CN101233680A - Low complexity soft detection in multiple transmit and receive antenna systems with M-QAM modulations - Google Patents

Abstract

This invention discloses a method for performing soft detection of transmitted signals modulated by M-QAM when a transmitter equipped with one or more transmit antennas, and the receiver has one or more receive antennas. This invention is built based on the fact that soft value of a single transmitted bit (or symbol) has a piece-wise linear behavior as a function of the received signal(s). The methodology to obtain such piece-wise linear functions are given for some M-QAM modulations in single transmit and single receive antenna systems and arbitrary constellation mapping. Also, the methodology is explained for the case where the number of transmit antennas is more than one by an example for 4-QAM modulation and two transmit antennas. A further required process to expand above embodiments to multiple receive antennas are also given.

Description

Low complexity soft detection in multiple transmit and receive antenna systems with M-QAM modulation

This application claims priority and benefit from U.S. non-provisional application entitled "Low Complex software Detection Multiple Transmit Antenna Systems with M-QAM Moudulaons" filed 25.7.2005 and U.S. non-provisional application entitled "Low Complex software Detection Multiple of Transmit Antenna Systems with M-QAMMoudulaons" filed 21.7.2006.

Technical Field

The present invention relates generally to wireless communication system design and, more particularly, to a method of reducing the complexity of symbol detection in multiple transmit and receive antenna systems utilizing M-QAM (quadrature amplitude modulation) modulation.

Background

Configuring a radio unit with multiple transmit and receive antennas, as in a multiple-input multiple-output (MIMO) system, is a preferred solution in future broadband communication systems because of its higher capacity and more robust performance. However, the multiple transmit antennas enlarge the size of the original constellation (constellation) such that each receive antenna observes a constellation whose size is exponential in the number of transmit antennas. Thus, detection of such systems is more complex than detection of a single transmit antenna system.

To reduce complexity, various sub-optimal (sub-optimal) algorithms have been designed. Most of these methods perform well when the receiver has more antennas than the transmitter. However, this requirement is undesirable for downlink transmissions where it is not economically justified to equip the subscriber unit with more than one antenna. Some other suboptimal algorithms have variable levels of computational complexity, which is undesirable in practical systems.

The optimal detector for a MIMO system is a Maximum Likelihood (ML) detector whose complexity grows exponentially with the number of transmit antennas. If the original constellation has M points, then using multiple antennas to transmit T independent symbols makes the ML detector approximately M complex^T. This effectively prevents the use of an ML detector in a MIMO system with appropriate moderate size modulation. Therefore, sub-optimal detectors that can provide a reasonable tradeoff between complexity and performance are of great interest.

Linear processing of signals received by multiple antennas is a suboptimal solution with low complexity. When there are more receive antennas than transmit antennas, the complexity of the detector can be reduced by using Zero Forcing (ZF) or Minimum Mean Square Error (MMSE) methods. However, in most broadband wireless communication systems, linear processing cannot be applied since it is preferable to have a single antenna subscriber unit.

Recently, other sub-optimal solutions exist such as zeroing and deleting (spherical decoding), and quasi-ML detection. These methods have either the same problem as the linear detector (exponential complexity problem) or random complexity when the transmitting and receiving antennas are different in number. These disadvantages prevent the above algorithm from being performed effectively in practice.

For these reasons, it is desirable to devise a method for low complexity soft detection in multiple transmit and receive antenna systems utilizing M-QAM modulation without the above-mentioned drawbacks.

Disclosure of Invention

In view of the foregoing, the following provides a method for low complexity soft detection in multiple transmit and receive antenna systems utilizing M-QAM modulation.

