Blast MIMO signal processing method and apparatus

A technique for generating a demodulation ordering used in receive signal processing operations in a BLAST MIMO receiver that is based on a relative comparison of near-to-far resistance measures among vectors forming the estimated channel transfer function matrix is disclosed. This near-to-far resistance comparison provides a resulting demodulation ordering believed equivalent to that provided by conventional V-BLAST techniques without requiring computation of the pseudoinverse of the estimated channel matrix. Also disclosed is a successive interference cancellation technique which employs Multi-Staged Nested Weiner Filtering (MSNWF) to recover soft estimates of the transmitted component-symbols from the vector observed at the BLAST MIMO receiver. Employing such MSNWF estimation is believed advantageous in that it avoids the need for matrix inversion operations involving the estimated channel matrix, Covariance Level Order Recursive-MSNWF (MSNWF-COR) or MSNWF Conjugate Gradient techniques may be conveniently implemented to provide the desired MSNWF estimation.

TECHNICAL FIELD

This invention is generally directed to communications, and is more particularly concerned with observed signal processing in Bell Labs Layered Space-Time or BLAST type Multiple Input Multiple Output (MIMO) communications.

BACKGROUND OF THE INVENTION

Multiple Input Multiple Output (MIMO) systems are becoming popular in wireless and wireline communications to leverage aspects of intersymbol interference to potentially increase the bandwidth efficiency of existing spectra. In the case of wireless systems, radio waves do not propagate simply from transmit antenna to receive antenna, but bounce and scatter randomly off objects in the environment. This scattering is known as multipath, as it results in multiple copies or images of the transmitted signal arriving at the receiver via different scattered paths. In conventional wireless systems, multipath represents a significant impediment to accurate transmission, because the images can arrive at the receiver at slightly different times, causing destructive intersymbol interference and leading to corruption or loss of the information borne by these images.

Using the BLAST MIMO wireless approach first proposed by G. J. Foschini in 1996, however, it is possible to exploit multipath, in that the scattering characteristics of the propagation environment are leveraged to enhance, rather than degrade, transmission accuracy. See G. J. Foschini, “Layered Space-Time Architecture for Wireless Communication in a Fading Environment When Using Multiple Antennas”,Bell Lab Technical Journal, Vol. 1, No. 2, Autumn 1996. This is done by treating multiple scattering paths as separate parallel subchannels, each capable of bearing distinct data. As proposed by Dr. Foschini, BLAST operates by splitting a discrete outbound datastream into multiple substreams and using an array of transmitter antennas to simultaneously launch the parallel substreams. All the substreams are transmitted in the same frequency band, so spectrum is efficiently utilized. Since the outbound data is being sent in parallel over multiple antennas, the effective transmission rate is increased in approximate proportion to the number of transmitter antennas used.

Another array of antennas is used to pick up the multiple transmitted substreams and their scattered images at the BLAST receiver. Each receive antenna picks up all of the incident transmitted substreams superimposed as observed components of the received signal vector, not separately. However, if the multipath scattering is sufficiently rich, then the multiple substreams are all scattered slightly differently, since they originate from different transmit antennas that are located at different points in space. These scattering differences allow the substreams to be identified and recovered from the observed components of the received signal vector.

In particular, the BLAST receiver signal processor(s) view the observed component signals constituting the received signal from all the receiver antennas simultaneously, first extracting the strongest substream, then proceeding with the remaining weaker signals, which are easier to recover once the stronger signals have been removed as a source of interference. Again, the ability to separate the substreams depends on the slight differences in the way the different substreams propagate through the environment. Thus, through BLAST, a multipath wireless channel is capable of bearing an enormous capacity of recoverable information, particularly in rich multipath scattering environments.

