EFFICIENT COVARIANCE COMPUTATION BY TABLE LOOKUP

BACKGROUND

The present invention relates generally to wireless receivers, and more particularly to interference suppression receivers.

Interference present in wireless communication signals impacts transmission power requirements, system capacity, data rates, etc. For example, lower interference levels enable data transmissions at lower transmission powers and/or at higher data rates. Thus, interference suppression represents an important element in wireless communications. Multi-path dispersion represents one source of interference in Code Division Multiple Access (CDMA) systems, such as Wideband CDMA and IS-2000. With dispersion, multiple echoes of the transmitted signal(s) arrive at the receiver with different relative delays. These echoes cause interference between successive symbols and result in a loss of orthogonality between symbols sent on different, orthogonal codes. However, receivers may take advantage of correlations between multi-path signals to reduce interference from the received signals. Wireless receivers may include an interference rejection equalizer (IRE) that takes advantage of the existing correlations to reduce multi-path interference, e.g., orthogonal interference due to own-cell interference and non-orthogonal interference due to other-cell interference.

Generalized RAKE (GRAKE) receivers and Chip Equalizers (CE) represent two types of IREs. For example, GRAKE receivers include a bank of RAKE fingers, where each RAKE finger generates a despread sample stream with a particular finger delay. An interference rejection combiner (IRC) generates an output signal with reduced interference by combining the despread sample streams while applying the appropriate combining weights w . The IRE typically determines the combining weights such that Rw = g , where g represents a vector of

channel coefficients for the multiple channel paths, and R represents a matrix of impairment correlations between the despread sample streams.

The IRE may estimate instantaneous impairment correlations R using a non-parametric approach, where the equalizer processes known pilot symbols embedded in the received signals to extract the impairment components. Based on the extracted impairment components, the receiver directly estimates the impairment correlations R . This type of approach typically requires a large number of pilot symbols. When the current measurement interval does not include a sufficient number of pilot symbols, the estimated impairment correlations R may be undesirably noisy. To remove at least some of the noise, the receiver may filter the estimated impairment correlations R . However, at high processing speeds, the resulting filtered impairment correlations represent more of a time average of the impairment correlations, instead of the desired instantaneous impairment correlations.

The IRE may alternatively estimate current impairment correlations R using a parametric approach. The parametric approach analytically constructs the impairment correlation matrix based on the available channel information. Because most of the multi-path interference comes from a limited number of well-defined sources, the parametric approach provides accurate impairment correlation estimates at both high and low processing speeds. However, the processing resources available to wireless devices may be insufficient for conventional parametric approaches.

SUMMARY A wireless receiver processes a received multi-path signal to determine a desired symbol estimate. The wireless receiver comprises an impairment processor, weight calculator, and interference rejection equalizer, e.g., a GRAKE or chip equalizer. The interference rejection equalizer separates the received signal into multiple sample streams, where each sample stream is associated with a different processing delay corresponding to one of the received signal paths. The impairment processor determines impairment correlations between the sample streams, while the weight calculator uses the impairment correlations to generate

weighting factors. The interference rejection equalizer subsequently applies the weighting factors to the sample streams and combines the weighted sample streams to simultaneously generate the desired symbol estimate while reducing interference in the desired symbol estimate. The impairment processor of the present invention uses one or more look-up tables to reduce the computational complexity associated with determining an impairment correlation between first and second sample streams. In one exemplary embodiment, the impairment processor iteratively computes multiple partial impairment correlations based on values selected from lookup table(s), and combines the partial impairment correlations to obtain a final impairment correlation between the first and second sample streams. For each correlation entry, the impairment processor computes an entry-specific pair of delay offsets corresponding to the respective processing and path delays of the first and second sample streams. The impairment processor computes an index value as a function of a difference between the pair of delay offsets, selects a pre-computed value from the look-up table based on the index value, and determines a pulse correlation estimate based on the selected pre-computed value.

Subsequently, the impairment processor determines the partial impairment correlation for that entry based on the pulse correlation estimate.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 shows a receiver according to one exemplary embodiment of the present invention.

Figure 2 shows a process for generating impairment correlations.

Figure 3 shows one exemplary impairment processor for the receiver of Figure 1.

Figure 4 shows one exemplary process for generating the pulse correlation estimates for the process of Figure 2 using the impairment processor of Figure 3. Figure 5 shows another exemplary process for generating the pulse correlation estimates for the process of Figure 2 using the impairment processor of Figure 3.