In one embodiment, a method of performing soft detection on an M-QAM modulated signal is disclosed, the method comprising: calculating first and second probabilities that selected bits of the transmitted symbol are equal to 0 and 1, respectively, and calculating Euclidean distances of the first and second probabilities; and deriving a soft detection value based on a difference between the euclidean distances of the first and second probabilities, wherein the soft detection value has a piece-wise linear (piece-wise) behavior with respect to the received signal. A method of performing soft detection on a transmit signal modulated by M-QAM is disclosed, the method comprising detecting a signal according to

<math><mrow> <msub> <mi>&lambda;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>&Element;</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo></mo> </mrow> </munder> <mi>Pr</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>|</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>&equiv;</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </munder> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>|</mo> <mo>|</mo> <mi>r</mi> <mo>-</mo> <mo>&lt;</mo> <mi>h</mi> <mo>,</mo> <mi>s</mi> <mo>></mo> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mn>2</mn> <mi>&sigma;</mi> </mrow> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> </mrow></math>

Calculating first and second probabilities that selected bits of a transmitted symbol are equal to 0 and 1, respectively, where r is the received signal, h is the channel gain, b is 0 or 1, S_b ^k，iRepresenting a subset of the spread modulation (the symbols of which have a value equal to^b∈{0，1}I bit of the k signal) and σ²Is a normal noise variance, the method further comprising basing the method on the first and second probabilities <math><mrow> <mi>log</mi> <msub> <mi>&Sigma;</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>&ap;</mo> <munder> <mi>max</mi> <mi>j</mi> </munder> <mi>log</mi> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow></math> First and second secondary probability values are estimated, respectively, and one or more soft detection values are derived based on a difference between the first and second secondary probability values.

The construction and method of operation of the invention, together with further objects and advantages thereof, will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.

Drawings

Fig. 1 shows a diagram for explaining soft detection values of m bits derived from sub-optimal euclidean distance matrices of a single transmit antenna system using 16QAM and 64QAM modulation.

Fig. 2 shows a diagram for explaining soft detection values derived from sub-optimal euclidean distance matrices of a dual transmit antenna system using 16QAM modulation and random channel realization (random channel equalization).

Fig. 3 shows a diagram illustrating soft detection values derived from a sub-optimal euclidean distance matrix of a dual transmit antenna complex random channel, each antenna using 4QAM modulation, and a random channel realization.

Fig. 4 illustrates a method for low complexity soft detection in a system with multiple receive antennas, in accordance with one embodiment of the present invention.

Detailed Description

A method of performing low complexity soft detection in a multiple transmit and receive antenna system using M-QAM modulation will be described in detail below.

The optimal method to perform soft detection is by assuming a single receive antenna and multiple transmit antennas T, and obtaining the channel gain h-h (h) at the receiver₁，h₂，...h_T) Some knowledge of. Assuming that the received signal is r, the transmitted signal S can be calculated by the following formula_kIs equal to b ∈ {0, 1 }:

<math><mrow> <msub> <mi>&lambda;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>&Element;</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo></mo> </mrow> </munder> <mi>Pr</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>|</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>&equiv;</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </munder> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>|</mo> <mo>|</mo> <mi>r</mi> <mo>-</mo> <mo>&lt;</mo> <mi>h</mi> <mo>,</mo> <mi>s</mi> <mo>></mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mn>2</mn> <mi>&sigma;</mi> </mrow> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> </mrow></math>

wherein,<..>is an inner product operation, and S_b ^k，iRepresents a subset of the spread modulation (the symbol of which has the ith bit of the k-th signal equal to b) and σ²Is the normal noise variance. Transmitting a symbol S_kThe log-likelihood ratio (LLR) of the ith bit of (b) is then equal to the difference of the above-mentioned probabilities of the two choices of b, i.e., f_k，i(r)＝λ_k，i(r，0)-λ_k，i(r，1)。

The above matrix calculation can be a very complex calculation depending on the constellation size and the number of transmit antennas T. By using approximations <math><mrow> <mi>log</mi> <msub> <mi>&Sigma;</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>&ap;</mo> <munder> <mi>max</mi> <mi>j</mi> </munder> <mi>log</mi> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> </mrow></math> The suboptimal Euclidean distance matrix is as follows:

<math><mrow> <msub> <mi>&lambda;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>max</mi> <mrow> <mi>s</mi> <mo>&Element;</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </munder> <mi>log</mi> <mi>Pr</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>|</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>&ap;</mo> <munder> <mi>min</mi> <mrow> <mi>s</mi> <mo>&Element;</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </munder> <msup> <mrow> <mo>|</mo> <mo>|</mo> <mi>r</mi> <mo>-</mo> <mo>&lt;</mo> <mi>h</mi> <mo>,</mo> <mi>s</mi> <mo>></mo> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>.</mo> </mrow></math>

the ML detector requires that the above expression be evaluated for all k e {1, 2.. T } happens and i e {1, 2.. M }, where M is the magnitude of the modulation used by each antenna.