In Dr. Foschini' original proposal, now known as diagonal BLAST or D-BLAST, enormous transmission capacities are realized through combining multi-element transmit and receive antenna arrays with an elegant diagonally layered inter-substream coding structure in which coded information blocks are dispersed across diagonals in space-time (known as space-time codes). In theory, this architecture permits transmission rates to grow linearly with the number of antennas used (assuming MTtransmit antennas and MRreceive antennas, where MT=MR) and can approach 90% of Shannon capacity. However, the complexities involved in implementing D-BLAST space-time coding currently limits its use to situations where maximum spectral efficiency is required, without regard for transceiver complexity or cost.

A simpler version of D-BLAST called vertical BLAST or V-BLAST has therefore been proposed by Dr. Foschini and colleagues at Bell Labs. See, e.g. P. W. Wolniansky et al., “V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel”, invited paper,Proc. ISSSE-98, Pisa, Italy, Sep. 29, 1998. Like D-BLAST and BLAST techniques generally, the outbound datastream is split into plural substreams and transmitted in parallel across plural transmitter antennas. However, unlike D-BLAST, no inter-substream space-time coding is performed, resulting in a much simpler and practical vector encoding process for the outbound datastream. Instead, an individual QAM transmitter-antenna pair is provided for transmitting each substream (MT transmitters total), and each substream is symbol encoded independently of the other substreams. These transmitters may be collectively thought of as a vector-valued transmitter, where components of each transmitted MT×1 column vector are symbols drawn from e.g. a QAM constellation. MR receive antennas are used, where MT≦MR.

V-BLAST's lack of inter-substream space-time coding and associated redundancy benefits does reduce the spectral efficiencies compared to D-BLAST. Nevertheless, where MT≦MR and channel conditions result in “rich scattering”, the V-BLAST architecture similarly offers capacity increases which progress approximately linearly with increases in the number of deployed transmitter-antenna pairs.

The secret behind V-BLAST lies in the use of successive interference cancellation demodulation techniques at the receiver, similar to those employed in multi-user communication systems like DS-CDMA. The observed datastream at the receiver, which is composed of the superposition of the MTtransmitted substreams, can be demodulated through successive interference cancellation and nulling to recover all the transmitted substreams. Proper demodulation and recovery of the transmitted datastream hinges critically in being able to determine the proper order in which the transmitted substreams should be demodulated. Described more fully in Foschini, such optimal substream ordering involves selecting the remaining substream with the best signal-to-noise ratio as the demodulation candidate at each iteration of the demodulation process.

As such, this form of V-BLAST demodulation, known as zero-forcing substream detection, is similar to zero-forcing decision feedback equalization (ZF-DFE). Accordingly, it is similarly effected by the noise-enhancement problem observed in zero-forcing equalizers as well as the error propagation problems characterized by decision feedback equalizers, as is well known in the art. Because of these drawbacks, recursive minimum mean-squared error estimation (MMSE) substream detection, based on MMSE decision feedback equalization used in adaptive antenna arrays, has been instead been proposed and utilized in a number of V-BLAST implementations in order to address the limitations of the zero-forcing techniques, including noise enhancement issues. See e.g. Wolniansky, and also G. D. Golden et al., “Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture”,Electronic Letters, Vol. 35, No. 1, January 1999. However, regardless of whether V-BLAST zero-forcing or MMSE substream detection is used, a computation of the Moore-Penrose pseudo-inverse of a successively deflating or decomposing matrix channel transfer function H is required for each parallel substream. Moreover, pseudo-inverse matrix computation (or simply “matrix inversion”) is required to initiate optimal substream ordering per datastream.

It should be appreciated that matrix inversion is a computationally complex and expensive operation and therefore not very attractive to implement though hardware, including application specific integrated circuits (ASICs).