Figure 6 shows one exemplary pulse correlation processor for the impairment processor of Figure 3.

Figure 7 shows another exemplary pulse correlation processor for the impairment processor of Figure 3. Figure 8 shows another exemplary pulse correlation processor for the impairment processor of Figure 3.

Figure 9 shows one exemplary hybrid process for generating the pulse correlation estimates for the process of Figure 2 using the impairment processor of Figure 3.

DETAILED DESCRIPTION

Figure 1 shows one exemplary interference rejection receiver 100 according to the present invention. Receiver 100 includes an interference rejection equalizer (IRE) 110, path searcher 120, weight calculator 130, channel estimator 140, impairment processor 150, and memory 160. IRE 110 generates output sample estimates z based on the received signal r , processing delays d generated by path searcher 120, and weighting factors w generated by the weight calculator 130. In one embodiment, IRE 1 10 comprises a delay processor 1 12 and interference rejection combiner (IRC) 1 14. Delay processor 112 generates a plurality of sample streams based on the received signal r and the processing delays d , and IRC 114 weights and combines the sample streams according to the weighting factors w . For example, when IRE 110 comprises a GRAKE receiver, the processing delays d comprise RAKE finger delays, and delay processor 112 comprises a bank of RAKE fingers that each generate a despread sample stream corresponding to each finger delay. IRC 1 14 weights and combines the despread sample streams to generate the desired output samples z . It will be appreciated that IRE 1 10 may comprise any interference rejection equalizer, including but not limited to, GRAKE receivers and chip equalizers.

Weight calculator 130 generates the weighting factors w based on channel coefficients g and

impairment correlations R . The channel estimator 140 generates the channel coefficients g based on the received signal r and physical path delays τ generated by the path searcher 120. While the channel estimator 140 generates one channel coefficient g for each of the

physical channel paths, it will be appreciated that the number of processing delays N _d generated

by path searcher 120 may differ from the number of physical channel paths N^ .

The impairment processor 150 generates the impairment correlations R between the sample streams output by delay processor 112 for one or more modeled impairment components. By combining the impairment correlation matrices according to:

^R = σ,λ 0 ⁾ where R _n represents the impairment correlation matrix for the n ^xu impairment component,

impairment processor 150 determines a composite impairment correlation matrix R .

Impairment processor 150 generates each element R(i,j) of an impairment correlation matrix

R _n according to:

*(U) = ∑ 1=1 ∑ q=l>, ^g X ^{, (2)}

where

U _lq = ∑ P{d _i -τ _ι -mT _c )P ^t (d _] -τ _q -mT _c ) . (3)

In Equation (2), g represents the complex channel coefficient for a physical channel path, N^

represents the number of physical channel paths, / and q represent indices for the physical

channel paths, and U ₁ represents the pulse correlation estimate associated with the / ^th and

q ^χ] " physical path. In Equation (3), /*(•) represents the end-to-end pulse shape including the

transmit and receive filter responses, d represents the processing delay, τ represents the path

delay, T _c represents the length of the chip period, m represents a chip period sample index,

and S represents the set of all m used to compute the impairment correlation i?(z,y) .

Figure 2 shows one exemplary process 200 for generating R(i,j) according to Equation (2).

After selecting processing delays {d,,^ ) (block 210), the impairment processor 150 initializes /

and q (block 220) and computes the pulse correlation estimate U _lq (block 230). The

impairment processor 150 then computes a partial impairment correlation R _lq {i,j^ according to:

(block 240). The impairment processor 150 increments / and q (blocks 250, 252, 260, 262)

and repeats blocks 230 - 240 for each value of / and q . To generate the final impairment

correlation R(i,j) between sample streams associated with the selected processing delays

j , the impairment processor 150 sums all partial impairment correlations R _lq (i,j) (block

270). The impairment processor 150 repeats process 200 for each element of each

impairment correlation matrix R _n .

When the impairment processor 150 computes an impairment correlation R(i,j) according to

Equation (2), the number of processing operations may be prohibitively large. For example, assume N _p = 6 paths, N _d = 10 processing delays, and a range of ±M = 6 chip samples for

each m . For this scenario, computing each R _n requires \N _d ² N _p ² (2M) = 21 ,600 complex

multiply and accumulate (MAC) operations. In advanced receivers that model more than one impairment component, several R _n must be formed per time unit, e.g., per 0.67 ms WCDMA

time slot. Such computations generally require significant processing resources.