Although lambda is_k，iMinimum value (min) in the calculation of (r, b)) Is a non-linear operation, however, the invention is based on the following simple observation: soft detection value f_k，i(r)＝λ_k，i(r，0)-λ_k，i(r, 1) has a piecewise linear behavior in terms of the received signal r. Thus, a soft detection value f is obtained or approximated_k，iThe linear equation of (r) also provides soft detection of transmitted bits and symbols.

Fig. 1 shows a diagram 100 comprising two graphs 102 and 104 for illustrating the derivation of m-bit soft detection values from a sub-optimal euclidean distance matrix for example 16QAM and 64QAM modulations in a single transmit antenna system, in accordance with one embodiment of the present invention.

The symmetry of the M-QAM constellation with Gray mapping (Gray mapping) simplifies soft detection, so that in an Additive White Gaussian Noise (AWGN) channel (when h ═ 1), Γ i (r) of the ith bit depends on re (r) or im (r). In fig. 102 and 104, M-bit soft detection values obtained from the suboptimal euclidean distance matrix are shown, where M is 2^mWherein the horizontal axis is Re (r) or im (r). Soft detection value b for 16QAM modulation is shown in fig. 102₀And b₁In fig. 104, soft detection value b for 64QAM modulation is shown₀、b₁And b₂. Note that b₀Representing a soft detection value f_0，0，b₁Representing soft values f_0，1，b₂Representing soft values f_0，2。

For fading channels, the soft values depend on re (r) and im (r) and have a similar shape to the curves in fig. 102 and 104, with the possibility of being shifted and/or extended. This is due to constellation rotation caused by the complex fading coefficient h. However, the soft detection value f_i(r) still has piecewise linear behavior.

H is expressed as h ═ h in complex fading_r+jh_i，r＝r_r+jr_iIn the example case of (a), the soft values for 4QAM modulation are:

Г₀(r)＝4(r_rh_i-r_ih_r)，Г₁(r)＝-4(r_rh_r-r_ih_i)。

for 16QAM modulation, assume ${\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="S2006800273765E00021.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=8(h_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="S2006800273765E00021.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+h_i^2),$ f₁＝4(r_rh_i-r_ih_r)，f₂＝4(r_rh_r+r_ih_i) Then the 4-bit soft detection value is:

Г₀(r)＝|f₁|-f₀ Г₁(r)max|f₁|，2|f₁|-f₀)sgn(f₁)

Г₂(r)＝|f₂|-f₀ Г₄(r)max|f₂|，2|f₂|-f₀)sgn(f₂)

for 64QAM modulation, assume ${\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="S2006800273765E00021.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=8(h_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="S2006800273765E00021.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+h_i^2),$ f₁＝4(r_rh_i-r_ih_r)，f₂＝4(r_rh_r+r_ih_i) Then the 4-bit soft detection value is:

Г₀(r)＝max(-|f₁|+f₀，|f₁|-3f₀)

Г₁(r)＝min(|f₁|-2f₀，2|f₁|-3f₀)

Г₂(r)＝max(|f₁|，2|f₁|-f₀，3|f₁|-3f₀，4|f₁|-6f₀)sgn(f₁)

Г₃(r)＝max(-|f₂|+f₀，|f₂|-3f₀)

Г₄(r)＝min(|f₂|-2f₀，2|f₂|-3f₀)

Г₅(r)＝max(-|f₂|，-2|f₂|+f₀，-3|f₂|+3f₀，-4|f₂|+6f₀)sgn(f₂)

this approach can be used to derive similar expressions for general M-QAM modulation, regardless of whether the mapping is gray mapping (as in the above example) or not.

