Data communication with embedded pilot information for timely channel estimation

Pilot data and data-bearer data are formed to be mutually orthogonal and in each other's null-space. Data to be transmitted is first modulated with the data-bearer matrix and then pilot data is added thereto. The pilot data may be added to each modulated symbol, thereby increasing significantly the density of pilot information available at the receiver for channel state estimation. When pilot data is added across an entire transmitted block of data, data detection performance is improved for even fast fading Rayleigh fading channels.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention described herein is related to data communication. More specifically, the invention is related to embedding pilot information into data at a transmitter for obtaining channel state information at a receiver.

2. Description of the Prior Art

Multiple-input multiple-output (MIMO) communication systems beneficially provide high capacity data communication with greater reliability than their single channel counterparts. Space-time (ST) coding has engendered transmit diversity so as to significantly improve the bit error rate (BER) of data transmission without an increase in transmission power. However, a major challenge in realizing such systems lies in providing the coherent detector with channel state information, which is a measure of the effects of the channel on the propagation of the signal. Typically, channel state information is estimated from a known signal transmitted through the channel for such purpose, where the known signal is commonly referred to as a training signal or pilot signal. Training signal techniques are widely applicable and are desirable when low computational complexity is inherent to their implementations.

Common pilot-aided channel estimation techniques for single-input single-output (SISO) and MIMO systems include the pilot symbol assisted modulation (PSAM) technique and the pilot-embedding technique. In PSAM, a pilot signal is time-multiplexed into the transmit data stream, which is then extracted at the receiver and used to ascertain the channel state information. Interpolation of multiple channel estimates is applied over a certain time period to improve accuracy. However, the signal from which channel information is derived is sparsely transmitted, which results in poor state tracking of the channel with respect to time. Unfortunately for these PSAM systems, increasing the time-density of the pilot signal consumes bandwidth otherwise used for real data and thus penalizes the system's efficiency.

Pilot-embedding, also referred to as the pilot-superimposed technique, adds a sequence of pilot signals directly to the data stream. Channel estimation and data detection are accomplished at the receiver through a soft-decoding procedure, such as the Viterbi algorithm. This technique achieves better bandwidth efficiency over PSAM since no time slots are sacrificed for pilot signal use. The pilot-embedding technique does, however, involve higher computational costs in the decoder and a longer delay in the channel estimation process.

The need exists in the field of data communication for channel state information acquisition, which is computationally affordable and able to track channels states in fast-fading channels.

SUMMARY OF THE INVENTION

In one aspect of the invention, a method is provided for data communication in which data symbols are first provided at a transmitter. Pilot data are added to each of the data symbols to form pilot-embedded data symbols, at least one of which is transmitted from a transmitting antenna defining one end of a data channel. At least one of the pilot-embedded data symbols is received at a receiving antenna defining an opposite end of the data channel. At least one channel state coefficient indicative of a characteristic of the data channel is estimated from the received pilot-embedded data symbols. The data symbols are recovered from the received pilot-embedded data symbols using the estimated channel state coefficient.

In another aspect of the invention, a method for data communication is provided which forms a block codeword from a sequence of data symbols. The codeword is modulated with a plurality of data bearing coefficients and a value from a plurality of pilot values is added thereto to form a pilot-embedded codeword. The pilot-embedded codeword is transmitted and subsequently received at a receiver. At least one channel state coefficient indicative of a characteristic of a corresponding data channel is estimated from the received codeword and the sequence of data symbols is recovered from the received pilot-embedded codeword using the estimated channel state coefficient.