In the past few years, research has been initiated in generally developing MMSE solutions which are computationally less complex and avoid the need for matrix inversion operations. This research started with the seminal paper on Multi-staged Nested Weiner Filters (MSNWF) by Goldstein, Reed and Scharf (J. S. Goldstein et al., “A Multistage Representation of the Weiner Filter Based on Orthogonal Projections”,IEEE Transactions on Information Theory, Vol. 44, No. 7, November 1998, incorporated herein fully by reference). This paper revealed a novel interpretation of the Weiner-Hopf solution was revealed, along with an inversion free method for computing the same. While the motivation behind this work was to design simple reduced rank estimators, the idea has since been detailed in M. L. Honig et al., “Performance of Reduced-Rank Linear Interference Suppression”,IEEE Transactions on Information Theory, Vol. 47, No. 5, July 2001, also incorporated herein fully by reference, which proposes a simplified MMSE demodulator for DS-CDMA based downlinks. Therefore, it would be desirable to develop matrix inversion-free demodulation techniques for BLAST and other types of MIMO communications systems.

SUMMARY OF THE INVENTION

In accordance with these and related desires, an aspect of the present invention is directed to generating a demodulation ordering used in receive signal processing operations in a BLAST MIMO receiver. This demodulation ordering is based on a relative comparison of near-to-far resistance measures among vectors forming the estimated channel transfer function matrix for the BLAST MIMO communications system including such receiver. This near-to-far resistance comparison results in a demodulation ordering equivalent to that provided by conventional V-BLAST techniques without the need for computing of the pseudoinverse of the estimated channel matrix.

Another aspect of the present invention is directed to successive interference cancellation which employs Multi-Staged Nested Weiner Filtering (MSNWF) to recover soft estimates of the transmitted component-symbols from the vector observed at the BLAST MIMO receiver. Employing MSNWF estimation consistent with this aspect of the present invention is believed advantageous in that it avoids the need for matrix inversion operations involving the estimated channel matrix. Consistent with the disclosed embodiments, Covariance Level Order Recursive-MSNWF (MSNWF-COR) or MSNWF Conjugate Gradient techniques may be conveniently employed in this MSNWF estimation.

Additional aspects and advantages of this invention will be apparent from the following detailed description of one or more embodiments, which proceeds with reference to the accompanying drawings.

DETAILED DESCRIPTION

A high level block diagram of a MR=6, MT=4 BLAST MIMO communication system according to an embodiment of the present invention is shown inFIG. 6. This communication system includes BLAST transmitter unit805and BLAST receiver unit807. As with known BLAST systems, the capacity of the BLAST MIMO communication system shown inFIG. 6is dependent on the number of transmit antennas being utilized. However, it should be realized that this number (four) shown here has been selected for illustration purposes only and in fact any combination of transmitter-antenna and receiver-antenna-pairs may be exploited without departing from the scope of the present invention as long as the number of receive antennas is at least equal to the number of transmit antennas being used for a given communications link.

The BLAST transmitter unit805is generally similar in configuration and operation to a conventional V-BLAST transmitter. As such, a single discreet datastream810is demultiplexed into MTsubstreams, and each substream is individually symbol encoded. Both of these operations are performed by the vector encoder815. The substreams can be encoded using a variety of known symbol formats, including such OFDM as BPSK, QPSK, and QAM constellations of varying size, including 16, 64 and 256 symbol constellations. The resulting substream symbols (x1. . . x4), forming the components of the transmitted column vector symbol x are then fed to its corresponding transmitter-antenna pair for upconversion and transmission across a preferably richly scattering propagation environment. Accordingly, x1. . . x4may be referred to here as component-symbols of the transmitted vector symbol x. For example, x1would be fed to QAM transmitter820and then radiated from antenna830coupled thereto. Likewise symbol x2would be fed into transmitter822and radiated from antenna832coupled thereto. It should be noted that transmitters820,822,824and826(and generally all transmitters of the BLAST system) operate co-channel at symbol rate 1/T symbols a second with synchronized symbol timing. Though not required, in this embodiment the same symbol constellation is used for each substream and that transmissions are organized into bursts of L symbols. The power launched by each transmitter is proportional to 1/MTso that the total radiated power is constant and independent of MT. Antenna830,832,834and836collectively form the antenna array838of the BLAST transmitter unit805.