The present invention significantly reduces the computational complexity associated with

R(i,j) by replacing a portion of the calculations with a simple look-up table operation. For

simplicity, the following describes the present invention in terms of computing one element

R(i,j) for one impairment correlation matrix R _n . The present invention applies to the

calculation of all of the impairment correlation elements R(i,j) for any impairment correlation

matrix R _n .

Equation (3) may be rewritten as:

U ₁₉ = Z P[A ₁ - InT ₁₁ )P ^' (A ₉ - mT _e ) , (5) meS where δ, = Cl ₁ - T ₁ and δ^ = d _j -τ _q . Equation (5) shows that the pulse correlation estimate U _lq

associated with non-orthogonal interference components (where the set S includes the m = 0

term) is not unique for all possible pairs of delay offsets |δ _z ,δ _? j . Instead, the pulse correlation

estimate U ₁ only depends on the difference between the delay offsets δ, - δ . Thus, when

memory 160 includes a look-up table 162 of pre-computed pulse correlation estimates associated with non-orthogonal interference components, the computations associated with each U _lq may be replaced with a simple look-up operation indexed by δ _z - δ _? .

Figure 3 shows one exemplary impairment processor 150 for generating each impairment correlation R(i,j) of the impairment correlation matrix R _n . Impairment processor 150

determines R(i,j) based on U _lq , which are determined based on pre-computed values Cl

selected from the look-up table 162 for each of the / and q physical path combinations. The impairment processor 150 comprises a pulse correlation estimator 151 and an impairment correlation estimator 152. Pulse correlation estimator 151 determines U _lq using process 230 as

shown in Figure 4. For each {/,g} pair of physical paths, the pulse correlation estimator 151

computes the delay offsets A ₁ and δ (block 231 ) according to:

A ₁ = d - T ₁ ' ' ' , (6)

and computes an index value A ₁ - A as a function of the difference between the computed

delay offsets (block 232). As illustrated by Equation (6), the index values change for each

{l,q} pair. Pulse correlation estimator 151 selects a pre-computed value Ofrom the look-up

table 162 for each index value (block 233), and determines each U _lq for an N^ x N^ matrix U

based on the selected pre-computed values Cl (block 234). In one embodiment, the pulse correlation estimator 151 equates one or more of the pulse correlation estimates U _lq to the

corresponding pre-computed values Cl selected from the look-up table 162. Impairment

correlation estimator 152 determines R(i,j) based on U by computing a partial impairment

correlation R _lq (i,j} for each U ₁ according to Equation (4), and combining the partial

impairment correlations, as shown by blocks 240 and 270 in Figure 2.

As described above, the present invention replaces the computations associated with U ₁ with a

look-up table operation. For the above example, computing one correlation matrix R _n

according to the present invention requires \N _d ² N _p ² = 1 ,800 MAC operations coupled with

-^N _j N _p = 1 ,800 look-up operations. A conventional system that relies solely on MAC

operations would require \N _d ² N _p ² (2M) = 21 ,600 MAC operations to compute the same

correlation matrix R _n . Thus, as long as the U _lq values generated by pulse correlation

estimator 151 have sufficient accuracy, the present invention provides significant processing savings without sacrificing performance.

The present invention may also be used with a receiver 100 that oversamples /*(•) . For this

embodiment, receiver 100 samples /*(•) at multiple samples per chip period. While the

relationship between U _lq and A ₁ - A _q holds, the one-dimensional table 162 indexed by A ₁ - A _q

does not consider the position of the samples relative to the main lobe of /*(•) . To account for

this, another embodiment of the present invention may store a two-dimensional look-up table 164 of pre-computed values associated with non-orthogonal impairment correlations in memory 160. The two-dimensional table 164 is indexed by the index value A ₁ - A _q and a sampling

phase P ₁ associated with the / ^th physical path.