In yet another aspect of the invention, a system for data communication is provided which includes a data encoder encoding data received at an input thereof into data symbols produced at an output thereof. A pilot embedder is coupled to the data encoder and adds pilot data to the data symbols to produce pilot-embedded data symbols at an output thereof. The system includes a transmitter coupled to the pilot embedder at an input thereof for transmitting the pilot-embedded data symbols over a plurality of time slots such that the pilot data is transmitted in each time slot. A receiver is coupled to the transmitter via at least one data channel and receives therethrough the pilot-embedded data symbols as modified by a characteristic of the corresponding data channel. A channel estimator is coupled to the receiver and estimates from the pilot data added to each of the data symbols the characteristic of the corresponding data channel for each of the pilot-embedded symbols received. A data detector is coupled to the channel estimator and recovers the data symbols from the pilot-embedded symbols in accordance with the estimated characteristic to produce at an output thereof estimated data symbols. A data decoder coupled to the data detector decodes the estimated data symbols in a manner complementary to the data encoder to reproduce the data at the receiver.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention simplifies channel estimation and data detection processes by taking advantage of the null-space and orthogonality principles of the data-bearing and pilot structure, as will be succinctly described below by way of certain underlying mathematical models. Exemplary system configurations will also be described that demonstrate implementations of the invention practicable from aspects derived from the models. It is to be noted that while the invention will be described herein primarily with reference to a MIMO embodiment thereof, other embodiments, including SISO embodiments, are within the intended scope of the invention.

In certain MIMO embodiments of the invention, a data-bearer matrix is used for projecting an ST data codeword matrix onto the orthogonal subspace of a pilot matrix. By virtue of the null-space and orthogonality properties, a block of the data matrix subjected to the invention is added into a block of pilot matrix, where the pilot and data matrices are mutually orthogonal. Improvement in channel estimation results from the provision of pilot information in every transmitted block without substantial penalty in computational complexity.

Fundamental aspects of the invention are now described in accordance with a MIMO channel and system model. The exemplary MIMO system is illustrated inFIG. 1and includes Lttransmit antennas at a transmitter100and Lrreceive antennas at a receiver160. Generally, for a given block index t, an ST codeword U(t) is characterized by a matrix of Lt×M symbols transmitted across the Lt, transmit antennas over M time slots. The received symbol matrix Y(t) at the receiver front-end can be expressed as:
Y(t)=H(t)U(t)+N(t),  (1)
where H(t) is the Lr×Ltchannel coefficient matrix and the Lr×M noise matrix N(t) is assumed to be complex white Gaussian distributed with zero mean and variance σ2/2(I(LrM×LtM)) per real dimension. The elements of H(t) are assumed to be independent complex Gaussian random variables with zero mean and variance of 0.5 per real dimension, or, equivalently, an independent flat Rayleigh fading channel is assumed. Unlike many systems of the prior art, the present invention is not limited to environments where quasi-static flat Rayleigh fading channels are presumed, but extends to nonquasi-static flat Rayleigh fading channels, where H(t) changes according to processes whose dominant frequency is much faster than M−1. Beneficial features of the invention provide information at the receiver to track the state of the channel even if the channel coefficient matrix H(t) is not constant over each symbol block.

Without loss of generality, a modulated data matrix Z(t)εLt×Mis defined as:
Z(t)=D(t)A,(2)
where D(t)εLt×Nis the ST codeword data matrix, AεN×Mis the data-bearer matrix, and N is the number of data time slots used in each ST codeword. In certain embodiments of the invention, the ST data matrix D(t) is formed to maintain the energy constraint E[∥D(t)∥2]=Lt, with ∥·∥ being the Frobenius norm. A pilot-embedded symbol matrix of the present invention may then be expressed as:
U(t)=Z(t)+P=D(t)A+P,(3)
where PεLt×Mis the pilot matrix.

Referring toFIG. 2, there is shown an exemplary pilot-embedded ST codeword structure200in accordance with the present invention. As is shown in the Figure, U(t) includes two main parts: modulated data sequences {Z(t)}iand pilot sequences {P}i, where i is the row index i=1, . . . , Lt. The data sequences {Z(t)}iinclude data-bearing symbols210and the pilot sequences {P}iinclude pilot symbols220. As is clear fromFIG. 2, the present invention provides pilot information in every time slot and in every spatial stream of the pilot-embedded ST symbol block200. The pilot-embedded ST symbol block200is transmitted into the MIMO channel via transmit antennas120a-120Ltat block time t=┌(kM+n)/M┐, where kε[0,∞)εI, nε[0,M−1)εI and ┌·┐ returns the largest integer no greater than its argument. Then, substituting Eq. (3) into Eq. (1) reveals that the received symbol matrix Y(t) is:
Y(t)=H(t)(D(t)A+P)+N(t)  (4)

