Filter Bank precoding for FIR equalization in high-rate MIMO communications

Abstract

Abstract-In this paper, the problem of designing finite-impulse-response (FIR) equalizers for multiple-input multiple-output (MIMO) FIR channels is considered. It is shown that an arbitrary MIMO frequency-selective channel can be rendered FIR equalizable by a suitable filter bank (FB) precoding operation that introduces redundancy at the transmitter. The expression for the minimum redundancy required to ensure FIR invertibility is derived. The analysis is extended to the case of MIMO multicarrier modulation. Optimum zero-forcing (ZF) and minimum mean-squared error (MMSE) solutions for the FIR equalizer are derived. Simulation results are provided to demonstrate that the proposed scheme achieves better performance than the block-processing methods while supporting a higher data rate.Index Terms-Filter bank, finite-impulse-response (FIR) equalization, multiple-input multiple-output (MIMO), polynomial matrix, pseudocirculant matrix, Smith form.

Novel System Inversion Algorithm With Application to Oversampled Perfect Reconstruction Filter Banks

“…Proof: (of Proposition 3) Remember that with (10) and (14) we have fixed a stabilizing solution to (8). We show existence of a stabilizing solution to (12)…”

“…With (14), this gives us expressions for the . Plugging them into (18) and (19) results in the recursion from the proposition.…”

“…Other inversion problems treated in the literature are, e.g., causal IIR inverses with minimal unweighted norm [9], [10] or minimal norm [11], [12]. Causal FIR inverses with minimal norm are treated in [13], [14]. The para-pseudoinverse, which in general is noncausal and IIR, is considered in [15]- [17].…”

Perfect reconstruction of signal—a new polynomial matrix inverse approach

“…On the other hand, in the approach based on the polynomial matrix calculus [12][13][14], the aforementioned dysfunction is eliminated by using the PSVD (polynomial SVD) [15][16][17]. Unfortunately, all mentioned approaches to the signal perfect reconstruction [18][19][20], also those including the Smith decomposition method [21], have not so far included the so-called degrees of freedom [22]. Therefore, they were solely related to a certain "optimal" solution associated with the application of the minimum-norm/least-squares inverses to an Eigen matrix obtained from the factorization process [11].…”

On the degree of MIMO systems

“…MIMO channels and wireless communications systems have generated a great deal of renewed interest in linear system theory [1], [3], [4]. Even though MIMO system theory is a very well-established field [2], certain specific questions that come up in the context of communications require revisiting the fundamentals in order to generate new results.…”