Turning now to the BLAST receiver unit807, six individual receiver antenna pairs are provided. Each of the receivers860,862. . .866are, individually, a conventional SISO (Single Input Single Output) symbol receiver such as a QAM receiver. These receivers also operate co-channel, each receiving the signals radiated from all MTtransmit antennas (i.e., from the antenna array838as shown inFIG. 6). The receiver antennas840,842, . . . ,846may be collectively referred to as the receiver antenna array850of the BLAST receiver unit807.

Once received, the observed, randomly superimposed components of the received vector signal Y recovered by each receiver860. . . to866(y1. . . y6) are then sent to the signal processor880of the BLAST receiver unit807where an estimate of the originally transmitted component-symbols {circumflex over (x)}1. . . {circumflex over (x)}{circumflex over (x4)} (generally denoted as {circumflex over (x)}ord-nin the figures) forming the transmitted symbol vector {circumflex over (x)} are recovered, symbol decoded, and the resulting substreams reassembled to form an estimate (RX data890) datastream of the transmitted datastream (TX data810). As is more clearly shown inFIG. 7, the signal processor880includes a transmitted component-symbol ordering unit910and a successive interference canceller920, having simultaneous access to all observed components y1. . . y6. The ordering unit910–920canceller920tandem is used to recover a likely estimate of the transmitted symbol vector {circumflex over (x)}, on a estimated component-symbol by component-symbol basis, as will be discussed in greater detail below. A conventional symbol decoder, such as a QAM symbol decoder930may be used to decode each estimated component-symbol ({circumflex over (x)}1. . . {circumflex over (x)}4) forming {circumflex over (x)} into a corresponding estimated substream, and then the substream multiplexor940is provided to reassemble the recovered substreams according to the sort order computed by the component-symbol ordering unit910into recovered datastream RX data890. This is done to provide a reasonably accurate facsimile of the original datastream TX data810of interest.

A channel estimation unit905is also provided as part of the signal processor880to derive an estimate of the matrix channel transfer function ĤMR×MT, in which a given component ĥijrepresents the complex transfer function from the transmitter i to the receiver j. As will be discussed in greater detail below, ĤMR×MTwill be used by the transmitted component-symbol ordering unit910to determine the proper sort order Sort(.) for the burst of vector symbols bearing, at least in part, the transmitted datastream. Moreover, ĤMR×MTwill be used by the successive interference canceller to obtain coefficients in applying MSNWF estimation according to the present embodiment. Finally, individual column vectors of ĤMR×MTwill be used to decode corresponding estimated component-symbols recovered by the successive interference canceller920.

Channel transfer function estimation, is, of course, necessary because the actual matrix channel transfer function HMR×MTis unknown at the receiver807. However, a number of known techniques may be used to estimate H accurately, using e.g. a training symbol sequence of known data embedded at the beginning of each burst. Indeed in the quasi stationary case in which the channel time variation is viewed as being negligible over the L symbol periods comprising a transmitter burst, and a flat-fading propagation environment is assumed, Ĥ approaches H. Therefore, so as not to obscure the teachings of the present invention, assume that the communications system shown inFIG. 6operates under such conditions and that, therefore, the estimation unit905can estimate H perfectly (Ĥ→H).

In the embodiment shown inFIGS. 6 and 7, the ordering unit910utilizes successive near-to-far resistance comparison among the MT column vectors ĥ0,ĥ1, . . . ,ĥMT−1forming the estimated channel matrix Ĥ via a near-to-far resistance unit to optimally order the observed components for recovering the estimated component-symbols {circumflex over (x)}1. . . {circumflex over (x)}MTthrough MMSE successive interference cancellation techniques. As will be discussed in more detail below, this technique avoids the need for determining a pseudo inverse of the estimated channel matrix Ĥ. However, in other embodiments, other relative signal-to-noise ordering techniques may be interchangeably used, such as conventional V-BLAST signal ordering techniques.

