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Journal of Electrical and Computer Engineering
Volume 2012 (2012), Article ID 571985, 10 pages
http://dx.doi.org/10.1155/2012/571985
Research Article

Interference Cancellation Using Replica Signal for HTRCI-MIMO/OFDM in Time-Variant Large Delay Spread Longer Than Guard Interval

1Graduate School of Information Sciences, Hiroshima City University, 3-4-1 Ozukahigashi, Asaminami-ku, Hiroshima 731-3194, Japan
2Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

Received 15 July 2011; Revised 22 February 2012; Accepted 12 March 2012

Academic Editor: Hanho Lee

Copyright © 2012 Yuta Ida et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Orthogonal frequency division multiplexing (OFDM) and multiple-input multiple-output (MIMO) are generally known as the effective techniques for high data rate services. In MIMO/OFDM systems, the channel estimation (CE) is very important to obtain an accurate channel state information (CSI). However, since the orthogonal pilot-based CE requires the large number of pilot symbols, the total transmission rate is degraded. To mitigate this problem, a high time resolution carrier interferometry (HTRCI) for MIMO/OFDM has been proposed. In wireless communication systems, if the maximum delay spread is longer than the guard interval (GI), the system performance is significantly degraded due to the intersymbol interference (ISI) and intercarrier interference (ICI). However, the conventional HTRCI-MIMO/OFDM does not consider the case with the time-variant large delay spread longer than the GI. In this paper, we propose the ISI and ICI compensation methods for a HTRCI-MIMO/OFDM in the time-variant large delay spread longer than the GI.

1. Introduction

Recently, the sophisticated terminal as a smart phone becomes widely used and many multimedia services are provided [1, 2]. High speed packet access (HSPA) using a wideband code division multiplexing access (W-CDMA) is used in the mobile communications and provides the data services with the maximum transmission rate of about 14 Mbps [3]. However, since the available frequency band is limited, a HSPA cannot improve the transmission rate more than now [4]. To solve this problem, orthogonal frequency division multiplexing (OFDM) and multiple-input multiple-output (MIMO) are actively used [59]. OFDM is a multicarrier digital modulation. The OFDM signal can be transmitted in parallel by using the many subcarriers that are mutually orthogonal. In MIMO systems, the signal of the several transmit antennas is transmitted in the same frequency band. Moreover, since each transmitted signal is sent over the independent channel, the space diversity can be obtained in the receiver. Therefore, a long term evolution (LTE) has been standardized as 3.9 G system using MIMO/OFDM systems [10, 11]. An LTE provides the maximum transmission rate of about 50–100 Mbps. Moreover, an LTE Advanced will support broadband data services with the maximum transmission rate of about 100 M–1 Gbps as 4 G systems.

Since the received signal is changed due to the amplitude and phase variations for a frequency selective fading, the channel estimation (CE) is important to compensate the channel variance. In the conventional MIMO/OFDM, the orthogonal pilot symbols-based CE is used to identify an accurate channel state information (CSI) [7]. However, since the orthogonal pilot-based CE requires the large number of pilot symbols and large transmission power, the transmission rate is degraded. To mitigate these problems, a high time resolution carrier interferometry (HTRCI) for MIMO/OFDM has been proposed [12].

In wireless communications, intersymbol interference (ISI) and intercarrier interference (ICI) are serious problems to mitigate the system performance. To prevent these problems, a guard interval (GI) is generally inserted. In general, GI is usually designed to be longer than the delay spread of the channel. However, if the maximum delay spread is longer than the GI, the system performance is significantly degraded due to the ISI and ICI. However, the conventional HTRCI-MIMO/OFDM does not consider the case with the time-variant large delay spread longer than the GI. In this paper, we propose the ISI and ICI compensation methods for a HTRCI-MIMO/OFDM in the time-variant large delay spread longer than the GI. Until this time, several schemes have proposed the ISI and ICI compensation methods due to the large delay spread channel. For example, [13] has proposed the ISI reduction method by extending the GI. However, since [13] has extended the GI length, the maximum throughput is degraded and the transmission power is also increased. Reference [14] has proposed the ISI and ICI compensation methods using the turbo equalization. However, [14] has large complexity by the iterative processing for the turbo equalizer. Reference [15] has proposed the ISI and ICI compensation methods using the estimated channel coefficients and the CSI to reproduce the interference components. However, the packet length becomes longer by using the training symbol. To mitigate the above-mentioned problems, we propose the time domain ISI compensation method with the replica signal based on the ICI compensation for a HTRCI-MIMO/OFDM in this paper. This paper is organized as follows. In Section 2, we present the system model. Then, we describe the proposed system in Section 3. In Section 4, we show the computer simulation results. Finally, the conclusion is given in Section 5.

