Channel Estimation

the near-optimum performance of the Log-MAP SDM detector, while imposing a substantially lower computational complexity, which renders it an attractive design alternative for practical systems.

• Finally, in Chapter 5 we amalgamated both the soft decision feedback aided MIMO channel estimation scheme of Chapter 2 as well as the Log-MAP SDM detection method derived in Chapter 4 into an iterative receiver architecture. Additionally, we carried out an analysis of the associated design trade- offs.

In the following chapter we will summarize some of the major conclusions of this study and propose promis- ing directions for future work.

6.1.1 Channel Estimation

The DDCE scheme proposed in Chapter 2 is suitable for employment in both OFDM and MC-CDMA systems. We analysed the achievable performance of the estimation scheme considered in conjunction with a realistic dispersive Rayleigh fading channel model having a realistic Fractionally-Spaced (FS) rather than an idealized Symbol-Spaced (SS) Power Delay Profile (PDP).

Specifically, in Section 2.5.1 we proposed the MMSE FD-CTF estimator, which is suitable for employ- ment in both OFDM and MC-CDMA systems. In Section 2.5 we continued our discourse with the derivation of both sample-spaced as well as fractionally-spaced CIR estimators. In Section 2.5.5 we performed a com- parison between the two methods considered and demonstrated the advantages of the fractionally-spaced scheme. Subsequently, in Section 2.6 we developed a parametric fractionally-spaced CIR tap tracking tech- nique, which facilitates low-complexity channel estimation in realistic channel conditions characterized by time-variant fractionally-spaced power delay profiles. More specifically, we employ the deflation PAST method of Algorithm 2 for the sake of recursive tracking of the CTF’s covariance matrix and for the sub- sequent tracking of the corresponding CIR taps. We demonstrated that the PAST-aided DDCE scheme proposed exhibits a good performance over the entire range of practical propagation conditions.

In Section 2.7 we discussed two major CIR tap prediction strategies, namely the robust predictor, which was capable of guaranteeing a certain level of performance under specified worst-case PDP conditions, as well as the adaptive RLS predictor. In Figures 2.18 and 2.19 of Section 2.7.5 we characterized and compared the achievable performance of both methods considered and drew conclusions concerning their relative merits. Specifically, we demonstrated that the RLS prediction technique outperforms its robust counterpart over the entire range of the relevant channel conditions.

Subsequently, in Section 2.9 we addressed the problem of channel estimation in multi-antenna aided multi-carrier systems. Specifically, we proposed a DDCE scheme, which is suitable for employment in

6.1.1. Channel Estimation 176

a wide range of multi-antenna aided multi-carrier systems capable of operating over the entire range of practical channel conditions. In particular, we considered a generic MIMO-OFDM system employing K

orthogonal frequency-domain subcarriers as well as havingmtandnrtransmit and receive antennas, respec- tively. The MIMO channel estimation scheme derived in Section 2.9 comprises an array ofKper-subcarrier MIMO-CTF estimators, followed by a (nr×mt)-dimensional array of parametric CIR estimators and a corresponding array of(nr×mt×L)CIR tap predictors, whereLis the number of CIR taps tracked per each link of the MIMO channel.

In Section 2.9.1 we explored a family of recursive MIMO-CTF tracking methods, which were combined with the aforementioned PAST-aided CIR-tracking method of Section 2.6 as well as with the RLS CIR tap prediction method of Section 2.7.4 in order to create an efficient channel estimation scheme for MIMO- OFDM systems. More specifically, in Section 2.9.1 we considered both hard- and soft-feedback assisted LMS and RLS CIR tap tracking algorithms as well as the modified RLS algorithm, which is capable of improved exploitation of the soft information associated with the decision-based estimates.

Finally, in Figures 2.24–2.27 of Section 2.9.1.5 we documented the achievable performance of the resultant MIMO-DDCE scheme employing the recursive CTF tracking of Section 2.9.1 followed by the parametric CIR tap tracking and CIR tap prediction techniques of Sections 2.6 and 2.7, respectively. We demonstrated that the MIMO-DDCE scheme proposed exhibits a good performance over the entire range of practical conditions. More specifically, both the BER as well as the corresponding MSE performance of the channel estimation scheme considered was characterized in the context of a turbo-coded MIMO-OFDM system in Figures 2.24–2.27. We demonstrated that the MIMO-DDCE scheme proposed remains effective in channel conditions associated with high terminal speeds of up to 130 km/h, which corresponds to the OFDM-symbol normalized Doppler frequency of 0.006. Additionally, we reported a virtually error-free performance for a rate1/2turbo-coded 8x8-QPSK-OFDM system, exhibiting a total bit rate of 8 bits/s/Hz and having a pilot overhead of only 10%, at an SNR of 10dB and normalized Doppler frequency of0.003, which corresponds to a mobile terminal speed of about 65 km/h.

In conclusion, the performance of the PAST aided MIMO-DDCE scheme derived in Chapter 2 may be characterized based on the MSE performance results depicted in Figure 6.1. More specifically, the MSEσ2

e

exhibited by the channel estimation scheme considered may be expressed as

σe2 = 1

κγ

Lmtnr

K , (6.1)

whereLis the number of the estimated CIR taps, whilemtand nrare the numbers of transmit and receive antennas, respectively. Correspondingly, Lmtnrdenotes the total number of the independent channel-related parameters estimated, whileγis the average SNR encountered at the receiver. Furthermore, we employ the estimation efficiency factorκof Equation 2.110. The value of the parameter κwas determined empirically using Equation 2.110, yieldingκ=4dB.

6.1.2. Signal Detection in MIMO Systems 177