Also, in the embodiment shown inFIGS. 6 and 7, the successive interference canceller920utilizes successive MSNWF estimation and interference cancellation as will be discussed below. In so doing, recursive matrix inversion is avoided. However, it should be noted that other MMSE or MMSE equivalent successive interference cancellation techniques may be alternatively and interchangeably employed as is known in the art, including the layered MMSE or zero-forcing processing set forth in Wolniansky article if the inclusion of matrix inversion operations are acceptable.

Observed component ordering according to an embodiment of the invention will now be detailed. The sorting or ordering algorithm undertaken by the component-symbol ordering unit910is adapted, in part, from algorithms which compute near-far resistance (NFR) measure calculations used in multiuser communications. Given N users in a multiuser system, each simultaneously transmitting a signal s, collectively resulting in the signal vector s{s1,s2, . . . ,sN}, the NFR for a given siis a measure of the signal to noise ratio (SNR) that can be achieved for si, independent of the power of its interferers which may constitute all or less than all of the remaining signals {s\si} (the notation {s\si} refers to the subset of s which includes all signals except for si, or alternatively, it means vector s decomposed by component si). Mathematically this is equivalent to determining the component of signal sithat is orthogonal to the interfering sub-space Gispanned by {s\si}. The “stronger” this orthogonal component is, the more resistant signal siis to multipath from the interferers. This component si* is easily found by subtracting from sithe projection of sionto the sub-space Gi. This can be written as:
si*=si−<si,Gj>Gi(1)

To compute Gi, one can just start with the signal set or vector s and derive the orthogonal basis vectors for each Giusing the well-known Gram-Schmidt orthogonalization or other suitable technique which generates a set of orthogonal basis vectors for Gi. si* can then be computed simply by using equation (1). Therefore, given set of N signals s, we compute the corresponding si* for each i, 1≦i≦N. The si* with the largest norm (max∥si*∥) will be the signal with the highest NFR and therefore the most robust to multiuser interference. Consistent with the present invention, upon determining the siwith the largest NFR (sk), we can then assume that the interferer is cancelled and therefore repeat the above procedure for s-{s\si} This process proceeds recursively until s has only one component signal. In this way one can obtain ordered list of signals with descending order of NFR measures.

FIG. 1illustrates an iteration of this NFR calculation process graphically as110, which is the subspace spanned by the signal vectors s2150and s3140of the three signal set s{s1,s2,s3}. s1*120is then computed using equation (1). The NFR measure may then be obtained for s1130as the 2-norm of S1* (denoted as ∥s1*∥). Note that the subspaces are then realized (not shown inFIG. 1) and the NFRs for s2and s3are likewise calculated. A comparison of the NFR values for s1, s2, and s3is then made, and the vector having the relatively highest NFR value is ordered first. If we assume that s1=sk, then, in keeping with the above, s depletes to {s2,s3}, the subspace are again realized (this time without consideration of s1). NFR values are again then calculated for s2and s3, and the relative maximum of these is ordered second. Then, the remaining signal s2or s3would be ordered last.

This descending NFR ordering process is leveraged in the BLAST MIMO embodiments shown inFIGS. 6 and 7to optimally order the detection and demodulation of the estimated component-symbols without the need for performing a matrix inversion operation. In so doing, the number of “signals” to order are determined by the number of transmitters (MT). Further, the signals to be ordered correspond to the column vectors ĥ0,ĥ1, . . . ,ĥMT−1of the channel estimate matrix Ĥ. Given these column vectors, the descending NFR ordering process follows the steps outlined in the flowchart ofFIG. 2and may be conveniently undertaken by the component-symbol ordering unit910shown inFIG. 7. The resulting array Sort(.), produced here by the comparison unit915, references the column vectors of Ĥ in successively descending NFR strength, which the inventor has discovered provides the optimal demodulation order required in V-BLAST signal processing. In fact, the process outlined inFIG. 2yields the same optimal ordering result as that provided by conventional V-Blast ordering, without the need to compute the inverse of the estimated channel matrix Ĥ, or perform other inverse matrix operations.