2. System Model

This section describes the system model, which employs the time-division multiplexing (TDM) transmission for multiple users. This system is illustrated in Figure 1.

fig1
Figure 1: Proposed system.
2.1. Channel Model

We assume that a propagation channel consists of 𝐿 discrete paths with different time delays. The impulse response between the 𝑚th transmit and 𝑛th receive antenna 𝑚,𝑛(𝜏,𝑡) is represented as follows: 𝑚,𝑛(𝜏,𝑡)=𝐿1𝑙=0𝑚,𝑛,𝑙(𝑡)𝛿𝜏𝜏𝑚,𝑛,𝑙,(1) where 𝑚,𝑛,𝑙, 𝜏𝑚,𝑛,𝑙 are the complex channel gain and the time delay of the 𝑙th propagation path, and 𝐿1𝑙=0𝐸|2𝑚,𝑛,𝑙|=1, where 𝐸|| denotes the ensemble average operation. The channel transfer function 𝐻𝑚,𝑛(𝑓,𝑡) is the Fourier transform of 𝑚,𝑛(𝜏,𝑡) and is given by 𝐻𝑚,𝑛(𝑓,𝑡)=0𝑚,𝑛=(𝜏,𝑡)exp(𝑗2𝜋𝑓𝜏)𝑑𝜏𝐿1𝑙=0𝑚,𝑛,𝑙(𝑡)exp𝑗2𝜋𝑓𝜏𝑚,𝑛,𝑙.(2)

2.2. HTRCI-MIMO/OFDM

The transmission block diagram of the proposed system is shown in Figure 1(a). Firstly, the coded binary information data sequence is modulated, and 𝑁𝑝 pilot symbols are appended at the beginning of the sequence. The HTRCI-MIMO/OFDM transmitted signal for the 𝑚th transmit antenna can be expressed in its equivalent baseband representation as follows: 𝑠𝑚(𝑡)=𝑁𝑝+𝑁𝑑1𝑖=0𝑔(𝑡𝑖𝑇)2𝑆𝑁𝑐𝑁𝑐1𝑘=0𝑢𝑚(𝑘,𝑖)exp𝑗2𝜋(𝑡𝑖𝑇)𝑘𝑇𝑠,(3) where 𝑁𝑑 and 𝑁𝑝 are the number of data and pilot symbols, 𝑁𝑐 is the number of subcarriers, 𝑇𝑠 is the effective symbol length, 𝑆 is the average transmission power, and 𝑇 is the OFDM symbol length, respectively. The frequency separation between adjacent orthogonal subcarriers is 1/𝑇𝑠 and can be expressed by using the 𝑘th subcarrier of the 𝑖th modulation symbol 𝑑𝑚(𝑘,𝑖) with |𝑑𝑚(𝑘,𝑖)|=1 for 𝑁𝑝𝑖𝑁𝑝+𝑁𝑑1 as follows: 𝑢𝑚(𝑘,𝑖)=𝑐PN(𝑘)𝑑𝑚(𝑘,𝑖),(4) where 𝑐PN is a long pseudonoise (PN) sequence as a scrambling code to reduce the peak-to-average power ratio (PAPR). GI is inserted in order to eliminate the ISI due to a multipath fading, and hence, we have 𝑇=𝑇𝑠+𝑇𝑔,(5) where 𝑇𝑔 is the GI length. In communication systems, 𝜀 is generally considered as 4 or 5, where 𝜀=𝑇𝑠/𝑇𝑔. In this paper, we assume 𝜀=4. In (3), the transmission pulse 𝑔(𝑡) is given by 𝑔(𝑡)=1for𝑇𝑔𝑡𝑇𝑠0otherwise.(6) For 0𝑖𝑁𝑝1, the transmitted pilot signal of the 𝑘th subcarrier for the 𝑚th transmit antenna element is given by 𝑑𝑚(𝑘,𝑖)=𝜁1𝜇=0𝑇exp𝑗2𝜋𝑚+2𝜇𝑔𝑘𝑇𝑠𝑚for𝑖=𝜁0otherwise,(7) where 𝜁=𝜀/2, 𝑚=mod(𝑚,𝜁), and 𝑥 stands for the integer lower and closer to 𝑥, respectively. In this case, the HTRCI-MIMO/OFDM pilot signal can multiplex the same impulse responses from the transmit antenna elements in each receive antenna element in 𝜁 times on the time domain without overlapping to each other. For example, if we consider 𝜀=4 and 2 transmit antenna elements, we obtain 𝑁𝑐1𝑘=0𝑑0(𝑘,0)={1,0,,1,0} and 𝑁𝑐1𝑘=0𝑑1(𝑘,0)={1,0,1,0,,1,0,1,0} as the pilot signal of the first and second transmit antenna elements from (7) as shown in Figure 2(a). In this case, since each pilot signal contains “0” components, we can identify the half of transmission power compared with the conventional MIMO/OFDM system using the orthogonal pilot. However, if 𝜏𝑚,𝑛,𝐿>𝑇𝑔, the conventional HTRCI-MIMO/OFDM can not obtain an accurate CSI, where 𝜏𝑚,𝑛,𝐿 is the maximum delay spread for the 𝑚th transmit and 𝑛th receive antenna. To solve this problem, we propose the new channel estimation using a HTRCI-MIMO/OFDM. Firstly, in the transmitter, we shift the channel impulse responses of (7) as follows: 𝑑𝑚(𝑘,𝑖)=𝜁1𝜇=0𝑇exp𝑗2𝜋2𝑚+𝜇𝑔𝑘𝑇𝑠𝑚for𝑖=𝜁0otherwise.(8) In (8), the channel impulse responses are shifted as shown in Figure 2(a). This operation enables estimating the maximum delay spread longer than the GI and to obtain an accurate CSI in the receiver.