Fig. 2 shows a diagram 200 comprising four graphs 202, 204, 206 and 208 for illustrating soft detection values derived from a sub-optimal euclidean distance matrix for a dual transmit antenna channel with 16QAM modulation and a random channel realization according to one embodiment of the present invention.

When T antennas (T ═ 2 in this example) transmit independent signals simultaneously, the signal received by the single antenna receiver at a particular time instance is <math><mrow> <mi>r</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>h</mi> <mi>k</mi> </msub> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>+</mo> <mi>n</mi> <mo>,</mo> </mrow></math> Wherein h is_kIs the channel gain of the kth transmit antenna, and n is normal white noise. Using the above formula, it is clear that the receiver can observe a magnitude ofM^TIs determined. However, for all k e {1, 2.. T } and i e {1, 2.. M }, the soft detection value f_k，i(r) still has piecewise linear behavior.

In graph 202, soft detection value b for 16QAM modulation is shown₀Or r_0，0In the graph 204, a soft detection value b is shown₁Or r_0，1. The soft detection value b for 16QAM modulation is shown in the graph 206₂Or r_0，2The soft detection value b is shown in the graph 208₃Or r_0，3. Note that in the graphs 202, 204, 206, and 208, the horizontal axis is re (r), and im (r) is fixed. For illustrative purposes, diagrams 202, 204, 206, and 208 are given only in a random implementation of a dual transmit antenna system (with 16QAM modulation).

Determining each soft value f for simplicity_k，iThe process of the linear equation of (r) may perform the following steps. Consider an example case of a dual transmit antenna system (T ═ 2), where | h₀|＜|h₁|，*₀∠h₀And *₁∠h₁The minimum angle θ that aligns the two M-QAM rotated constellations can be found. Note that the M-QAM constellation is pi/2 invariant, so θ ═ mod (*)₁，π/2)-mod(*₀π/2), and | θ | < π/4. Instead of the actual channel (h)₀，h₁)＝(|h₀|∠*₀，|h₁|∠*₁) The channel can be assumed to be (| h)₀|∠*₀+θ，|h₁|∠*₁). The rotation and subsequent calculation of f based on the rotation_k，i(r) makes the algorithm suboptimal. However, it provides some r_k，i(r) required characteristics and makes it easy to calculate data to calculate Γ_k，iCoefficients of the linear equation of (r).

Fig. 3 shows a diagram 300 comprising four graphs 302, 304, 306, and 308, illustrating the derivation of soft detection values from a sub-optimal euclidean distance matrix for a dual transmit antenna complex random channel, wherein each antenna utilizes 4QAM modulation, in accordance with one embodiment of the present invention. For purposes of illustration, diagram 300 shows a random implementation of a dual transmit antenna system (using 16 QAM).

In this example, graph 302 shows a soft detection value f_k，i(r), k is 0, 1 and i is 0, 1, the horizontal axis is re (r), and im (r) is equal to-2. In diagram 302, a soft detection value f is shown_0，0The exact and approximate values of, the soft detection values f are shown in the graph 304_0，1The exact value and the detected value. The soft detection value f is shown in the diagram 306_1，0The exact and approximate values of (a), the soft detection value f is shown in the graph 308_1，1The exact value and the detected value. For all four graphs 302, 304, 306 and 308, the exact soft detection values f are derived from the ML detector_k，i(r) and represented by a solid line, the approximate soft detection value f is derived from the algorithm described above_k，i(r) and is indicated by a dotted line.

Graphs 302, 304, 306, and 308 show Γ derived from a ML detector and the sub-optimal algorithm described above_k，i(r) there is a difference therebetween. The difference depends on the random channel coefficients and most importantly on the ratio | h₀|/|h₁And theta. Ratio | h₀|/|h₁The larger | and the smaller θ, the smaller the difference.