The ordering unit910and comparison unit915may be conveniently implemented using a variety of hardware and/or software configurations depending on design considerations such as vector symbol transmission rate, expected propagation environment characteristics, and overall system complexity. As such configurations may include, but are certainly not limited to combinations incorporating one or more of discrete logic, application specific integrated circuitry, and/or programmed special-purpose or general purpose information processor(s), such as one or more programmable digital signal processors, microprocessors, or microcontrollers capable of accessing memory or other computer readable media containing program code causing such information processor(s) to execute the processing steps outlined inFIG. 2. Of course, a single information processor with sufficient resources can provide the functionality of the component-symbol ordering unit910in isolation, or in combination with other signal processing functions, such as successive interference cancellation and/or component-symbol decoding, as will be discussed in greater detail below.

Turning now to transmitted component-symbol estimation and successive interference cancellation consistent with the present invention,FIG. 8illustrates a more detailed view of the successive interference canceller920deployed in the signal processor880shown inFIGS. 6 and 7. The interference canceller920is generally arranged here as an MT deep (with MT here=4) estimator-slicer-canceller cascade generally similar to conventional layered MMSE interference cancellers used in V-BLAST MIMO systems. Each individual estimator-slicer-canceller (such as estimator1010in series with slicer1012and cancellation unit1014can be thought of as a separate estimation and cancellation stage or unit within the larger cascade). However, unlike those systems, MultiStage Nested Werner Filters (“MSNWF”)1010,1020,1030and1040configurable by estimated channel matrix Ĥ and the sorting ordering Sort(.) are used instead of conventional MMSE filters. As will be described in more detail below with reference toFIGS. 3,4A and4B, these MSNWFs provide soft decision estimation of the likely transmitted component-symbols {circumflex over (x)}1. . . {circumflex over (x)}4sequentially in accordance with the sorting order Sort(.) without the need for computing any matrix inversions of the estimated channel matrix Ĥ. As MSNWF1010must filter the entire observed vector Y, it includes an MT dimensional filterbank. MSNWF1020filters Y′, which corresponds to Y without the strongest interferer estimated component-symbol {circumflex over (x)}ord−1(which was cancelled out of Y by cancellation unit1014), and is therefore of dimension MT-1. Likewise, MSNWF1030filters Y″=Y′−ĥSort(2)·{circumflex over (x)}ord-2and thus is of MT−2 dimensions. MSNWF1040filters Y′″=Y″Sort(3)·{circumflex over (x)}ord-3, and in this case (MT=4) comprises, a one-dimensional MSNWF filter.

Still referring toFIG. 8, a slicer1012,1022,1032and1042is provided coupled to the output of the MSNWFs1010,1020,1030and1040respectively to quantize the soft symbol-component decisions generated by the MSNWFs to enable ready symbol decoding by the symbol decoder930shown inFIG. 7. The cancellation units1014,1024, and1034in this embodiment each include a column vector selector unit (such as unit1018) to select the column vector ĥ0,ĥ1, . . . ,ĥMT−1corresponding to the estimated symbol-component just recovered using the Sort(.) parameter.

Note that in the embodiment shown inFIG. 8, the depth of the canceller cascade is 4 since MT=4 as shown inFIG. 6(and so only four component-symbols corresponding to the four transmitted substreams need be recovered). However, it should be appreciated that the canceller920, and the individual MSNWFs themselves, can be arranged to handle any number of transmitted component-symbols, as long as the number of receive antennae MR meet or exceed MT.

The MSNWF filters used in matrix inversion-free component-symbol estimation according to the embodiment shown inFIG. 8will now be explored in more detail. In recent times, MSNWF has been proposed as a computationally simple method to approximate the MMSE solution. Therefore it makes sense to explore opportunities to suggest its application in areas where MMSE estimators are utilized. As discussed above, variants of V-BLAST MIMO systems utilize MMSE to demodulate the individual datastreams instead of the ZF-DFE approach proposed in Wolniansky. Layered MMSE combines the enhanced performance (lower noise enhancement issues than in zero-forcing algorithms) offered by MMSE with the proven benefits of successive interference cancellation. However the MMSE solution requires the computation of the pseudo inverse of the estimated channel matrix formed using the observation vector. MSNWF presents an attractive alternative to computing the approximate MMSE solution without the need for matrix inversion operations.

