel. Thus, the choice of variable CP length is preferable to large and fixed CP length because it offers improved spectral efficiency. Furthermore, these results showed that increasing the CP length beyond the optimum length does not resultin further improvement of the system capacity and the system performance.
Finally, it may be concluded that the CP length is an essential aspect of the OFDM system. When the CP selected optimally based on the channel parameters, the overall system performance is improved. This is accomplished through