Figure 5 shows one exemplary pulse correlation estimation process 230 for an oversampling receiver 100. Pulse correlation estimator 151 computes the delay offsets A ₁ and A _q for each of

the / and q physical paths (block 231 ), and computes the index value A ₁ - A _q as a function of

the difference between the computed delay offsets (block 232). The pulse correlation estimator 151 further computes the sampling phase P ₁ (block 235) according to:

P ₁ = A ₁ XnOd(T ₀ ) , (7)

where mod(-) represents the modulo operation. Based on the sampling phase p, and index

value A ₁ - A _q for each [l,q] pair, pulse correlation estimator 151 selects pre-computed values

Ofrom the two-dimensional look-up table 164 (block 236). The pulse correlation estimator 151 determines each U _lq for the I x q matrix U based on the selected pre-computed values (block

234). The impairment correlation estimator 152 determines R(i,j) as discussed above.

The sizes of look-up tables 162, 164 depend on the desired resolution and the desired sample set S for m . For example, two-dimensional look-up table 164 will accurately represent the calculation of Equation (3) for 4x oversampling (OS4) when table 164 covers differences between delay offsets δ _z - δ _? for up to ± 6 chip periods. Such a look-up table 164 for non-

orthogonal impairment components would require 12 chips x 4 differences x 4 offsets = 192 table entries. An exemplary one-dimensional look-up table 164 for non-orthogonal impairment

components (assuming sampling offset is neglected) would require 12 chips x 4 differences = 48 entries.

When /*(•) is symmetric, such as for a raised cosine (RC) or root raised cosine (RRC) pulse,

the following equalities hold:

U(A, -*,) *> & {A, -A ₁ )

Equation (8) shows that the pre-computed values corresponding to negative delay offset differences may be derived from the pre-computed values corresponding to positive delay offset differences. Thus, it is sufficient to store the pre-computed values for only the positive delay offset differences. This generally reduces the size of the tables 162, 164 by half, e.g., 96 entries for the OS4 example above. For this scenario, pulse correlation estimator 151 may comprise a conjugate element 153 and a switch 154, as shown in Figure 6. When A ₁ - A is positive,

switch 154 sets U _lq equal to the pre-computed value selected from the look-up table 162, 164.

When A ₁ - A _q is negative, switch 154 sets U _lq equal to the complex conjugate of the selected

pre-computed value, as output by the conjugate element 153. It will be appreciated that further or alternative memory savings may be made by recognizing that some delay offsets yield equivalent results, e.g., the % and % sampling phases for OS4. By selectively eliminating any repeated values, the exemplary OS4 two-dimensional table 164 discussed above may be further reduced from 96 entries to 6 x 4 differences x 3 offsets = 72 entries.

The pulse correlation function U _lq of Equation (3) is an inherently smooth function. Thus,

further table size reductions may be achieved when the pulse correlation estimator 151 interpolates between multiple pre-computed values selected from the look-up table 162, 164. Figure 7 shows one exemplary pulse correlation estimator 151 comprising an interpolator 155. For this embodiment, the pulse correlation estimator 151 selects two or more pre-computed

values from a look-up table 162, 164 based on A ₁ - A _q (or A ₁ - A _q and p, ). Interpolator 155

interpolates between the selected values to generate the desired pulse correlation estimate U _lq .

While not explicitly shown, the interpolator 155 may be used with the conjugate element 153 and switch 154 of Figure 6.

The above describes the present invention in terms of impairment correlations R(i,j)

associated with non-orthogonal impairment components, such as impairments due to other-cell interference. The present invention may also be used to determine impairment correlations

R(i,j) associated with impairment sources that are orthogonal to the desired signal if perfectly

aligned, such as impairments due to own-cell interference. In such cases, the set S does not contain the m = 0 term. The delay offsets A ₁ , A _q associated with orthogonal impairment

components generally have values close to 0. As the values of the delay offsets A ₁ , A _q

approach 0, the effect of the m = 0 term on U _lq changes relative to the above-described non-

orthogonal case. Thus, the above-discussed non-orthogonal approach is not appropriate for orthogonal impairment components. To address this, the present invention may generate U _lq based on pre-computed values

selected from a two-dimensional look-up table 166 associated with orthogonal impairment components. The pulse correlation estimator 151 indexes the orthogonal look-up table 166 using A ₁ and δ to select each of the pre-computed values Cl. Pulse correlation estimator 151

then derives each element U _lq of the pulse correlation matrix U based on the selected values.

For the OS4 example, one exemplary look-up table 166 for orthogonal components requires (6 x 4) ² /2 = 288 entries.