Given a BLAST MIMO system made up of MT transmit antennas and MR receive antennas (MR>=MT) we can write the following simple model for the received observed vector Y, such that
Y=Hx+N=h0·x0+h1·x1+ . . . +hMT−1+N,(2)
where x is the (MT×1) column vector [x0x1x2. . . xMT−1]Tof transmitted component-symbols, and Y is the (MR×1) column vector representing the observed components or received samples, N is the (MR×1) column vector representing the additive white Gaussian distributed noise with zero mean and variance σn2. H is the channel transfer matrix made up of the column vectors {h0, h1, . . . , hMT−1} described above. The MMSE estimator WMMSEfor estimating X given observed vector Y and channel matrix H is given by the Weiner-Hopf equation:
WMMSE=Ryy−1Rxy,  (3)
where Ryyis the correlation matrix formed using Y and Rxyis the cross-correlation vector.

As suggested in Goldstein, Multistage Nested Weiner Filters provide an alternative approach to derive WMMSEthat can be computed without the inversion of the correlation matrix. Besides, the ‘nested’ aspect of MSNWF presents an elegant method that breaks a higher dimensional problem recursively into lower dimensional sub-problems and then combines the solutions of each of these sub-problems to obtain the final solution. The MSNWF approach has been shown to be equivalent to finding the MMSE solution in the Krylov subspace formed by the vectors {b, Ab, A2b, . . . ,AMTb} (see e.g. Honig).

FIG. 3illustrates the general configuration of an MSNWF filter as proposed by Goldstein and M. D. Zoltowski et al., “The Relationship Between Multi-Staged Nested Weiner Filter and Conjugate-Gradient Based Optimization”, which is incorporated herein by reference. This filter includes an analysis section302used to break up a higher dimensional estimator into a sequence of lower dimensional estimators using forward recursion techniques, and a synthesis section304which combines the lower dimensional estimates using backward recursion to compute the final MMSE estimate. InFIG. 3, the notation pirefers to column vectors of N=MR dimension while each Biform blocking matrices of dimension (N−i)×N. Note that as the computations advance in the analysis section302, Bi becomes progressively smaller (as i increases).

With continuing reference to Zoltowski, the MSNWF estimator configuration shown inFIG. 3can be modified to that shown inFIG. 4A, depicting a Covariance Level Order Recursive-MSNWF (COR-MSNWF) configuration of an MMSE equivalent estimator. In particular, in COR-MSNWF, the forwardly recursive analysis section shown inFIG. 3is replaced by the analysis filterbank402to generate T0. . . TN−1, where Tjis computed as follows:
Ti=(Πk=0,i=1Bk·H)hi(4)

The MSNWF filter configuration can be simplified even further if a MSNWF-Conjugate Gradient (MSNWF-CG) structure proposed in Zoltowski is employed. This MSNWF variant is depicted inFIG. 4B. As shown here, the simplified analysis section402is carried over from the MSNWF-COR configuration shown inFIG. 4A. However, a new synthesis section454is proposed that eliminates the need for recursion. The synthesis coefficients V0. . . VN−1differ from, but are based on synthesis coefficients W0. . . WN−1used in the base MSNWF and MSNWF-COR alternatives presented inFIGS. 3 and 4Arespectively.