In accordance with the invention, the data bearer matrix A and the pilot matrix P are chosen to satisfy the following:
APT=0εN×Lt(5)
PAT=0εLt×N(6)
AAT=αIεN×N(7)
PPT=αIεLt×Lt,  (8)
where β is a real-valued data power factor for controlling the data-part power and α is a real-valued pilot power factor for controlling the pilot-part power. The matrices 0 and I are the zero matrix and the identity matrix, respectively. The present invention exploits the null-space property of Eqs. (5) and (6) and the orthogonality properties of Eqs. (7) and (8) to enable the embedding of the pilot symbols onto every symbol in the transmitted codeword block in such a manner as to be efficiently recovered at the receiver.

In mathematical terms, the data-bearer matrix A projects the ST data matrix D(t) onto the orthogonal space of the pilot matrix P. Eqs. (7) and (8) imply that Rank (A)=N and Rank (P)=Lt, where Rank (•) returns the rank of its matrix argument. To satisfy the null-space requirement of Eqs. (5) and (6), the minimum number of columns in A and P must be equal to the sum of the rank of A and P. Consequently, the number of time slots M of the pilot-embedded ST symbol codeword U(t) must satisfy the inequality:
Rank(A)+Rank(P)≦M.(9)

The present invention establishes the matrices A and P to fulfill the requirements of Eqs. (5)-(8) and applies the symbol patterns formed by the matrices as shown inFIG. 3A. The incoming data stream is encoded at block310, where error coding is applied, constellation symbols are selected and any block coding is performed. The encoded data is then modulated by the pattern defined by data-bearer matrix A, as indicated at block315. Such modulation may be performed, for example, by matrix multiplication in a digital signal processor (DSP). Process flow is transferred to block320, where the pilot data pattern defined by the matrix P is added to the modulated data. The addition of the pilot symbols may be performed by, for example, matrix addition in a DSP. The pilot-embedded data are then transmitted into the channel, as indicated at block325.

Matrices A and P may be formed in a number of ways to meet the above criteria with varying pilot information density resulting thereby. For example, in a Time-Multiplexing (TM) based system, the structures of the data-bearer and pilot matrices may be:
A=√{square root over (β)}[0(N×Lt);I(N×N)],
P=√{square root over (α)}[I(Lt×Lt);0(Lt×N)], M=N+Lt.  (10)
In this embodiment, the pilot signal is based on the Lt×Ltidentity matrix and is multiplexed into the channel separate from the data as modulated by A. The PSAM system previously described is subsumed into this category of system.

In ST-Block-Code (STBC) based systems, the matrices may be:
A=√{square root over (β)}[0(N×τ);I(N×N)],
P=√{square root over (α)}[STBC(Lt×τ);0(Lt×N)], M=N+τ,(11)
where τ is the number of time slots used for transmitting one ST block code of pilot information. The primary difference between this and the TM-based structure is that it employs a normalized known ST block code structure for the pilot block instead of the identity matrix, but still multiplexes the pilot symbols into the data.

In a Code-Multiplexing (CM) based system, exemplary matrices are:
A=√{square root over (β)}WH[1:N](N×M),
P=√{square root over (α)}WH[N+1:M](Lt×M), M=N+Lt,  (12)
where WH[x:y] denotes a sub-matrix created by splitting the M×M normalized Walsh-Hadamard matrix starting with the xthrow and ending with the ythrow. The pilot information using these matrices is distributed evenly over the transmitted ST symbol block. Certain embodiments of the invention implement pilot embedding processes in accordance with the CM-based matrices to achieve channel estimation which is superior to the other two systems described.