fig2
Figure 2: The concept of a HTRCI-MIMO/OFDM to apply the maximum delay spread longer than the GI for 2 transmit antenna elements and 𝜀=4.

The received structure is illustrated in Figure 1(b). By applying the FFT operation, the received signal 𝑟𝑛(𝑡) is resolved into 𝑁𝑐 subcarriers. The received signal for the 𝑛th receive antenna 𝑟𝑛(𝑡) in the equivalent baseband representation can be expressed as follows: 𝑟𝑛(𝑡)=𝑀1𝑚=0𝑚,𝑛(𝜏,𝑡)𝑠𝑚(𝑡𝜏)𝑑𝜏+𝑛𝑛(𝑡),(9) where 𝑀 is the number of transmit antennas and 𝑛𝑛(𝑡) is additive white Gaussian noise (AWGN) with a single-sided power spectral density of 𝑁0 for the 𝑛th receive antenna, respectively. The 𝑘th subcarrier ̃𝑟𝑛(𝑘,𝑖) is given by ̃𝑟𝑛1(𝑘,𝑖)=𝑇𝑠𝑖𝑇+𝑇𝑠𝑖𝑇𝑟𝑛(𝑡)exp𝑗2𝜋(𝑡𝑖𝑇)𝑘𝑇𝑠=𝑑𝑡2𝑆𝑁𝑐𝑀1𝑁𝑚=0𝑐1𝑒=0𝑢𝑚1(𝑒,𝑖)𝑇𝑠𝑇𝑠0exp𝑗2𝜋(𝑒𝑘)𝑡𝑇𝑠𝑚,𝑛(𝜏,𝑡+𝑖𝑇)𝑔(𝑡𝜏)exp𝑗2𝜋𝑒𝜏𝑇𝑠𝑑𝜏𝑑𝑡+̂𝑛𝑛(𝑘,𝑖),(10) where ̂𝑛𝑛(𝑘,𝑖) is AWGN noise with zero mean and a variance of 2𝑁0/𝑇𝑠. After abbreviating, (10) can be rewritten as follows: ̃𝑟𝑛1(𝑘,𝑖)𝑇𝑠2𝑆𝑁𝑐𝑀1𝑁𝑚=0𝑐1𝑒=0𝑢𝑚(𝑒,𝑖)𝑇𝑠0exp𝑗2𝜋(𝑒𝑘)𝑡𝑇𝑠𝑚,𝑛(𝜏,𝑡+𝑖𝑇)𝑔(𝑡𝜏)exp𝑗2𝜋𝑒𝜏𝑇𝑠𝑑𝜏𝑑𝑡+̂𝑛𝑛=(𝑘,𝑖)2𝑆𝑁𝑐𝑀1𝑚=0𝐻𝑚,𝑛𝑘𝑇𝑠𝑢,𝑖𝑇𝑚(𝑘,𝑖)+̂𝑛𝑛(𝑘,𝑖).(11) After descrambling, the output signal ̂𝑟𝑛(𝑘,𝑖) for the 𝑛th receive antenna element is given by ̂𝑟𝑛𝑐(𝑘,𝑖)=PN(𝑘)||𝑐PN||(𝑘)2̃𝑟𝑛=(𝑘,𝑖)2𝑆𝑁𝑐𝑀1𝑚=0𝐻𝑚,𝑛𝑘𝑇𝑠𝑑,𝑖𝑇𝑚(𝑘,𝑖)+̂𝑛𝑛(𝑘,𝑖),(12) where () is a complex conjugate and 𝑐PN(𝑘)/|𝑐PN(𝑘)|2 is the descrambling operation, respectively. Observing (11) and (12), the noise components are the same notation. In this paper, the descrambling operation is to rotate the phase of each subcarrier by using a PN code. Since 𝜀=𝑇𝑠/𝑇𝑔, a HTRCI-MIMO/OFDM can multiplex the same impulse responses in 𝜁 times on the time domain. After the pilot signal separation, the pilot signal is converted to the time domain signal ̂𝑟𝑛(𝑡) again as ̂𝑟𝑛(𝑡)=𝑁𝑝1𝑖=02𝑃𝑁𝑐𝑁𝑐1𝑘=0̂𝑟𝑛(𝑘,𝑖)exp𝑗2𝜋(𝑡𝑖𝑇)𝑘𝑇𝑠=𝑁𝑝1𝑖=02𝑃𝑁𝑐𝑀1𝑚=0𝑚,𝑛(𝜏,𝑡+𝑖𝑇)𝑁𝑐1𝑘=0𝑑𝑚(𝑘,𝑖)exp𝑗2𝜋(𝑡𝑖𝑇)𝑘𝑇𝑠+̃𝑛𝑛=(𝑡)𝑁𝑝1𝑖=02𝑃𝑁𝑐𝑀1𝑚=0𝐿1𝑙=0𝑚,𝑛,𝑙1(𝑡+𝑖𝑇)𝜁𝜁1𝜇=0𝛿𝜏𝜏𝑚,𝑛,𝑙𝜏(2𝑚+𝜇)𝑇𝑔+̃𝑛𝑛(𝑡),(13) where 