In order to better appreciate the benefits conferred by these embodiments, consider the following MT=4, MR=4, example such that H=[h0,h1,h2,h3]. Referring to the relationships stated above in equation (2), and without loss of generality assume that the sorted order for demodulating the layered data stream is {0,1,2,3} in 0thlayer is demodulated first and so on. For the 0thlayer, the MMSE estimator is given by
W0=[HHH+πn2I]−1·h0*,  (5)
where HHis the Hermitian (conjugate transpose) of H, and h0* is the conjugate of h0. Now consider H1=H\h0, H2=H1\1,H3=H2\h2. Then,
W1=[H1H1H+πn2I]−1·h1*,  (6)
W2=[H2H2H+πn2I]−1·h2* and  (7)
W3=[H3H3H+πn2I]−1·h3*  (8)
represent the MMSE estimators to be used for the demodulation of layers1,2and3. One can now compute W0,W1,W2and W3without using matrix inversion by using e.g. Zoltowski's MSNWF-CG method. Here, I represents an MR×MR identity matrix. This results in an exact Layered-MMSE solution that is inversion free and with a computation complexity of O(MR3) rather than O(MR4) that conventional MMSE estimation would entail.

It should be noted that, of the three MSNWF alternative structures presented inFIGS. 3,4A and4B respectively, the MSNWF-CG alternative ofFIG. 4Bis believed to be the simplest to implement as an ASIC or in discrete logic. By contrast, the MSNWF alternative presented inFIG. 3is believed to provide the most elegant solution if MSNWF approximation is to be implemented in software and/or firmware. In any case, these MSNWF alternatives provide a way to arrive at the MMSE solution without the need of computing any matrix inversions, although they do require multiplying a matrix with a column vector. All the numerical computations are simple and do not suffer from numerical instability problems as in the case of computing matrix inverses. As will be appreciated by those skilled in the art, any of these alternative MSNWF configurations may be interchangeably used to configure the MSNWF filters1010,1020,1030and1040shown in the canceller920(FIGS. 7 and 8) to perform the recovery of estimated component-symbols transmitted by a MIMO BLAST transmitter such as transmitter805shown inFIG. 6.

In another embodiment, one or more functions of the successive interference canceller920, including the aforementioned MSNWF estimation, can be performed by one or more information processors programmed in accordance with the processing steps outlined in the flowchart ofFIG. 9. Accordingly, the canceller920may be conveniently implemented in hardware, software or a combination thereof as long as the required estimation and interference cancellation functions can be undertaken within vector symbol transmission rate and timing requirements. Referring briefly toFIG. 9, it is assumed in this embodiment that initial channel estimation and component-symbol demodulation ordering consistent with the present invention has been performed, and both Ĥ and Sort(.) are available as inputs. Thus, component-symbol ordering and estimation/successive interference processing may be handled sequentially, since the Sort(.) in this case, being dependent on initial channel estimates, is deemed to be valid throughout the transmitted vector symbol burst. Though not shown in the figures, in other embodiments consistent with known V-BLAST ordering and component-symbol estimation processing flow, component-symbol ordering may be performed together with component-symbol estimation and interference cancellation in a staged recursive manner on a per component-symbol basis of each vector symbol, and may be useful where e.g. Ĥ is anticipated to change appreciably within a burst.

Moreover, steps1222,1220, and1224are shown inFIG. 9being executed in a substantially parallel manner. However, consistent with the teachings of the present invention, no such parallelism is required and indeed the steps can be entirely sequentially executed as long as overall timing requirements can be observed.

The layered MSNWF structures previously discussed includes inner-product operations on (MR×1) dimension vectors. The output of each MSNWF estimator, labeled as Z in the figures, can be written as:
Z=Σi=1:MTβi·<tj, Y>=Σi=1:MT<βi,tj, Y>(9)
FIG. 5shows an adaptive variant of the configuration shown inFIG. 8which utilizes the differences between the soft decisions generated by the MSNWF filters and the hard decisions rendered by the follow-up slicers to adaptively tailor the MSNWF filtering over time. The adaptation performed by the adaptation units716,726, and736can be blind, data-aided or decision-directed using any of the well-known techniques like least-mean-square (LMS) etc. The architecture can also be made completely adaptive or partially adaptive in which the higher order datastreams can be demodulated using the MSNWF-CG approximation of MMSE while the lower order estimators can be made adaptive.