At the receiver end of the channel, the recovery of the original data is achieved through the fundamental method steps ofFIG. 3B. The pilot-embedded data are received, as indicated at block330. Flow is transferred to block335where estimation of the channel state information proceeds on the received signal modeled by Eq. (4). Described mathematically, the process begins by post-multiplying the received symbol matrix Y(t) by the transpose of the pilot matrix PT. From the null-space and orthogonality properties of Eqs. (5) and (8) and dividing the result by α,

n⁡(t)=1α⁢(I⊗N⁡(t))⁢vec⁡(PT),(16)
where the size of I{circle around (X)}N (t) is LtLr×LtM. In the presence of white Gaussian-distributed N(t), the mean of the pilot-projected noise vector n(t) is,

μn⁡(t)=1α⁢E⁡[(I⊗N⁡(t))⁢vec⁡(PT)]=0(Lt⁢Lr×1)(17)
and the covariance is given by,

Vn⁡(t)=1α2⁢E⁡[((I⊗N⁡(t))⁢vec⁡(PT))⁢((I⊗N⁡(t))⁢vec⁡(PT))H]=σ22⁢α2⁢Diag⁡(Bi),⁢Bi=∑j=1M⁢Pi,j2⁢I(Lr×Lr),i⁢∈{1,⁢…⁢,Lt},per⁢⁢real⁢⁢dimension,(18)
where Pi,jis the ithrow jthcolumn element of the pilot matrix P, Diag(•) returns a diagonal matrix by concatenating the submatrices of its argument, and superscripted H indicates the complex conjugate transpose of the argument matrix. Using Eq. (8), it is observed that

∑j=1M⁢Pi,j2=α,∀i.
Thus, the covariance matrix can be rewritten to,

Vn⁡(t)=σ22⁢α⁢I(Lt⁢Lr×Lt⁢Lr),per⁢⁢real⁢⁢dimension.(19)
The pilot-projected noise vector n(t) is a complex white Gaussian vector and a log-likelihood function can be formed:

ln⁡(p⁡(y⁡(t)⁢❘⁢h⁡(t)))=ln⁡(1πL⁢det(Vn⁡(t)))-(y⁡(t)-h⁡(t))H⁢Vn⁡(t)-1⁡(y⁡(t)-h⁡(t)),(20)
where L=LtLrand det(•) returns the determinant of its argument.

Eq. (20) serves as a basis for channel estimation, such as through a unconstrained Maximum-Likelihood (ML) channel estimator, which maximizes the log-likelihood function,

h^⁡(t)=maxh⁡(t)⁢{ln⁡(p⁡(y⁡(t)⁢❘⁢h⁡(t)))}.(21)
Differentiating Eq. (20) and equating the result to zero results in,
ĥ(t)=y(t) orĤ(t)=Y1(t),  (22)
which indicates that the ML estimator is the pilot-projected received vector y(t) (or matrix Y1(t)) itself.

To improve the estimation, certain embodiments of the invention employ an L-tap Linear Minimum Mean-Squared Error (LMMSE) channel estimator. The L-tap LMMSE channel estimator is given mathematically by,
hj,iLMMSE(t)=wj,iHĥj,iL(t),  (23)
where hj,iLMMSE(t) denotes the jthrow ithcolumn element of the LMMSE-estimated channel matrix, wj,i=[wj,i(0) . . . wj,i(L−1)]Tdenotes the L-tap finite impulse response (FIR) linear filter's weight vector, and ĥj,iL(t)=[ĥj,i(t) . . . ĥj,i(t−L+1)]Tdenotes the L-element input vector constructed from the jthrow ithcolumn element of the ML-estimated channel matrix in Eq. (22) taking values in the time interval [t−L+1,t]. The optimization criterion, assuming wide-sense stationary channels, for the L-tap LMMSE estimator is,

J⁡(wj,i)=arg⁢⁢minwj,i⁢E⁡[hj,i⁡(t)-wj,iH⁢h^j,iL⁡(t)2],(24)
where hj,i(t) denotes the jthrow ithcolumn element of the true channel matrix H(t) in Eq. (1), i.e., the channel state information if perfect knowledge of such were obtainable.