𝑃 is the transmission pilot signal power and ̃𝑛𝑛(𝑡) is the noise component, respectively. Here, if 𝜏𝑚,𝑛,𝐿>𝑇𝑔, since the channel impulse responses of the different time window overlap the desired channel impulse responses, the accurate CSI can not be obtained. Therefore, we process as follows. At the receiver, in Figure 2(b), the overlapped channel impulse responses show the same amplitude for the transmitted pilot signal without the shift in the different time window. In this case, we can not estimate the maximum delay spread. On the other hand, the overlapped channel impulse responses show the different amplitude for the transmitted pilot signal with the shift in the different time window. Therefore, we can estimate the maximum delay spread from the different amplitude in the different time windows. Next, we eliminate the channel impulse responses of the different time window. The channel impulse responses of the different time window can be eliminated by using the channel impulse responses of the GI. These channel impulse responses do not contain the channel impulse responses of the different time window. This is because the pilot signal of the GI is the head of packet and it does not contain the channel impulse responses of the different time window. Therefore, we can eliminate the channel impulse responses of the different time window. From the above process, the frequency response of the 𝑘th subcarrier between the 𝑚th transmit and 𝑛th receive antenna 𝐻𝑚,𝑛(𝑘) for 𝜏𝑚,𝑛,𝐿>𝑇𝑔 is obtained by 𝐻𝑚,𝑛=(𝑘)𝑁𝑐𝜁2𝑃𝑀1𝑁𝑚=0𝑐1𝑒=01𝑇𝑠𝑇𝑠0𝐿1𝑙=0𝐿1𝑙=𝐿1𝑚,𝑛,𝑙(𝑡+𝜌𝑇)𝜁1𝜇=0𝛿𝜏𝜏𝑚,𝑛,𝑙𝜏(2𝑚+𝜇)𝑇𝑔𝛿𝜏𝜏𝑚,𝑛,𝑙exp𝑗2𝜋𝑒𝜏𝑇𝑠𝑑𝜏𝑑𝑡+𝜂𝑚,𝑛(𝑘)for𝐿𝑇𝑔𝑚,𝜌=𝜁,(14) where 𝜂𝑚,𝑛(𝑘) is AWGN component with 𝐸[|𝜂𝑚,𝑛(𝑘)|]2=𝐸[|̂𝑛𝑛(𝑘,𝑖)/𝜁|]2=𝜎2/𝜁.

