EFFICIENT IMPLEMENTATION OF FILTERS FOR MIMO FADING

Abstract

A single finite impulse response filter designed to operate on a single signal is used in conjunction with an input multiplexer that interleaves samples from multiple signals and an output decimator. The output of the decimator contains interleaved samples of the multiple signals with independent filtering applied to each.

Description

BACKGROUND

Multi-path fading is a contributing factor to microwave radio receiver error rates. Its effects can be reduced by employing transmitters with multiple outputs and receivers with multiple inputs. Simulating the dynamic multi-path fading behavior of such multi-input, multi-output (MIMO) communication channels is necessary to properly characterize the microwave radio equipment.

The most general linear model for a MIMO multi-path fader is shown in FIG. 1. Each Filter (m,n) block represents a time varying filter. Any set of band limited signals can be down converted and sampled so the filtering may be applied using a discrete time digital filter operating on a complex (I/Q) data sequence. Generally, each filter is implemented as an independent Finite Impulse Response (FIR) filter with time-varying complex coefficients (taps). After filtering, the signals can be up-converted and reconstructed as continuous time waveforms.

The key parameters associated with this multi-path fader are: the number of input and output channels supported, the filter sample rate, the number of taps in each filter, the maximum rate at which the filter taps can be updated, and the precision of the filter math.

SUMMARY

A MIMO multi-path fader can be constructed using a single finite impulse response filter designed to operate on a single signal in conjunction with an input multiplexer that interleaves samples from multiple signals and an output decimator. The output of the decimator contains interleaved samples of the multiple signals with independent filtering applied to each.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a functional block diagram of prior art multi-path fader.

FIG. 2 illustrates a functional block diagram according to the present invention.

FIG. 3 illustrates an efficient implementation of a single channel finite impulse response (FIR) filter by transforming to the frequency domain, multiplying, and transforming back to the time domain.

DETAILED DESCRIPTION

FIG. 2 illustrates a functional block diagram of a multi-path fader according to the present invention. A multi-path fader can be constructed using a single finite impulse response (FIR) filter designed to operate on a single signal in conjunction with an input multiplexer that interleaves samples from multiple signals and an output decimator. The output of the decimator (implemented as a demultiplexor) contains interleaved samples of the multiple signals with independent filtering applied to each.

The input multiplexer implements the data interleave pattern (shown in Table 1) used to emulate all six filters of a 3-input, 2-output MIMO system in a single FIR filter. The top row shows the composite tap sequence where each c_m,n,k is the k^th tap from filter (m,n). The subsequent rows show the corresponding data alignment versus clock cycle, where x_n,r is the r^th sample of input n. New data enters at the left and is shifted right one column per clock interval. The right column shows outputs computed as the inner product of that row with the taps, where y_m,r is the r^th sample of output m.

TABLE 1
Interleaved Taps/Data for a 3 × 2 MIMO composite filter
c0,0,k	c1,0,k	c0,1,k	c1,1,k	c0,2,k	c1,2,k	c0,0,k+1	c1,0,k+1
X2,r	0	x0,r−1	0	X1,r−1	0	x2,r−1	0	(none)
0	X2,r	0	x0,r−1	0	x1,r−1	0	x2,r−1	(none)
X1,r	0	x2,r	0	X0,r−1	0	x1,r−1	0	(none)
0	X1,r	0	X2,r	0	x0,r−1	0	x1,r−1	(none)
X0,r	0	x1,r	0	X2,r	0	x0,r−1	0	y0,r
0	X0,r	0	X1,r	0	x2,r	0	x0,r−1	y1,r

The filter tap pattern from Table-1 may be generalized to any number of inputs, outputs, and taps by using the algebraic representation in Equation 1, where N is the number of inputs, M is the number of outputs, K is the number of taps in each filter. The c_i′ values are the taps of the composite filter with interleaved coefficients, where 0≦i<KNM.

c _i ′=c _m,n,k ,i=kNM+nM+m,0≦n<N,0≦m<M,0≦k<K  Equation (1)

The input sequence, x_j′, for the generalized composite filter is derived from the N individual input sequences as shown in equation-2, where x_n,r is the r^th sample of input n.

$\begin{array}{cc}{x}_j^{\prime }=\{\begin{array}{cc}{x}_{N-1-\left(j\mathrm{mod}\mathrm{NM}\right)/M,\mathrm{Floor}\left(j/\mathrm{NM}\right)},& \mathrm{when}j\mathrm{mod}M=0\\ 0& \mathrm{otherwise}\end{array}& \mathrm{Equation}\left(2\right)\end{array}$

The output decimator extracts the individual multiple sample outputs from the composite filter output sequence y_p′ using Equation 3, where y_m,r is the r^th sample of output m. All outputs failing the stated condition are discarded.

y _{p mod MN,Floor(p/MN)} =y _p ′,pmodMN<M  Equation (3)

The relative alignment of the composite input index, j, in Equation 2 and the output index, p, in Equation 3 must be appropriately defined. This is accomplished by assigning the p=0 index to the inner product computed when the j=M(N−1) input sample (i.e. x_0,0) is aligned with the first composite filter tap (i=0).

From the preceding formulas, the single composite filter must have M times N as many taps as the individual filters, and its computational rate is increased by the same factor. This is an acceptable tradeoff when a single, high-speed, long tap-count filter is more efficiently implemented than multiple smaller filters. At this point, digital signal processing techniques, such as that disclosed by Oppenheim and Schafer in “Discrete-Time Signal Processing,” Prentice Hall, 1989, Section 8.9, Linear Convolution Using the Discrete Fourier Transform, pp 548-561, can be applied to the signal to improve computational efficiency. To illustrate, the real or complex filter coefficients may be transformed from the time domain to the frequency domain via a Fast Fourier Transform (FFT), multiplied, and then transformed from the frequency domain to the time domain via an inverse FFT (as shown in FIG. 3).

Claims

1. A circuit comprising: an input multiplexer that interleaves samples from multiple signals, having a multiplexed signal;a single finite impulse response filter designed to operate on a single signal, having a filter output, receiving the multiplexed signal as an input signal; anda decimator/demultiplexer, receiving the filter output, having multiple output signals, wherein the multiple output signals contain samples of the multiple signals with independent filtering applied to each.

2. A circuit, as in claim 1, the single finite impulse response filter including: performing sequentially, transforming blocks of the input signal from the time domain into the frequency domain;multiplying by frequency domain coefficients; andtransforming from the frequency domain to the time domain.

3. A circuit, as in claim 2, wherein each block of the input signal is multiplied by a unique set of frequency domain coefficients.

4. A circuit, as in claim 2, wherein the frequency domain coefficients are Fourier transforms of interleaved time domain coefficients.

5. A circuit as in claim 1 wherein the time domain filter coefficients are complex.