By Jinho Choi

ISBN-10: 0521864860

ISBN-13: 9780521864862

Adaptive sign processing (ASP) and iterative sign processing (ISP) are vital strategies in bettering receiver functionality in verbal exchange platforms. utilizing examples from functional transceiver designs, this 2006 ebook describes the basic conception and useful elements of either tools, supplying a hyperlink among the 2 the place attainable. the 1st components of the ebook take care of ASP and ISP respectively, every one within the context of receiver layout over intersymbol interference (ISI) channels. within the 3rd half, the functions of ASP and ISP to receiver layout in different interference-limited channels, together with CDMA and MIMO, are thought of; the writer makes an attempt to demonstrate how the 2 recommendations can be utilized to unravel difficulties in channels that experience inherent uncertainty. Containing illustrations and labored examples, this ebook is acceptable for graduate scholars and researchers in electric engineering, in addition to practitioners within the telecommunications undefined.

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Example text

The role of the MMSE equalizer is to minimize the error between the output of the equalizer and the desired signal. Since the error is also a random variable, the mean square error (MSE) or the mean absolute error can be used to indicate an average performance. Suppose that the MSE between the output of a causal LE, dl , and the desired signal, sl = bl−m¯ , is to be minimized. We assume that {bm } is independent identically distributed (iid). In addition, assume that E[bl ] = 0 and E[|bl |2 ] = σb2 .

This means that the spectral density of n(t) is given by Sn ( f ) = N0 /2, ∀ f , where f denotes the frequency. The corresponding autocorrelation function is given by Rn (τ ) = E[n(t)n(t − τ )] = (N0 /2)δ(τ ). The sampled signal of y(t) at every T seconds (we assume a critical sampling) is given by yl = y(lT ) = g(lT − τ )¯v (τ − mT ) dτ +n l bm m =g(t)∗¯v (t)|t=(l−m)T = bm h l−m + n l m = bl ∗ h l + n l , where n l = g(lT − τ )n(τ ) dτ and h l−m = g(t) ∗ v¯ (t)|t=(l−m)T . Here, n l is the sampled noise and {h m } is the discrete-time CIR.

This is the same result as in Eq. 51). Consequently, we can see that the eigenspread of Ry plays a key role in deciding the rate of convergence of the SD algorithm. Since the eigenspread of Ry depends on the CIR, {hp }, it is interesting to characterize ISI channels for the rate of convergence. The covariance matrix Ry given in Eq. 11) is a Toeplitz matrix. 4 Adaptive linear equalizers autocorrelation r y (m) = E[yl yl−m ] (Gray, 2006). It can be shown that lim M→∞ max0≤ω<2π Sy (ω) λmax = , λmin min0≤ω<2π Sy (ω) where Sy (ω) is the power spectral density given by r y (m)e−jmω Sy (ω) = m = H (ejω )H ∗ (ejω ) + N0 , 0 ≤ ω < 2π.

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Adaptive and Iterative Signal Processing in Communications by Jinho Choi

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