3. Proposed System

3.1. Rewritten Matrix Form

After the pilot signal separation, (13) for 𝜏𝑚,𝑛,𝐿𝑇𝑔 can be rewritten in the matrix form as follows: 𝐑𝑖,𝑛=𝑀1𝑚=0𝝀𝑖,𝑚,𝑛𝐹𝐃𝑖,𝑚+𝐍𝑖,𝑛,(15) where 𝝀𝑖,𝑚,𝑛 is the 𝑁𝑐×𝑁𝑐 time-domain channel matrix for the 𝑖th symbol between the 𝑚th transmit and 𝑛th receive antenna, 𝐍𝑖,𝑛 is the 𝑁𝑐×1 noise matrix, and 𝐹 is the IFFT operation, respectively. However, (15) for 𝜏𝑚,𝑛,𝐿>𝑇𝑔 is rewritten as follows: 𝐑𝑖,𝑛=𝑀1𝑚=0𝝀isi,𝑖1,𝑚,𝑛𝐹𝐃𝑖1,𝑚+𝝀ici,𝑖,𝑚,𝑛𝐹𝐃𝑖,𝑚+𝐍𝑖,𝑛,(16) where 𝝀isi,𝑖1,𝑚,𝑛, 𝝀ici,𝑖,𝑚,𝑛 denote the ISI and ICI channel matrices for the (𝑖1)th and 𝑖th symbols between the 𝑚th transmit and 𝑛th receive antenna, respectively. Observing (16), since the received signal 𝐑𝑖,𝑛 contains the ISI and ICI terms, these equalization processing are necessary.

3.2. ISI and ICI Equalization

In 𝜏𝑚,𝑛,𝐿>𝑇𝑔, since the first data symbol of 𝐑𝑖,𝑛 does not contain the ISI [16], (16) for 𝑖=0 is obtained as 𝐑0,𝑛=𝑀1𝑚=0𝝀ici,0,𝑚,𝑛𝐹𝐃0,𝑚+𝐍0,𝑛.(17) However, the data symbols for 𝑖>0 have the ISI. Here, the ISI equalization is performed by using the previous detected symbol 𝐃𝑖1,𝑚,𝑛 and the estimated ISI channel matrix 𝝀isi,𝑚,𝑛. The estimated ISI channel matrix 𝝀isi,𝑚,𝑛 consists of the estimated channel impulse response. The estimated channel impulse response 𝑚,𝑛,𝑙(𝑡)𝛿(𝜏𝜏𝑚,𝑛,𝑙) is obtained by the channel response 𝐻𝑚,𝑛(𝑘) after the IFFT operation, where 𝐿𝑙𝐿1. Therefore, the ISI equalized signal 𝐑𝑖,𝑛 is given by 𝐑𝑖,𝑛=𝐑𝑖,𝑛𝑀1𝑚=0𝝀isi,𝑚,𝑛𝐹𝐃𝑖1,𝑚=𝑀1𝑚=0𝝀ici,𝑖,𝑚,𝑛𝐹𝐃𝑖,𝑚+𝐍𝑖,𝑛,(18) where 𝐍𝑖,𝑛 is the noise term with the residual ISI. After the FFT operation, by using maximum likelihood detection (MLD), the detected signal 𝐃𝑖𝐃=[𝑖,0𝐃,,𝑖,𝑚𝐃,,𝑖,𝑀1]𝑇 is obtained as follows: 𝐃𝑖𝐃=argmin𝑁1𝑛=0𝑀1𝑚=0𝐹1𝐑𝑖,𝑛𝐇𝑚,𝑛𝐃𝑖,𝑚2,(19) where ()𝑇 is the transpose operation, 𝑁 is the number of receive antennas, 𝐃𝑖,𝑚 is the constellation of the symbol replica candidates as 𝑀1𝑚=0𝐶1𝑐=0𝐃𝑖,𝑚,𝑐, 𝐶 is the modulation level, and 𝐇𝑚,𝑛 is the matrix form of 𝐻𝑚,𝑛(𝑘), respectively. From (19), ISI is eliminated from the received signal. However, the orthogonality is destroyed by the detected signal due to the ISI compensation. If ICI is eliminated from (19), the detected signal 𝐃𝑖,𝑚 can be more accurately detected.