The optimal LMMSE weight vector wj,ioptis given by,

wj,iopt=Rh^j,i⁡(t)L-1⁢ph^j,i⁡(t)L,(25)
where Rĥj,iL(t)=E[ĥj,iL(t)ĥj,iHL(t)] and pĥj,iL(t)=E[hj,i*(t)ĥj,iL(t)]. Taking Eqs, (14), (19) and (22) and considering that the channel and noise coefficients are uncorrelated, the autocorrelation matrix Rĥj,iL(t)may be simplified to,

hj,iLMMSE⁡(t)=[(Rhj,i⁡(t)L+σ2α⁢IL×L)-1⁢phj,i⁡(t)L]H⁢h^j,iL⁡(t).(28)
The channel estimation process335, as described through its underlying mathematics above, may be achieved through programmed instruction sequences on a DSP.

As is shown inFIG. 3B, once the channel estimates have been obtained, flow is transferred to block340, where the data detection process is executed. The data part of the received signal is extracted by post-multiplying the received symbol matrix Y(t) by the transpose of the data bearer matrix A. Using the null-space and orthogonality properties of Eqs. (6) and (7), and dividing by β, the data-bearer projected received symbol matrix is given by,

∑j=1M⁢⁢Ai,j2=β,∀i
and following from the preceding analysis of P, the statistics of the data-bearer projected noise vector n′(t) are,
μn′(t)=0(LrN×1),  (31)

Vn′⁡(t)=σ22⁢β⁢I(Lr⁢N×Lr⁢N)⁢⁢per⁢⁢real⁢⁢dimension,(32)
where μn′(t)and Vn′(t)are the mean vector and covariance matrix of the data-bearer projected noise vector n′(t), respectively.

In certain embodiments of the invention, a maximum likelihood receiver is employed for detecting the transmitted data matrix D(t) by using the estimated channel coefficient matrix Ĥ(t) as the channel state information. Since n′(t) is i.i.d. white Gaussian, a suitable maximum likelihood receiver computes a decision metric and selects a codeword that minimizes the decision metric, such as.

Once the data estimates have been acquired, the process ofFIG. 3Bproceeds to block345, where the data estimates are decoded in a manner complementary to that at the receiver, thereby recovering the original data stream.

Referring once again toFIG. 1, the exemplary system configuration is now viewed in light of the descriptions above. The system ofFIG. 1is intended to illustrate the fundamental functional blocks of a data communication system consistent with the present invention. Certain of the functions illustrated may be carried out on respective DSPs at the receiver and transmitter ends or may be implemented in discrete single functional modules. Moreover, although the system is illustrated as a MIMO system, the number of antennas at the receiver160and transmitter100may include the single antenna case at both locations to implement an SISO system operating consistent with the present invention.

As is illustrated in the Figure, the input sequence is provided at the transmitter1100to block coder105, which encodes the incoming data into a block codeword D(t). Such coding may include forward error correction coding, constellation symbol selection and ST block coding. The codeword D(t) is provided to pilot embedder110, where the codeword is modulated by a data pattern consistent with matrix A and the pilot symbols are added in accordance with the embedding scheme chosen from, for example, the matrix structures described above. Preferably, the system will embed the pilot information in each symbol of the modulated codeword, such as through the CM based system described above. The pilot-embedded codeword is then transmitted into the MIMO channel170by a suitable RF transmitter and antennas120a-120Lt.

At the receiver160, the codeword is received by RF module140and is provided to channel estimator145. The channel estimator, which is provided with knowledge of the matrix P, such as through storing a copy thereof in a memory device, is preferably a LMMSE estimator to provide the estimated channel state information Ĥ(t) to ascertain the characteristics of the channel. The estimated channel state information and the received codeword are provided to data detector150, which determines the estimated codeword {circumflex over (D)}(t) from the estimated channel state information and a copy of the matrix A. The data detector150maintains a copy of the data-bearer matrix A, such as by storing such in a memory device. The estimated codeword is decoded by decoder155in a manner complementary to the coding operation at the transmitter100. The decoder then produces the recovered sequence. Numerical examples of the signal processing and performance are given below.

