Since an OFDM system is vulnerable to mobility and CFO, various techniques have been pro-posed to cope with these two kinds of ICI. First, we discuss the mobility-induced ICI problem.
Two algorithms are well-known, namely, 1) the zero-forcing (ZF) method and 2) minimum mean square error (MMSE) method. Unfortunately, these methods require the inversion of an
=^ ICI matrix, where is the number of subcarriers. Except for a matrix inversion, the MMSE method also needs to conduct an extra matrix multiplication. Thus, its com-putational complexity is even higher than that of the ZF method. The payoff for the higher complexity is its enhanced performance. If is large, the computational complexity of both algorithms can become prohibitively high. Systems with a lot of subcarriers are not uncommon in real-world applications. For example, for the application of DVB, the number of subcarriers can be as large as 8192. To solve the problem of a large ICI matrix inversion, a simpler ICI equalizer for the ZF method was developed in [16]. As mentioned, ICI on a subcarrier mainly comes from a few neighboring subcarriers. Thus, ICI from the other subcarriers can then be ignored. This method has good performance in low-mobility environments. In high-mobility environments, however, the number of insignificant ICI terms will be decreased and the com-putational complexity will be significantly increased.
Successive interference cancellation (SIC) and parallel interference cancellation (PIC) are two well-known multiuser interference (MUI) cancellation techniques in
code-division-multiple-access (CDMA) systems. Since the characteristic of ICI is similar to that of MUI, these methods can be directly applied to ICI mitigation in OFDM systems. A method combining the MMSE and SIC techniques was first proposed in [17]. Later, it was improved with a recursive method in [18], reducing the required complexity further. Although good performance can be achieved with these methods, the required complexity is still high and the time delay can be intolerably large. The PIC technique was then employed to solve the problem [19], [20], [21], [22], [23].
Although the processing delay is greatly reduced, the performance is discounted as well. Other approaches use transmitter frequency-domain coding or beamforming to reduce ICI or to en-hance the received signal-to-interference-noise-ratio (SINR). Interested readers may see [24], [25], [26], [27].
Apart from the processing in the frequency domain, some researchers also explore that in the time domain. In [28], a time-domain filtering technique maximizing the signal-to-ICI-plus-noise ratio was proposed for single-input-single-output(SISO)/multiple-input-multiple-output (MIMO) OFDM systems. One disadvantage of this method is that it requires matrix operations to solve a generalized eigenvalue problem. Another approach involves the use of a time-variant time-domain equalizer, making the time-variant channel less variant. Transferring the equalizer from time-domain to frequency-domain, one can obtain a frequency-domain per-tone equalizer (PTEQ). The PTEQ was originally proposed to deal with the insufficient CP problem in OFDM systems. Lately, it is extended to suppress ICI in SISO/MIMO-OFDM systems [29], [30], [31], [32], [33]. The PTEQ is well-known for its good performance; however, its implementation complexity and storage requirement can be high. In [34], a two-stage equalizer was proposed.
In the first stage, a time-domain windowing technique is used to shorten the ICI response in the frequency domain. In the second stage, an iterative MMSE method is used to suppress the residual ICI. Although the windowing approach is simple, the iterative MMSE processing is not trivial. To further enhance the system performance, another approach called turbo equalization can be applied to mitigate ICI [35], [36], [37]. In [37], a block turbo MMSE method was proposed. The main feature is that this method uses the whole ICI matrix to obtain the MMSE
solution although it ignores some insignificant ICI terms.
Next, we discuss the CFO-induced ICI mitigation problem. For OFDM and OFDMA down-link systems, the CFO can be easily estimated and compensated in the receiver [38], [39]. How-ever, for OFDMA uplink systems, the problem is more involved. In the literature, various ICI mitigation methods have been proposed to solve the problem. One direct method is to estimate CFO in the base station and transmit the information back to mobile stations for CFO correc-tion. Another approach is to transmit redundant information in subcarriers such that ICI can be cancelled with a simple method in the receiver end. This approach is called the self-ICI-cancellation [24], [40], [41], [42], [43], [44]. However, these methods mentioned above will sacrifice the transmission rate.
Yet another viable approach eliminates the need for extra transmission overhead by com-pensating for ICI in the receiver. CFO compensation methods for OFDMA uplink systems have been reported [45], [46], [47], [48], [49], [50], [51]. The simplest method is to treat the CFO-induced ICI as that in OFDM systems and to compensate for ICI with a time-domain phase de-rotation operation for each user [45]. This approach can suppress self-ICI, but it does not take MUI into account. In [46], a post-FFT CFO compensation method was proposed, improving the performance of the phase de-rotation approach. Unfortunately, the MUI problem still remains.
In [47], a scheme combining the method in [46] with the PIC technique was developed. Other PIC-related works can be found in [48], [49]. It is simple to observe that the CFO-induced ICI on a subcarrier mainly comes from neighboring subcarriers. Thus, the method in [50] modifies the CFO-induced ICI matrix into a banded matrix, and reduces the computational complexity of the ZF and MMSE methods. However, its performance may be compromised due to the sim-plification. Taking advantage of an interleaved-OFDMA structure, the authors in [51] proposed a method that divides the whole system into several smaller subsystems, after which the MMSE method was applied to the subsystems. This method has good performance, and it requires low computational complexity; however, it is only applicable to an ideal interleaved structure (i.e., uniform subcarrier-spacing for each user). The aforementioned methods were developed
for CFO-compensation. CFO estimation methods have also been reported for OFDMA uplink systems [52], [53], [54], [55].