For T2 and 4QAM, f_k，i(r) is expressed in the following general form:

<math><mrow> <msub> <mi>&Gamma;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>h</mi> <mi>p</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mi>R</mi> <mo>,</mo> </mtd> <mtd> <mi>Re</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>c</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>h</mi> <mi>p</mi> </msub> <mo>+</mo> <msub> <mi>c</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mi>R</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&le;</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>d</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>h</mi> <mi>p</mi> </msub> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mi>R</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&le;</mo> <mi>Re</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow></math>

wherein, R ═ Re (h) is obtained₁r^*) Or R ═ Im (h)₁r^*) Possibly depending on k, i. Due to h_p＝|h₀|*|h₁I coefficient a_k，i、b_k，i、c_k，i、d_k，i、e_k，iIs fixed or is the ratio | h₀|/|h₁A linear function of | and a threshold value t_k，j，w_k，jIs im (r), h₁And h_pAs a function of (c). Note that the above representation can be extended to other constellations where the line re (r) is segmented into parts (relative to the three parts above), but for h_pAnd R still have the same linear relationship.

For systems with more than one receive antenna, the above-described embodiments need to be performed separately for each receive antenna, and for each k, i, the resulting f for each receive antenna_k，i(r) according to <math><mrow> <mi>r</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>h</mi> <mi>k</mi> </msub> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>+</mo> <mi>n</mi> </mrow></math> Are added, where h_kIs the channel gain of the kth transmit antenna, and n is normal white noise.

Fig. 4 illustrates the aforementioned method for low complexity soft detection in a system with multiple receive antennas according to one embodiment of the present invention. The values derived from the single antenna soft detection 400 are added and the sum 430 still remains linear.

The above description provides many different embodiments, or embodiments for implementing different features of the invention. Specific embodiments of components and processes are described to illustrate the invention. These are, of course, merely embodiments and are not intended to limit the invention from that described in the claims.

Although the invention has been described in terms of one or more specific examples, it is not intended to be limited to the details shown, since various modifications and structural changes may be made therein without departing from the spirit of the invention and within the scope and range of equivalents of the claims. Accordingly, as the following claims set forth below should be construed broadly and properly, in a manner consistent with the scope of the invention.

Claims (12)

1. A method for performing soft detection of a transmitted signal modulated by M-QAM, the method comprising the steps of:

according to <math><mrow> <msub> <mi>&lambda;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>&Element;</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo></mo> </mrow> </munder> <mi>Pr</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>|</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>&equiv;</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </munder> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>|</mo> <mo>|</mo> <mi>r</mi> <mo>-</mo> <mo>&lt;</mo> <mi>h</mi> <mo>,</mo> <mi>s</mi> <mo>></mo> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mn>2</mn> <mi>&sigma;</mi> </mrow> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> </mrow></math> Calculating first and second probabilities that selected bits of a transmitted symbol of the transmitted signal are equal to 0 and 1, respectively, where r is a received signal, h is a channel gain, b is 0 or 1, S_b ^k，iRepresents a subset of the spread modulation of the ith bit of the kth signal whose sign has a value equal to b ∈ {0, 1}, and σ²Is the normal noise variance; based on the first and second probabilities, according to <math><mrow> <mi>log</mi> <msub> <mi>&Sigma;</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>&ap;</mo> <munder> <mi>max</mi> <mi>j</mi> </munder> <mi>log</mi> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow></math> Estimating a first and a second secondary probability, respectively; and is

One or more soft detection values are obtained based on a difference between the first and second secondary probabilities.

2. The method of claim 1, further comprising:

transmitting the signal through a first predetermined number of transmit antennas;

receiving the transmitted signal through a second predetermined number of receive antennas;

calculating the soft detection value for the signal received by each receiving antenna; and is

Summing all of the soft detection values computed from each receive antenna to obtain a true soft detection value.

3. The method of claim 2, wherein the first predetermined number is 1.

4. The method of claim 2, further comprising determining, by the single receive antenna, when the first predetermined number of transmit antennas is greater than 1 <math><mrow> <mi>r</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>h</mi> <mi>k</mi> </msub> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>+</mo> <mi>n</mi> </mrow></math> Combining all received signals to obtain the transmitted signal, wherein h_kIs the channel gain of the kth transmit antenna, and n is normal white noise.