As was indicated above, the values α and β may be used to control power allocation to each of the data and pilot portions of the signal. It should be clear to the skilled artisan that performance of a data communication system is dependent on the power percentages of the data and pilot portions. Considering a MIMO system where the power of the pilot-embedded ST symbol matrix U(t) is constant, the block power allocated to U(t) normalized to the number of transmit antennas Ltcan be expressed as,

Ps=E⁡[U⁡(t)2]Lt=E⁡[D⁢(t)⁢A2]Lt+E⁡[P2]Lt=Ps′+Pp=β+α,(34)
where p′s=β is the normalized block power allocated to the data part and Pp=α is the normalized block power allocated to the pilot part.

To determine the optimal power allocation, a Probability of Error Upper Bound (PEUB) mismatch factor is defined as,

Minimizing the PEUB mismatch factor η with respect to the pilot-power factor α subject to the constraints of constant block power and acceptable MSE of the channel estimation optimizes the power allocation and is implemented as such in certain embodiments of the invention. Substituting β=Ps−α into Eq. (35), the minimization problem is given by,

minα⁢((N-Lt)⁢α+Ps⁢Lt(α+σ2)⁢(Ps-α)),(36)
where MSE≦T with T being a predetermined acceptability threshold. Differentiating Eq. (36) and equating the result to zero provides the optimal pilot power factor,

α*={Ps-σ22,N=LtPs⁢Lt-Ps⁢N⁡(Ps⁢Lt+σ2⁡(Lt-N))(Lt-N),N≠Lt(37)
where the MSE of the channel estimation must satisfy,

MSE=σ2⁢Lt⁢Lrα≤T.(38)
The remaining amount of fixed power is then β=Ps−α*.

The optimum pilot power factor α* exists for N≠Ltif and only if the signal-to-noise ratio (SNR) is at least (N−Lt). For the case where N=Ltand the SNR satisfies,

Lt+2⁢Lt2⁢LrT≤SNR<∞,(39)
the range of the optimum pilot power factor is given by,

Lt⁢Lr⁢PsT+2⁢Lt⁢Lr≤α*<Ps2.(40)
It follows that for N=Lt,

Certain aspects of the invention will now be demonstrated through numerical examples. An orthogonal ST block code is formed according to:

D⁡(t)=[s1⁡(t)-s2*⁡(t)s3*⁡(t)2s3*⁡(t)2s2⁡(t)s1*⁡(t)s3*⁡(t)2-s3*⁡(t)2s3⁡(t)2s3⁡(t)2-s1⁡(t)-s1*⁡(t)+s2⁡(t)-s2*⁡(t)2s2⁡(t)+s2*⁡(t)+s1⁡(t)-s1*⁡(t)2s3⁡(t)2-s3⁡(t)2-s2⁡(t)-s2*⁡(t)+s1⁡(t)-s1*⁡(t)2-s1⁡(t)+s1*⁡(t)+s2⁡(t)-s2*⁡(t)2],(42)
where si(t), iε{1, . . . , 3} are the ST symbols corresponding to the chosen modulation constellation, e.g., 4-PSK (Phase-Shift Keying), 8-PSK. For comparison, a set of TM based matrices will be,

ATM=β⁡[00001000000001000000001000000001],⁢PTM=α⁡[10000000010000000010000000010000],(43)
and a set of STBC based matrices will be,

ACM=β8⁡[1111-1-1-1-11-11-1-11-1111-1-1-1-1111-1-11-111-1],⁢PCM=α8⁡[111111111-11-11-11-111-1-111-1-11-1-111-1-11].(45)
The three different embedding structures derived from Eqs. (10)-(12), respectively, will be evaluated in both quasi-static and nonquasi-static flat Rayleigh fading channels. In the nonquasi-static scenarios, the performances of the pilot-embedded MIMO systems are demonstrated for channels of varying Doppler shift representing different mobility speeds of a moving receiver. The bit error rate (BER) and MSE will be used as a performance measure against ideal channel coefficients, i.e., where perfect channel state information is given. In the demonstrations, the perfectly known channel cases do not contain pilot information, i.e., the transmitted ST codeword U(t) is simply U(t)=D(t)A. Additionally, pilot-embedded MIMO systems are compared having power allocation in accordance with the optimal allocation described above and having power allocation of the prior art. In the demonstrations, the transmit rate and total transmit energy are the same for all schemes.

