# Channel Impulse Response Power

Hey guys, I simply plotted the accumulator values (samples) around the first path index to visualize the CIR. After tinkering the values together I got a typical CIR plot. So far so good…I have several questions.
Could anyone explain, what the values represent? Or better: What are the unit of the values? I know it indicates power or energy (area under the curve) but these are only qualitative statements. (same applies to F1, F2, F3 and peak amplitude - IP_DIAG2 …4 and IP_DIAG0) - And yes, all of these values have to be casted as float and divided by 4 which is discussed in another thread due to 2 fractional bits. (a right bit shift twice is also sufficient) This information is missing in the register section in the Manual.
Back to the topic that leads me to the Channel Impulse Response Power C (section 4.7.2 in the User Manual). We can get the value from register IP_DIAG1. But same question as above: What does the value represent? The Manual says: “This 17-bit field reports the channel area in the CIR accumulated using the preamble sequence. This gives a measure of the receive power of the preamble.” Can we give it a unit?
The values vary from 5 (hand over one antenna) to 25 (5-10cm distance between two modules) and they react very delayed. So it would be interesting how the value is calculated or measured…Does anyone know?
Thank you so much!

1 Like

Thanks a lot for your question Fourier, how much I know related to response power I am sharing with you -

### Channel and Signal Models

Consider an information [bearing signal] with a lowpass equivalent band-width of |f| < 1/2T Hz sent through a channel with [coherence bandwidth] ≪ 1/T Hz, and corrupted by [additive noise]. Assume the channel can be modeled as a linear [FIR filter]. Then, using the familiar baseband discrete-time equivalent representation for all quantities (by employing the Karhunen-Loève expansion; see, for example, [1]) the received sample measured at time k is given by

(1)r(k)=Nf−1∑m=0fm(k)d(k−m)+n(k)

where the (unknown) transmitted data symbols {d(k )} (with rate 1/T symbols/s) are drawn from a memoryless, finite [alphabet source]. This measurement model is illustrated in Figure 1. The bandlimited noise sequence {n(k)} is assumed to be white, i.e., E[n(k)n*(l)]=σ2nδk,l where σ n2 is the noise variance and δ k,l is the [Kronecker delta] function, and it has a circular Gaussian p.d.f.

The channel impulse response is of length Nf, and the coefficients {fm(k)} represent the convolution of the transmit filter, the actual communication medium, and the whitening matched filter (WMF) [1]. Also note that perfect synchronization, or equivalently, sampling of the matched filter output at the optimum times is implicitly assumed in Eq. (1).3 It should be mentioned that when the ISI channel is unknown, the WMF in Figure 1 cannot be accurately defined. However, by assuming a high [signal-to-noise-ratio] (SNR) condition, an approximate WMF can be constructed from the [autocorrelation function] of the received signal. Basically, I have used this methodology on my project HRMS for the retail sector. Synchronization is achieved by performing a peak-detection test on the [autocorrelation sequence].

In the development of the [Kalman filter] channel estimator, it is assumed that the coefficients {fm(k)} evolve according to the following complex Gaussian autoregressive (AR) process model:

(2)fk+1=Ffk+wk

where the channel [parameter vector] is

(3)fk=f0k,f1k,…,fNf−1kT,

F∈CNf×Nf is a one-step [transition matrix], and wk∈CNf is a zero-mean circular [white Gaussian noise vector] with [covariance matrix] Q∈CNf×Nf. Assuming a [diagonal matrix] for F, Eq. (2) can be viewed as a fading [multipath channel] model. The value of F determines the [Doppler spread] or coherence time of the channel; i.e., small diagonal entries of F yield fast channel fades, and thus a large Doppler spread (or small coherence time [1]). The stability of the AR model is ensured by proper choice of the transition matrix F; for example, if Q = 0.0001I, we may choose F = 0.999I or F = 0.995I, etc.

We define the following notation. The cumulative measurement sequence up to time k is denoted by

(4)rk=rk,rk−1,…,r0,

and similarly the cumulative ith data sequence is

(5)dik=dik,dik−1,…,di0

where i = 1,…,M k + 1 (M is the size of the source alphabet; e.g., M = 4 for QPSK). A subsequence of length Nf is defined by Gaussian.