5. The method of claim 2, wherein the second predetermined number is 1.

6. The method of claim 2, wherein the second predetermined number is greater than 1.

7. A method for performing soft detection of a transmitted signal modulated by M-QAM, the method comprising the steps of:

transmitting signals through a first predetermined number of transmit antennas;

receiving the transmitted signal through a second predetermined number of receive antennas;

according to <math><mrow> <msub> <mi>&lambda;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>&Element;</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo></mo> </mrow> </munder> <mi>Pr</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>|</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>&equiv;</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </munder> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>|</mo> <mo>|</mo> <mi>r</mi> <mo>-</mo> <mo>&lt;</mo> <mi>h</mi> <mo>,</mo> <mi>s</mi> <mo>></mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mn>2</mn> <mi>&sigma;</mi> </mrow> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> </mrow></math> Calculating first and second probabilities that selected bits of a transmitted symbol of the transmitted signal are equal to 0 and 1, respectively, where r is a received signal, h is a channel gain, b is 0 or 1, S_b ^k，iRepresents a subset of the spread modulation of the ith bit of the kth signal whose sign has a value equal to b ∈ {0, 1}, and σ²Is the normal noise variance;

based on the first and second probabilities, according to <math><mrow> <mi>log</mi> <msub> <mi>&Sigma;</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>&ap;</mo> <munder> <mi>max</mi> <mi>j</mi> </munder> <mi>log</mi> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow></math> Estimating a first and a second secondary probability, respectively; and is

Obtaining, for each receive antenna, one or more soft detection values independently of a difference between the first and second secondary optimal probabilities;

summing all of the soft detection values computed from each receive antenna to obtain a true soft detection value.

8. The method of claim 7, wherein the first predetermined number is 1.

9. The method of claim 7, further comprising determining, by the single receive antenna, when the first predetermined number of transmit antennas is greater than 1 <math><mrow> <mi>r</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>h</mi> <mi>k</mi> </msub> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>+</mo> <mi>n</mi> </mrow></math> Combining all received signals to obtain the transmitted signal, wherein h_kIs the channel gain of the kth transmit antenna, and n is normal white noise.

10. The method of claim 7, wherein the second predetermined number is 1.

11. The method of claim 7, wherein the second predetermined number is greater than 1.

12. A method for performing soft detection of a transmitted signal modulated by M-QAM, the method comprising the steps of:

transmitting a signal through a plurality of transmit antennas;

receiving the transmitted signal through a single receive antenna;

according to <math><mrow> <mi>r</mi> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>h</mi> <mi>k</mi> </msub> <msub> <mi>S</mi> <mi>k</mi> </msub> <mo>+</mo> <mi>n</mi> </mrow></math> Combining all received transmission signals, wherein h_kIs the channel gain of the kth transmit antenna, and n is normal white noise;

according to <math><mrow> <msub> <mi>&lambda;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>&Element;</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo></mo> </mrow> </munder> <mi>Pr</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>|</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>&equiv;</mo> <mi>log</mi> <munder> <mi>&Sigma;</mi> <mrow> <mi>s</mi> <mo>=</mo> <msubsup> <mi>S</mi> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> </mrow> </munder> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>|</mo> <mo>|</mo> <mi>r</mi> <mo>-</mo> <mo>&lt;</mo> <mi>h</mi> <mo>,</mo> <mi>s</mi> <mo>></mo> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mn>2</mn> <mi>&sigma;</mi> </mrow> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> </mrow></math> Calculating first and second probabilities that selected bits of a transmitted symbol of the transmitted signal are equal to 0 and 1, respectively, where r is a received signal, h is a channel gain, b is 0 or 1, S_b ^k，iRepresents a subset of the spread modulation of the ith bit of the kth signal whose sign has a value equal to b ∈ {0, 1}, and σ²Is the normal noise variance;

based on the first and second probabilities, according to <math><mrow> <mi>log</mi> <msub> <mi>&Sigma;</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>&ap;</mo> <munder> <mi>max</mi> <mi>j</mi> </munder> <mi>log</mi> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow></math> Estimating a first and a second secondary probability, respectively; and is

Deriving one or more soft detection values based on a difference between the first and second secondary probabilities.

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