3.3. Replica Signal Insertion Based on ICI Equalization

To eliminate the ICI, we consider the orthogonality reconstruction with inserting the detected signal after the ISI compensation. The ICI equalized signal ̆𝐑𝑖,𝑛 with inserting eliminated the part of signal using the previous detected symbol 𝐃𝑖,𝑚 is given by ̆𝐑𝑖,𝑛=𝐑𝑖,𝑛+𝑀1𝑚=0𝝀ici,𝑚,𝑛𝐹𝐃𝑖,𝑚=𝑀1𝑚=0𝝀𝑖,𝑚,𝑛𝐹𝐃𝑖,𝑚+̆𝐍𝑖,𝑛,(20) where 𝝀ici,𝑚,𝑛 is the estimated ICI channel matrix and ̆𝐍𝑖,𝑛 is the noise term with the residual ISI and residual ICI, respectively.  𝝀ici,𝑚,𝑛 consists of the estimated channel impulse responses 𝑚,𝑛,𝑙(𝑡)𝛿(𝜏𝜏𝑚,𝑛,𝑙). After the FFT operation, the detected signal ̆𝐃𝑖̆𝐃=[𝑖,0̆𝐃,,𝑖,𝑚̆𝐃,,𝑖,𝑀1]𝑇 is obtained as follows: ̆𝐃𝑖𝐃=argmin𝑁1𝑛=0𝑀1𝑚=0𝐹1̆𝐑𝑖,𝑛𝐇𝑚,𝑛𝐃𝑖,𝑚2.(21) Observing (19) and (21), since ICI is eliminated, ̆𝐃𝑖,𝑚 is the more accurately detected signal compared with 𝐃𝑖,𝑚.

3.4. Complexity Comparison

Here, we compare the complexity of the conventional and proposed methods. Firstly, we show the complexity of [14]. The authors of [14] have proposed the ISI and ICI compensations using the turbo equalization. From Table  1 of [14], the complexity of [14] is given by 𝐶[14]=𝑁𝑁𝑠𝑀𝑁𝑐+4𝑁𝑐𝑁𝑀2+3𝑁𝑐𝑁𝑀+𝑁𝑁𝑐log2𝑁𝑐𝑁+6𝑁𝑠+𝐿𝑀𝑁𝑐𝑁𝑑=𝑁𝑁𝑐𝑁𝑑𝑀7𝑁𝑠+4𝑀+6𝐿+3+log2𝑁𝑐,(22) where 𝑁𝑠 is the number of sampling points for GI and effective symbol. Next, we show the complexity of our proposed method. Firstly, the complexity of (18) is obtained by 𝐶isi=𝑁𝑁𝑐𝑁𝑑𝐶1𝑀+𝑀𝑁𝑐𝑁𝑑1log𝑁𝑐.(23) For (23), the first term is the complexity of MLD and the second term is the complexity of IFFT. Next, the complexity of (20) is obtained by 𝐶ici=𝑁𝑁𝑐𝑁𝑑𝐶𝑀+𝑀𝑁𝑁𝑐𝑁𝑑log𝑁𝑐=𝑁𝑁𝑐𝑁𝑑1+𝑁𝑁𝑐𝐶𝑀+𝑀𝑁𝑐𝑁𝑑1+𝑀𝑁𝑐log𝑁𝑐.(24) For (24), the first and second terms are the complexity of MLD and IFFT of (23). Finally, the complexity of (21) is 𝐶MLD=𝑁𝑁𝑐𝑁𝑑𝐶𝑀=𝑁𝑁𝑐𝑁𝑑1+𝑁𝑁𝑐𝐶𝑀.(25) Therefore, the complexity of the proposed method is obtained by 𝐶pro=𝐶isi+𝐶ici+𝐶𝑀𝐿𝐷=𝑁𝑐𝑁3𝑁𝑑𝐶1𝑀𝑁+𝑀𝑑1log𝑁𝑐.(26) For example, when 𝑀=𝑁=2, 𝑁𝑐=64, 𝑁𝑑=20, 𝑁𝑠=80, 𝐿=2, and 𝐶=4, the complexities of [14] and the proposed method are 3000320 and 130560 from (22) and (26). Therefore, the proposed method is small compared with [14].