Alternatively, the present invention may eliminate the need for a separate orthogonal look-up table 166 by excluding the m = 0 term when generating U ₁ from the non-orthogonal look-up

table 162, 164. To that end, the pulse correlation estimator 151 may derive U _lq for the

orthogonal impairment components by applying a correction value ξ _lq to a pre-computed value

Cl selected from the non-orthogonal look-up table 162, 164. Figure 8 shows one exemplary pulse correlation estimator 151 comprising a correction processor 156 and combiner 157. The correction processor 156 determines the correction term ξ _lq based on the delay offsets A ₁ , A _q .

To exclude the m = 0 term, the combiner 157 subtracts the correction term from the pre- computed value Cl selected from the non-orthogonal look-up table 162, 164 according to:

In one embodiment, the correction processor 156 may derive the correction term ξ _lq based on

one or more pre-computed values selected from a pulse look-up table 168 stored in memory 160. For example, the correction processor 156 may derive ξ _lq according to:

ξ _lq = P(A ₁ )P- (A ₉ ) , (10)

where P ^* represents the complex conjugate of P . Alternatively, correction processor 133 may derive ξ _lq from multiple pre-computed values Cl selected from the non-orthogonal look-up table

162, 164 when /*( ^• ) corresponds to a symmetric pulse shape function, such as an RC or RRC

pulse shape function. In this case, the correction processor 156 may derive ξ _lq according to:

Where Cl represents the complex conjugate of Cl.

By using the correction term ξ _lq , pulse correlation estimator 151 reduces the memory

requirements for determining impairment correlations R(i,j) for orthogonal impairment

components. The correction term ξ _lq from Equations (10) and (1 1 ) may be used with both over-

sampled and non-oversampled receivers 100. Further, one or more of the table reduction

techniques described above with respect to Figures 6 and 7 may be used with the correction process of Figure 8.

The impact of the m = 0 term decreases as A ₁ , A _q increases, and may be considered

insignificant beyond some distance, e.g., ± 3 - 5chip periods. Thus, to further reduce the processing requirements for U , the pulse correlation estimator 151 according to the present invention may implement a hybrid approach, whereby the orthogonal approach is applied to a subset of A ₁ , A _q values, and the non-orthogonal approach is applied to the remaining A ₁ , A _q

values. Figure 9 shows one exemplary hybrid process 204. Pulse correlation estimator 151 computes the delay offsets A ₁ and A _q for each of the / and q physical paths (block 231 ), and

computes the index value A ₁ - A _q as a function of the difference between the computed delay

offsets (block 232). When the greater of A ₁ and A _q equals or exceeds a predetermined

threshold T (block 237), the pulse correlation estimator 151 generates U ₁ using the above-

described non-orthogonal approach (blocks 233, 234). For example, pulse correlation estimator 151 may determine U _lq based on pre-computed values selected from look-up table 162 as

indexed by δ _z - δ _? . When the greater of δj and U l is less than a predetermined threshold

(block 237), the pulse correlation estimator 151 generates U _lq using the above-described

orthogonal approach (blocks 238, 234). For example, pulse correlation estimator 151 may generate U ₁ according to Equation (9). Impairment correlation estimator 152 then generates

R(i,j) based on the pulse correlation estimates U _lq for each [l,q] pair.

The above-described impairment processor 150 may be used for any pulse form and any physical channel, e.g., a physical channel that may be modeled as a finite impulse response filter. Further, the determined impairment correlation matrix may be used to generate combining weights for any IRE 150. Exemplary IREs 150 include, but are not limited to, Generalized RAKE

(GRAKE) receivers and chip equalizers (CE). For example, when the IRE 150 is a GRAKE

receiver, R(i,j) represents the impairment correlation between despread sample streams

output by the z ^th and 7 ^th RAKE fingers. When the IRE 150 is a CE structure, R(i,j)

represents the impairment correlation between chip samples output by the z ^th and 7 ^th tap delay lines.

By using look-up tables to determine the pulse correlation values U ₁ , the present invention

significantly reduces the processing requirements associated with the impairment processor 150. Because the present invention either uses look-up tables with sufficient resolution or uses some amount of minimal processing to achieve the desired resolution from pre-computed values selected from a look-up table, the look-up table solution described herein does not suffer from the accuracy problems associated with past complexity reduction solutions. The present invention may, of course, be carried out in other ways than those specifically set forth herein without departing from essential characteristics of the invention. The present embodiments are to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.