For all three data bearer and pilot structures, the noise term N(t) is established to be independent complex Gaussian random variables with zero mean and variance σ2/2 per real dimension. The normalized ST symbol block power Psis one (1) W/ST symbol block. The number of time slots M is 8 time slots per ST symbol block and the number of transmit antennas Ltis four (4). The number of data time slots N=M−Ltis four (4) time slots/ST codeword symbol block. The modulation scheme is 4-PSK and the acceptable threshold of the MSE of the channel estimation T is set to 0.5. The number of LMMSE estimator taps is set to three (3).

In the quasi-static flat Rayleigh fading channel, the channel coefficients are taken from normalized time-varying channel modeled in accordance with that of “Multipath Interference”, Jakes, Jr., W. C.,Microwave Mobile Communication, W. C. Jakes, Jr., Ed., Wiley, NY, pp. 67-68. The fast fading is simulated using fd*Ts=0.08, where fd is the Doppler shift and Tsis the symbol period.

FIG. 4shows the MSEs of the channel estimation of the pilot-embedded MIMO system having optimal power allocation and that of the prior art with a single receive antenna and two receive antennas Lr. It is to be observed from the Figure that the LMMSE channel estimator outperforms the simple ML estimator as shown by the MSE of both processes.

InFIG. 5, the BERs of the pilot-embedded MIMO system having optimal power allocation consistent with the present invention is demonstrated against the ideal MIMO system. Again, the cases of Lr=1 and Lr=2 are shown. It is to be observed that, at BER=10−4, the difference in SNR between the ideal channel, i.e., where perfect knowledge of the channel state is assumed, and the ML channel estimator is about 2.3 dB for both one and two antenna receiver systems. The LMMSE estimator, on the other hand, achieves ideal-channel error probability for the single antenna receiver and about 0.5 dB for the two antenna receiver.

Referring toFIG. 6, there is shown a comparison in terms of BER between the optimal power allocation scheme of the present invention and that of the prior art. The comparison is made in both one and two antenna receivers with the CM based data-bearer and pilot matrices applied. It is noteworthy that the two power allocation schemes are quite close at BER=10−4, resulting from the very small difference in allocated power between the two strategies in that region, as illustrated inFIG. 7.

In nonquasi-static fading channels, the channel coefficient matrix H(t) is not constant over a ST symbol block. In the demonstrations that follow, the channel state information H(t) changes symmetrically twice over one ST symbol block.

The single antenna receiver operating in nonquasi-static fading conditions under the present invention is illustrated inFIG. 8. The fading dynamic is illustrated for fd*Ts=0.0021 (slow fading), 0.0165, 0.0142 and 0.0741 (fast fading). It is particularly noteworthy that the CM based matrices provide lower MSE than either of the TM and STBC matrix structures. The difference is quite apparent in the higher SNR regions.

The BERs of the single antenna receiver pilot-embedded systems in the previously defined nonquasi-static fading are illustrated inFIG. 9. It is to be noted that when the fd*Tsis small, all three matrix structures produce similar results. However, when the Doppler shift increases, the CM based embedding structure provides much better detection than either of the TM and STBC structures.

FIGS. 10 and 11illustrate the scenarios ofFIGS. 8 and 9, but where two receiver antennas are deployed. Again, the CM based embedding system provides the best results in terms of both MSE of channel estimation and BER of data detection.

The descriptions above are intended to illustrate possible implementations of the present invention and are not restrictive. Many variations, modifications and alternatives will become apparent to the skilled artisan upon review of this disclosure. For example, components equivalent to those shown and described may be substituted therefor, elements and methods individually described may be combined, and elements described as discrete may be distributed across many components. The scope of the invention should therefore be determined not with reference to the description above, but with reference to the appended Claims, along with their full range of equivalents.