4. Computer Simulated Results

In this section, we show the performance of the proposed method. Figure 1 shows the simulation model of the proposed system. In this simulation, we assumed that 2 × 2 and 4 × 4 MIMO systems. On the transmitter, the pilot signal is assigned for each transmitter using (8). In this case, the proposed system can multiplex the same impulse responses from the transmit antenna elements in each receive antenna element in 𝜁 times on the time domain. These have been found to be efficient for the transmission of the OFDM signal over the frequency selective fading channel. After serial to parallel (S/P) converted, the coded bits are QPSK modulated, and then the pilot signal and data signal are multiplexed with the scrambling using a PN code to reduce the PAPR. The OFDM time signal is generated by the IFFT operation and is transmitted to the frequency-selective and time-variant radio channel after the cyclic extension has been inserted. The transmitted signal is subject to the broadband channel propagation. In this simulation, we assume that OFDM symbol period is 5 μs and guard interval is 1 μs for 𝜀=4, and 𝐿=2,3 path Rayleigh fadings. The maximum Doppler frequency is 10 Hz. In the receiver, guard interval is erased from the received signal and the received signal is converted S/P. The parallel sequences are passed to the FFT operator and convert the signal back to the frequency domain. After the descrambling and IFFT operation, each impulse response for all combination of the transmit and receive antenna elements can be estimated by extracting and averages 𝜁 times impulse responses using the time windows with (14). In 𝜏𝑚,𝑛,𝐿>𝑇𝑔, the HTRCI-MIMO/OFDM pilot signal contains the overlapped channel impulse responses from the different time window. However, the pilot signal of the GI does not contain the overlapped channel impulse responses. By using this signal, the channel impulse responses of the different time window are eliminated from the overlapped channel impulse responses as shown in Figure 2(b). The frequency domain data signal is detected and demodulated by using the MLD algorithm. Since the detected data signal contains the ISI and ICI, these equalization processing are necessary. The ISI equalization is performed with the previous detected symbol and estimated ISI channel matrix as (18). From (18), ISI is eliminated. However, the orthogonality is destroyed by the detected signal due to the ISI compensation. To reconstruct the orthogonality, the ICI equalization is performed by using the replica signal insertion as (20). Finally, the data signal is detected as (21). The packet consists of 𝑁𝑝=1,2 pilot symbols and 𝑁𝑑=20 data symbols. Table 1 shows the simulation parameters.

tab1
Table 1: Simulation parameters.

Figures 3 and 4 show the BER of the conventional and proposed methods for 2 × 2 and 4 × 4 MIMO systems at Doppler frequency of 10 Hz. The number of maximum delay spread is 4 and 16 in 2 × 2 and 4 × 4 MIMO systems, respectively. From the simulation results, the BER performance for no ISI and ICI compensation is increased about 22 and 300 times compared with no ISI and ICI case in 2 × 2 and 4 × 4 MIMO systems, respectively. For the conventional method, the BER performance shows the error floor in high 𝐸𝑏/𝑁0. This is because the residual ISI and ICI are remained. The proposed method shows approximately the same BER performance compared with no ISI and ICI case. Therefore, the proposed method can eliminate the ISI and ICI. Next, we compare the 2- and 3-path models. The 2-path model contains the channel impulse responses of the different time window in the time domain HTRCI-MIMO/OFDM pilot signal. However, they do not overlap the desired channel impulse responses. On the other hand, the 3-path model overlaps the desired channel impulse responses. Therefore, the channel impulse responses of the different time window are eliminated by using the channel impulse responses of the GI. From the simulation results, the 2-path model shows the better BER performance than that of the 3-path model in low 𝐸𝑏/𝑁0. It means that CSI degrades due to the eliminated processing of the overlapped channel impulse responses in the 3-path model.

571985.fig.003
Figure 3: The BER of the conventional and proposed methods for 2 × 2 MIMO system at Doppler frequency of 10 Hz.
571985.fig.004
Figure 4: The BER of the conventional and proposed methods for 4 × 4 MIMO system at Doppler frequency of 10 Hz.

Figures 5 and 6 show the BER of the proposed method for 2 × 2 and 4 × 4 MIMO systems at Doppler frequency of 10 Hz. The number of maximum delay spread is 4 and 16 in 2 × 2 and 4 × 4 MIMO systems, respectively. For the proposed method without the noise, the noise is not added in the channel impulse responses of the GI. From the simulation results, the 2- and 3-path models without the noise show the approximately same BER performance. Therefore, the 3-path model with the noise degrades due to the noise of the GI.

571985.fig.005
Figure 5: The BER of the proposed method for 2 × 2 MIMO system at Doppler frequency of 10 Hz.
571985.fig.006
Figure 6: The BER of the proposed method for 4 × 4 MIMO system at Doppler frequency of 10 Hz.

Figures 7 and 8 show the BER versus the number of maximum delay spread for the conventional and proposed methods with 2 × 2 and 4 × 4 MIMO systems at Doppler frequency of 10 Hz. Here, 𝐸𝑏/𝑁0 per received antenna is 20 and 15 dBs in 2 × 2 and 4 × 4 MIMO systems, respectively. In 2 × 2 MIMO system, the BER performances of no ISI and ICI compensation and conventional method are increased about 5 times. On the other hand, the BER performance of the proposed method is increased about 2 times. Therefore, the proposed method can suppress the ISI and ICI due to the changing of the number of maximum delay spread. In 4 × 4 MIMO system, the BER performance of no ISI and ICI compensation and the conventional method are increased about 170 and 80 times. On the other hand, the BER performance of the proposed method is increased about 4 times and the proposed method can suppress the ISI and ICI as 2 × 2 MIMO system. However, the BER performance of the proposed method with the 2-path model is increased about 36 times compared with 3-path model. This is because the channel impulse responses of the GI for the second time domain HTRCI-MIMO/OFDM pilot symbol are overlapped from the first pilot symbol in 4 × 4 MIMO system.

571985.fig.007
Figure 7: The BER versus the number of maximum delay spread for the conventional and proposed methods with 2 × 2 MIMO system at Doppler frequency of 10 Hz.
571985.fig.008
Figure 8: The BER versus the number of maximum delay spread for the conventional and proposed methods with 4 × 4 MIMO system at Doppler frequency of 10 Hz.

Figure 9 shows the throughput performance of the conventional and proposed methods for 2 × 2 and 4 × 4 MIMO systems at Doppler frequency of 10 Hz. The number of maximum delay spread is 4 and 16 in 2 × 2 and 4 × 4 MIMO systems, respectively. The throughput 𝑇𝑡𝑝 is given by 𝑇𝑡𝑝=𝑁𝑑𝑁𝑐𝐶𝑅𝑀𝑁𝑝+𝑁𝑑𝑇1𝑃per,(27) where 𝑅 is the coding rate and 𝑃per is the packet error rate (PER), respectively. The extension of the GI length is the simple method to prevent the problem of the maximum delay spread [13]. However, the throughput performance is degrade with this method. This is because the number of carriers 𝑁𝑐 decreases for (27) when the OFDM symbol length 𝑇 is the same as no ISI and ICI case. In this simulation, 𝑁𝑐 decreases from 64 to 48, and the GI length 𝑇𝑔 increases from 16 to 32. On the other hand, the proposed method can maintain the number of carriers 𝑁𝑐. From (27), the maximum throughout for no ISI and ICI case is about 48.8 and 93.1 Mbps in 2 × 2 and 4 × 4 MIMO systems, respectively. Therefore, the proposed method shows the best throughput performance and can achieve the maximum throughput performance as the same no ISI and ICI case.

571985.fig.009
Figure 9: The throughput of the conventional and proposed methods for 2 × 2 and 4 × 4 MIMO systems at Doppler frequency of 10 Hz.

5. Conclusion

In this paper, we have focused on the large delay spread channel and proposed the ISI and ICI compensation methods for a HTRCI-MIMO/OFDM. In the proposed method, we have performed the time domain ISI compensation method with the replica signal based on the ICI compensation. From the simulation results, the proposed method has achieved the approximately same BER performance like the case with no ISI and ICI. Moreover, the proposed method can suppress the ISI and ICI due to the changing of the number of maximum delay spread. Finally, the proposed method has shown the best throughput performance and can achieve the same maximum throughput performance compared with no ISI and ICI case.

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